https://en.xen.wiki/api.php?action=feedcontributions&feedformat=atom&user=FloraC Xenharmonic Wiki - User contributions [en] 2026-06-20T02:51:57Z User contributions MediaWiki 1.43.6 https://en.xen.wiki/index.php?title=Talk:Minortone_family&diff=232435 Talk:Minortone family 2026-06-19T16:58:13Z <p>FloraC: Created page with &quot;== Extensions == I&#039;m taking the liberty of changing &#039;&#039;hemidomain&#039;&#039; to &#039;&#039;semidomain&#039;&#039;, obviously. Besides that, the main problem is the ore temperament, whose 13-limit extension I don&#039;t think is canonical. The 46 &amp; 125f extension is simpler and better, with 5 gensteps landing convincingly at a ~22/13, but for now I&#039;m simply gonna give 46 &amp; 125 a distinct name. —~~~~&quot;</p> <hr /> <div>== Extensions ==<br /> I'm taking the liberty of changing ''hemidomain'' to ''semidomain'', obviously. Besides that, the main problem is the ore temperament, whose 13-limit extension I don't think is canonical. The 46 &amp; 125f extension is simpler and better, with 5 gensteps landing convincingly at a ~22/13, but for now I'm simply gonna give 46 &amp; 125 a distinct name. —[[User:FloraC|FloraC]] ([[User talk:FloraC|talk]]) 16:57, 19 June 2026 (UTC)</div> FloraC https://en.xen.wiki/index.php?title=User:FloraC/Workbench&diff=232434 User:FloraC/Workbench 2026-06-19T16:54:24Z <p>FloraC: </p> <hr /> <div>== Temperament pages ==<br /> Notes: <br /> # Order: <br /> #* [[Subgroup]]<br /> #* [[Comma list]]<br /> #* [[Mapping]] (mapping generators) / subgroup-val mapping &amp; gencom mapping<br /> #* [[Optimal tuning]]s ([[WE]] and [[CWE]])<br /> #* [[Optimal ET sequence]]<br /> #* [[Badness]]<br /> # Only keep [[minimax tuning]] and [[tuning ranges]] if they don't exist in the dedicated temperament page. Since minimax tunings are based on tonality diamonds, it should explicitly state the ''odd'' limit, or a diamond function of ratios.<br /> # Relocate [[algebraic generator]] to the intro to the temperament. <br /> # Remove lattice basis, [[projection pair]], and [[complexity spectrum]], but determine if any of them is worth relocating to their collection pages. <br /> # Comma list should be the Tenney-minimal commas sufficient to define the temperament, stated in [[Normal forms #Normal forms for commas]]. <br /> # For subgroup temperaments, &quot;mapping&quot; becomes &quot;subgroup-val mapping&quot; and &quot;gencom mapping&quot;&quot;. <br /> # In mapping generators, make sure all the ratios as used in the mapping, including the period, are present. <br /> #* If the subgroup is trivial, simply show &quot;WE&quot;/&quot;CWE&quot;, otherwise show &quot;subgroup/inharmonic WE/CWE&quot; instead. <br /> # Make sure there are cent symbols after cent values. <br /> <br /> Get a family for: <br /> * &lt;s&gt;Ripple (3 different 7-limit extensions)&lt;/s&gt; done<br /> * &lt;s&gt;Smate (2 different 7-limit extensions)&lt;/s&gt; done<br /> * &lt;s&gt;Passion (4 different 7-limit extensions, 3 strong and 1 weak)&lt;/s&gt; done<br /> * &lt;s&gt;Undim&lt;/s&gt; done<br /> * &lt;s&gt;Quintaleap&lt;/s&gt; done<br /> * &lt;s&gt;Quindromeda&lt;/s&gt; done<br /> * Parakleismic (many reasonable but unnamed 7-limit extensions)<br /> * Schismatic rank-3 family (many reasonable but unnamed 7-limit extensions)<br /> <br /> Progress: <br /> * &lt;s&gt;Meantone family&lt;/s&gt;<br /> * &lt;s&gt;Didymus rank-3 family&lt;/s&gt;<br /> * &lt;s&gt;Archytas clan&lt;/s&gt;<br /> * &lt;s&gt;Archytas family&lt;/s&gt;<br /> * &lt;s&gt;Father family&lt;/s&gt;<br /> * &lt;s&gt;Trienstonic clan&lt;/s&gt;<br /> * &lt;s&gt;Septisemi temperaments&lt;/s&gt;<br /> * &lt;s&gt;Semaphoresmic clan&lt;/s&gt;<br /> * &lt;s&gt;Semaphoresmic family&lt;/s&gt;<br /> * &lt;s&gt;Jubilismic clan&lt;/s&gt;<br /> * &lt;s&gt;Jubilismic family&lt;/s&gt;<br /> * &lt;s&gt;Mint temperaments&lt;/s&gt;<br /> * &lt;s&gt;Mint family&lt;/s&gt;<br /> * &lt;s&gt;Augmented family&lt;/s&gt;<br /> * &lt;s&gt;Diminished family&lt;/s&gt;<br /> * &lt;s&gt;Passion family&lt;/s&gt;<br /> * &lt;s&gt;Ripple family&lt;/s&gt;<br /> * &lt;s&gt;Dicot family&lt;/s&gt;<br /> * &lt;s&gt;Bug family&lt;/s&gt;<br /> * &lt;s&gt;Mavila family&lt;/s&gt;<br /> * &lt;s&gt;Smate family&lt;/s&gt;<br /> * &lt;s&gt;Gamelismic clan&lt;/s&gt;<br /> * &lt;s&gt;Gamelismic family&lt;/s&gt;<br /> * &lt;s&gt;Marvel temperaments&lt;/s&gt;<br /> * &lt;s&gt;Marvel family&lt;/s&gt;<br /> * &lt;s&gt;Starling temperaments&lt;/s&gt;<br /> * &lt;s&gt;Starling family&lt;/s&gt;<br /> * &lt;s&gt;Sensamagic clan&lt;/s&gt;<br /> * &lt;s&gt;Sensamagic family&lt;/s&gt;<br /> * &lt;s&gt;Magic family&lt;/s&gt;<br /> * &lt;s&gt;Sensipent family&lt;/s&gt;<br /> * &lt;s&gt;Keemic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Keemic family&lt;/s&gt;<br /> * &lt;s&gt;Sengic family&lt;/s&gt;<br /> * &lt;s&gt;Schismatic family&lt;/s&gt;<br /> * &lt;s&gt;Kleismic family&lt;/s&gt;<br /> * &lt;s&gt;Kleismic rank-3 family&lt;/s&gt;<br /> * [[Würschmidt family]]<br /> * [[Unicorn family]]<br /> * [[Immunity family]]<br /> * [[Fifive family]]<br /> * [[Trisedodge family]]<br /> * [[Quintosec family]]<br /> * [[Quintile family]]<br /> * [[Sycamore family]]<br /> * &lt;s&gt;Semicomma family&lt;/s&gt;<br /> * &lt;s&gt;Orwellismic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Orwellismic family&lt;/s&gt;<br /> * [[Hemimean clan]]<br /> * [[Hemimean family]]<br /> * &lt;s&gt;Aberschismic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Aberschismic family&lt;/s&gt;<br /> * &lt;s&gt;Porwell temperaments&lt;/s&gt;<br /> * &lt;s&gt;Porwell family&lt;/s&gt;<br /> * &lt;s&gt;Hemimage temperaments&lt;/s&gt;<br /> * [[Hemimage family]]<br /> * &lt;s&gt;Porcupine family&lt;/s&gt;<br /> * &lt;s&gt;Porcupine rank-3 family&lt;/s&gt;<br /> * &lt;s&gt;Tetracot family&lt;/s&gt;<br /> * &lt;s&gt;Diaschismic family&lt;/s&gt;<br /> * &lt;s&gt;Diaschismic rank-3 family&lt;/s&gt;<br /> * &lt;s&gt;Compton family&lt;/s&gt;<br /> * &lt;s&gt;Amity family&lt;/s&gt;<br /> * &lt;s&gt;Misty family&lt;/s&gt;<br /> * &lt;s&gt;Undim family&lt;/s&gt;<br /> * &lt;s&gt;Lehmerismic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Kalismic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Ragismic microtemperaments&lt;/s&gt;<br /> * &lt;s&gt;Ragismic family&lt;/s&gt;<br /> * &lt;s&gt;Landscape microtemperaments&lt;/s&gt;<br /> * &lt;s&gt;Landscape family&lt;/s&gt;<br /> * &lt;s&gt;Dimcomp family&lt;/s&gt;<br /> * &lt;s&gt;Canopic clan&lt;/s&gt;<br /> * &lt;s&gt;Quince clan&lt;/s&gt;<br /> * &lt;s&gt;Breedsmic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Breed family&lt;/s&gt;<br /> * [[Escapade family]]<br /> * &lt;s&gt;Gravity family&lt;/s&gt;<br /> * &lt;s&gt;Buzzardsmic clan&lt;/s&gt;<br /> * [[Cataharry temperaments]]<br /> * [[Cataharry family]]<br /> * [[Varunismic temperaments]]<br /> * [[Triwellismic temperaments]]<br /> * &lt;s&gt;Rastmic rank-3 clan&lt;/s&gt;<br /> * &lt;s&gt;Biyatismic clan&lt;/s&gt;<br /> * &lt;s&gt;Ptolemismic clan&lt;/s&gt;<br /> * &lt;s&gt;Valinorsmic clan&lt;/s&gt;<br /> * &lt;s&gt;Pentacircle clan&lt;/s&gt;<br /> * &lt;s&gt;Keenanismic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Keenanismic family&lt;/s&gt;<br /> * &lt;s&gt;Werckismic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Swetismic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Wizmic microtemperaments&lt;/s&gt;<br /> * &lt;s&gt;Metric microtemperaments&lt;/s&gt;<br /> * [[Horwell temperaments]]<br /> * [[Horwell family]]<br /> * [[Luna family]]<br /> * &lt;s&gt;Vulture family&lt;/s&gt;<br /> * &lt;s&gt;Alphatricot family&lt;/s&gt;<br /> * &lt;s&gt;Minortone family&lt;/s&gt;<br /> * [[Gammic family]]<br /> * &lt;s&gt;Vishnu family&lt;/s&gt;<br /> * &lt;s&gt;Garischismic clan&lt;/s&gt;<br /> * &lt;s&gt;Garischismic family&lt;/s&gt;<br /> * &lt;s&gt;Canousmic temperaments&lt;/s&gt;<br /> * &lt;s&gt;Canou family&lt;/s&gt;<br /> * &lt;s&gt;Semicanousmic clan&lt;/s&gt;<br /> * &lt;s&gt;Semiporwellismic clan&lt;/s&gt;<br /> * &lt;s&gt;Olympic clan&lt;/s&gt;<br /> * &lt;s&gt;Alphaxenic rank-3 clan&lt;/s&gt;<br /> * &lt;s&gt;Mirwomo temperaments&lt;/s&gt;<br /> * &lt;s&gt;Gariboh clan&lt;/s&gt;<br /> * &lt;s&gt;Gariboh family&lt;/s&gt;<br /> * &lt;s&gt;Octagar temperaments&lt;/s&gt;<br /> * &lt;s&gt;Octagar family&lt;/s&gt;<br /> * &lt;s&gt;Whitewood family&lt;/s&gt;<br /> * [[Wesley family]]<br /> * [[Quartonic family]]<br /> * &lt;s&gt;Mabila family&lt;/s&gt;<br /> * [[Maquila family]]<br /> * [[Maja family]]<br /> * [[Ditonmic family]]<br /> * [[Greenwoodmic temperaments]]<br /> * &lt;s&gt;Avicennmic temperaments&lt;/s&gt;<br /> * [[Keegic temperaments]]<br /> * &lt;s&gt;Very low accuracy temperaments&lt;/s&gt;<br /> * [[Very high accuracy temperaments]]<br /> * &lt;s&gt;Catalog of rank-4 temperaments&lt;/s&gt;<br /> * [[Equivalence continuum|Equivalence continua]]<br /> ** &lt;s&gt;Syntonic–diatonic equivalence continuum&lt;/s&gt;<br /> ** &lt;s&gt;Syntonic–chromatic equivalence continuum&lt;/s&gt;<br /> ** &lt;s&gt;Syntonic–kleismic equivalence continuum&lt;/s&gt;<br /> ** [[Syntonic–31 equivalence continuum]]<br /> ** [[Diaschismic–gothmic equivalence continuum]]<br /> ** &lt;s&gt;Schismic–commatic equivalence continuum&lt;/s&gt;<br /> ** [[Schismic–countercommatic equivalence continuum]]<br /> ** [[Schismic–Mercator equivalence continuum]]<br /> ** [[Archytas–diatonic equivalence continuum]]<br /> * [[Fractional-octave temperaments]]<br /> * [[Subgroup temperaments]]<br /> <br /> == Scale trees ==<br /> ; 6-tone<br /> : &lt;s&gt;1L 5s&lt;/s&gt;, &lt;s&gt;2L 4s&lt;/s&gt;, &lt;s&gt;3L 3s&lt;/s&gt;, &lt;s&gt;4L 2s&lt;/s&gt;, &lt;s&gt;5L 1s&lt;/s&gt;<br /> <br /> ; 7-tone<br /> : &lt;s&gt;1L 6s&lt;/s&gt;, &lt;s&gt;2L 5s&lt;/s&gt;, &lt;s&gt;3L 4s&lt;/s&gt;, &lt;s&gt;4L 3s&lt;/s&gt;, &lt;s&gt;5L 2s&lt;/s&gt;, &lt;s&gt;6L 1s&lt;/s&gt;<br /> <br /> ; 8-tone<br /> : [[1L 7s]], &lt;s&gt;2L 6s&lt;/s&gt;, &lt;s&gt;3L 5s&lt;/s&gt;, &lt;s&gt;4L 4s&lt;/s&gt;, &lt;s&gt;5L 3s&lt;/s&gt;, &lt;s&gt;6L 2s&lt;/s&gt;, [[7L 1s]]<br /> <br /> ; 9-tone<br /> : [[1L 8s]], [[2L 7s]], &lt;s&gt;3L 6s&lt;/s&gt;, &lt;s&gt;4L 5s&lt;/s&gt;, &lt;s&gt;5L 4s&lt;/s&gt;, &lt;s&gt;6L 3s&lt;/s&gt;, [[7L 2s]], [[8L 1s]]<br /> <br /> ; 10-tone<br /> : [[1L 9s]], &lt;s&gt;2L 8s&lt;/s&gt;, &lt;s&gt;3L 7s&lt;/s&gt;, &lt;s&gt;4L 6s&lt;/s&gt;, &lt;s&gt;5L 5s&lt;/s&gt;, &lt;s&gt;6L 4s&lt;/s&gt;, &lt;s&gt;7L 3s&lt;/s&gt;, [[8L 2s]], [[9L 1s]]<br /> <br /> ; 11-tone<br /> : [[1L 10s]], [[2L 9s]], [[3L 8s]], &lt;s&gt;4L 7s&lt;/s&gt;, &lt;s&gt;5L 6s&lt;/s&gt;, &lt;s&gt;6L 5s&lt;/s&gt;, &lt;s&gt;7L 4s&lt;/s&gt;, [[8L 3s]], [[9L 2s]], [[10L 1s]]<br /> <br /> ; 12-tone<br /> : [[1L 11s]], [[2L 10s]], [[3L 9s]], [[4L 8s]], &lt;s&gt;5L 7s&lt;/s&gt;, &lt;s&gt;6L 6s&lt;/s&gt;, &lt;s&gt;7L 5s&lt;/s&gt;, [[8L 4s]], [[9L 3s]], [[10L 2s]], [[11L 1s]]</div> FloraC https://en.xen.wiki/index.php?title=Minortone_family&diff=232433 Minortone family 2026-06-19T15:09:52Z <p>FloraC: Switch to Sintel&#039;s badness, WE &amp; CWE tunings. Improve intro to each entry</p> <hr /> <div>{{Technical data page}}<br /> The '''minortone family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[minortone comma]] ({{monzo|legend=1| -16 35 -17 }}). <br /> <br /> == Minortone ==<br /> The head of this family is the 5-limit minortone temperament, a super-accurate microtemperament with generator a minor tone of [[10/9]], seventeen of which make the [[6/1|6th harmonic]], and another eighteen generators make the interval class of the [[5/1|5th harmonic]]. Its [[ploidacot]] is beta-17-cot. The generator should be tuned about 1/16 of a cent flat, with 6&lt;sup&gt;1/17&lt;/sup&gt; being 0.06423 cents flat and 40&lt;sup&gt;1/35&lt;/sup&gt; being 0.06234 cents flat. [[171edo|171-]], [[559edo|559-]] and [[730edo]] are among the possible edo tunings.<br /> <br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: {{monzo| -16 35 -17 }}<br /> <br /> {{Mapping|legend=1| 1 -1 -3 | 0 17 35 }}<br /> : mapping generators: ~2, ~10/9<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0036{{c}}, ~10/9 = 182.4670{{c}}<br /> : [[error map]]: {{val| +0.004 -0.020 +0.020 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 182.4666{{c}}<br /> : error map: {{val| 0.000 -0.023 +0.017 }}<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091, 25859b }}<br /> <br /> [[Badness]] (Sintel): 0.698<br /> <br /> == Mitonic ==<br /> Mitonic takes advantage of the fact that [[32/21]] is only a [[ragisma]] shy of (10/9)&lt;sup&gt;4&lt;/sup&gt;, and so this 7-limit interpretation where 21 generators gives a ~8/7, if not quite so super-accurate, is more or less inevitable. While [[559edo|559]] or [[730edo|730]] are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. Generator chains of 46 or 79 notes can be used for this temperament.<br /> <br /> Extending mitonic to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: mineral (46 &amp; 171) and ore (46 &amp; 125). Mineral tempers out 441/440 and 16384/16335 in the 11-limit. Ore tempers out 385/384 and 1331/1323 in the 11-limit, and maps [[11/8]] to three generators. In the 17-limit, both mineral and ore temper out 833/832, 1225/1224, 1701/1700, and 4096/4095 (2.3.5.7.13.17 commas). The word ''mineral'' is related to ''mine'' (an excavation from which ore or solid minerals are taken) and ''miner'' (a person who works in a mine, also as a pun on ''minor'').<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 2100875/2097152<br /> <br /> {{Mapping|legend=1| 1 -1 -3 6 | 0 17 35 -21 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0963{{c}}, ~10/9 = 182.4727{{c}}<br /> : [[error map]]: {{val| +0.096 -0.015 -0.057 -0.176 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~10/9 = 182.4592{{c}}<br /> : error map: {{val| 0.000 -0.149 -0.243 -0.468 }}<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}<br /> <br /> [[Badness]] (Sintel): 0.637<br /> <br /> === Mineral ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 4375/4374, 16384/16335<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 | 0 17 35 -21 -43 }}<br /> <br /> Optimal tuning: <br /> * WE: ~2 = 1200.8759{{c}}, ~10/9 = 182.4631{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4818{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125e, 171, 217 }}<br /> <br /> Badness (Sintel): 1.95<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 364/363, 441/440, 3584/3575, 4375/4374<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 11 | 0 17 35 -21 -43 -48 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.8808{{c}}, ~10/9 = 182.4633{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4816{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125e, 171, 217 }}<br /> <br /> Badness (Sintel): 1.37<br /> <br /> ==== 17-limit ====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 364/363, 441/440, 595/594, 1156/1155, 3584/3575<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 11 5 | 0 17 35 -21 -43 -48 -6 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.8923{{c}}, ~10/9 = 182.4650{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4816{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125e, 171, 217 }}<br /> <br /> Badness (Sintel): 1.01<br /> <br /> === Ore ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 385/384, 1331/1323, 4375/4374<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 | 0 17 35 -21 3 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.3408{{c}}, ~10/9 = 182.5004{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4518{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125, 171e }}<br /> <br /> Badness (Sintel): 1.77<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 352/351, 385/384, 1331/1323, 3267/3250<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 11 | 0 17 35 -21 3 -48 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1200.1737{{c}}, ~10/9 = 182.4966{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4705{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125, 171e }}<br /> <br /> Badness (Sintel): 1.91<br /> <br /> ===== 17-limit =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 352/351, 385/384, 561/560, 715/714, 1452/1445<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 11 5 | 0 17 35 -21 3 -48 -6 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1200.1403{{c}}, ~10/9 = 182.4924{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4712{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125, 171e }}<br /> <br /> Badness (Sintel): 1.45<br /> <br /> ==== Goldmine ====<br /> The goldmine temperament (46 &amp; 79) is another 13-limit extension of ore, equating [[13/12]] with [[14/13]] and [[16/13]] with two [[10/9]]s.<br /> <br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 169/168, 325/324, 385/384, 1331/1323<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 4 | 0 17 35 -21 3 -2 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1200.5647{{c}}, ~10/9 = 182.5224{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4409{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 79, 125f, 171ef }}<br /> <br /> Badness (Sintel): 1.62<br /> <br /> ===== 17-limit =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 169/168, 273/272, 325/324, 385/384, 1331/1323<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 4 5 | 0 17 35 -21 3 -2 -6 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1200.4506{{c}}, ~10/9 = 182.5124{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~10/9 = 182.4465{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125f, 171ef }}<br /> <br /> Badness (Sintel): 1.40<br /> <br /> === Seminar ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 2100875/2097152<br /> <br /> Mapping: {{mapping| 2 -2 -6 12 13 | 0 17 35 -21 -20 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 600.0535{{c}}, ~10/9 = 182.4735{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~10/9 = 182.4578{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 250, 296, 342, 3466cddee, 3808bcddeee, …, 5176bccdddeeee }}<br /> <br /> Badness (Sintel): 0.886<br /> <br /> == Domain ==<br /> Domain adds the [[landscape comma]], 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[terrain]].<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 250047/250000, 645700815/645657712<br /> <br /> {{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}<br /> : mapping generators: ~63/50, ~10/9<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~63/50 = 400.0013{{c}}, ~10/9 = 182.4672{{c}}<br /> : [[error map]]: {{val| +0.004 -0.016 +0.028 -0.016 }}<br /> * [[CWE]]: ~63/50 = 400.0000{{c}}, ~10/9 = 182.4668{{c}}<br /> : error map: {{val| 0.000 -0.020 +0.024 -0.021 }}<br /> <br /> {{Optimal ET sequence|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}<br /> <br /> [[Badness]] (Sintel): 0.354<br /> <br /> === Hemidomain ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 151263/151250, 1771561/1771470<br /> <br /> Mapping: {{mapping| 6 -6 -18 -16 -13 | 0 17 35 36 37 }}<br /> : mapping generators: ~55/49, ~10/9<br /> <br /> Optimal tunings: <br /> * WE: ~55/49 = 200.0009{{c}}, ~10/9 = 182.4669{{c}}<br /> * CWE: ~55/49 = 200.0000{{c}}, ~10/9 = 182.4675{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 342, 1164, 1506, 1848, 4038, 5886, 9924 }}<br /> <br /> Badness (Sintel): 0.360<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Minortone family| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_family&diff=232432 Vishnu family 2026-06-19T11:14:10Z <p>FloraC: + more intro to each entry</p> <hr /> <div>{{Technical data page}}<br /> The '''vishnu family''' [[tempering out|tempers out]] the [[vishnu comma]] ({{monzo|legend=1| 23 6 -14 }}, [[ratio]]: 6 115 295 232 / 6 103 515 625), an [[unnoticeable comma]] of about 3.34 [[cent]]s in size. <br /> <br /> == Vishnu ==<br /> The generator for the vishnu temperament is a [[25/24|classical chromatic semitone]], seven of which make a [[4/3|perfect fourth]], and [[5/4]] is found as a half-octave period minus three generators. Its [[ploidacot]] is diploid epsilon-heptacot. It is a member of the [[diaschismic–gothmic equivalence continuum]] with {{nowrap| ''n'' {{=}} 7/2 }}; thus it is most naturally used as a 34-form. <br /> <br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}<br /> : mapping generators: ~78125/55296, ~25/24<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~78125/55296 = 599.9771{{c}}, ~25/24 = 71.1405{{c}}<br /> : [[error map]]: {{val| -0.046 -0.030 +0.150 }}<br /> * [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1482{{c}}<br /> : error map: {{val| 0.000 +0.007 +0.242 }}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}<br /> <br /> [[Badness]] (Sintel): 0.731<br /> <br /> === Overview to extensions ===<br /> The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 &amp; 152) adds [[4375/4374]]. Narayana (84 &amp; 118) adds [[65625/65536]]. Vishnean (16 &amp; 50) adds [[126/125]]. There is also an unnamed 50 &amp; 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu. <br /> <br /> Quarvish (68 &amp; 270) adds [[2401/2400]], splitting the generator in four. Decavish adds [[420175/419904]], with a 1/10-octave period. <br /> <br /> == Septimal vishnu ==<br /> Septimal vishnu may be described as the {{nowrap| 118 &amp; 152 }} temperament, tempering out 4375/4374, the [[ragisma]], and 29360128/29296875, the [[quasiorwellisma]], aside from the vishnu comma. [[270edo]] is an excellent tuning for this temperament, with generator 16\270 (71.{{overline|1}} cents), but it can be tuned to [[422edo]], [[692edo]], or [[962edo]]. It extends naturally to the [[11-limit]] by identifying a stack of four [[5/4]]'s as [[11/9]], tempering out [[5632/5625]]. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 29360128/29296875<br /> <br /> {{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~10125/7168 = 599.9486{{c}}, ~25/24 = 71.1014{{c}}<br /> : [[error map]]: {{val| -0.103 +0.129 +0.125 -0.092 }}<br /> * [[CWE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1106{{c}}<br /> : error map: {{val| 0.000 +0.271 +0.354 +0.081 }}<br /> <br /> {{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}<br /> <br /> [[Badness]] (Sintel): 1.06<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9549{{c}}, ~25/24 = 71.0994{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1077{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502 }}<br /> <br /> Badness (Sintel): 0.469<br /> <br /> ==== Acyuta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9475{{c}}, ~25/24 = 71.0947{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1028{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}<br /> <br /> Badness (Sintel): 0.653<br /> <br /> ==== Ananta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}<br /> <br /> Optimal tuning: <br /> * WE: ~99/70 = 599.9940{{c}}, ~25/24 = 71.1163{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1170{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}<br /> <br /> Badness (Sintel): 0.978<br /> <br /> == Narayana ==<br /> Named by [[Xenllium]] in 2021, narayana tempers out 65625/65536, the [[horwell comma]], as well as 321489/320000, the [[varunisma]], and may be described as the {{nowrap| 84 &amp; 118 }} temperament. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 65625/65536, 321489/320000<br /> <br /> {{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~567/400 = 600.1141{{c}}, ~25/24 = 71.2783{{c}}<br /> : [[error map]]: {{val| +0.228 -0.447 +0.422 -0.362 }}<br /> * [[CWE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2659{{c}}<br /> : error map: {{val| 0.000 -0.816 -0.111 -0.976 }}<br /> <br /> {{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}<br /> <br /> [[Badness]] (Sintel): 2.39<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 8019/8000, 65625/65536<br /> <br /> Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 600.0992{{c}}, ~25/24 = 71.2593{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2501{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}<br /> <br /> Badness (Sintel): 1.52<br /> <br /> == Vishnean ==<br /> Named by [[Petr Pařízek]] in 2011&lt;ref name=&quot;petr's long post&quot;&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']&lt;/ref&gt;, vishnean is a low-complexity low-accuracy extension of vishnu that tempers out 126/125, the [[starling comma]]. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 540225/524288<br /> <br /> {{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~735/512 = 600.8754{{c}}, ~25/24 = 71.8834{{c}}<br /> : [[error map]]: {{val| +1.751 -1.637 +2.413 -5.031 }}<br /> * [[CWE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.7141{{c}}<br /> : error map: {{val| 0.000 -3.954 -1.456 -10.255 }}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}<br /> <br /> [[Badness]] (Sintel): 4.08<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 385/384, 1350/1331<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}<br /> <br /> Optimal tunings: <br /> * WE: ~63/44 = 600.7144{{c}}, ~25/24 = 72.0091{{c}}<br /> * CWE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.8588{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Sintel): 2.38<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 105/104, 126/125, 144/143, 847/845<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}<br /> <br /> Optimal tunings: <br /> * WE: ~55/39 = 600.5983{{c}}, ~25/24 = 71.9975{{c}}<br /> * CWE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.8699{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Sintel): 1.68<br /> <br /> == Quarvish ==<br /> Quarvish tempers out 2401/2400, the [[breedsma]], and may be described as the {{nowrap| 68 &amp; 202 }} temperament. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 2401/2400, 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}<br /> : mapping generators: ~78125/55296, ~110592/109375<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~78125/55296 = 599.9874{{c}}, ~110592/109375 = 17.7862{{c}}<br /> : [[error map]]: {{val| -0.025 -0.020 +0.189 -0.123 }}<br /> * [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~110592/109375 = 17.7873{{c}}<br /> : error map: {{val| 0.000 +0.002 +0.239 -0.060 }}<br /> <br /> {{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> [[Badness]] (Sintel): 1.14<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 2401/2400, 9801/9800, 172032/171875<br /> <br /> Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9884{{c}}, ~99/98 = 17.7865{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~99/98 = 17.7870{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> Badness (Sintel): 0.657<br /> <br /> == Decavish ==<br /> Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 &amp; 270 }} temperament. It was named by [[Xenllium]] in 2021 for the fact that its period is 1/10 octave. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 420175/419904, 2202927104/2197265625<br /> <br /> {{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}<br /> : mapping generators: ~15/14, ~54/49<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~15/14 = 119.9957{{c}}, ~54/49 = 168.8645{{c}} (~36/35 = 48.8689{{c}})<br /> : [[error map]]: {{val| -0.043 +0.071 +0.197 -0.242 }}<br /> * [[CWE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8658{{c}} (~36/35 = 48.8658{{c}})<br /> : error map: {{val| 0.000 +0.106 +0.284 -0.168 }}<br /> <br /> {{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}<br /> <br /> [[Badness]] (Sintel): 2.90<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 41503/41472, 172032/171875<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~15/14 = 119.9997{{c}}, ~54/49 = 168.8587{{c}} (~36/35 = 48.8590{{c}})<br /> * CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8589{{c}} (~36/35 = 48.8589{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}<br /> <br /> Badness (Sintel): 1.22<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}<br /> <br /> Optimal tunings: <br /> * WE: ~15/14 = 120.0037{{c}}, ~54/49 = 168.8537{{c}} (~36/35 = 48.8500{{c}})<br /> * CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8506{{c}} (~36/35 = 48.8506{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, …, 220, 270, 590, 860, 1130 }}<br /> <br /> Badness (Sintel): 0.905<br /> <br /> == References ==<br /> &lt;references/&gt;<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Vishnu family| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_family&diff=232431 Vishnu family 2026-06-19T10:24:11Z <p>FloraC: + overview to extensions. Sorting</p> <hr /> <div>{{Technical data page}}<br /> The '''vishnu family''' [[tempering out|tempers out]] the [[vishnu comma]] ({{monzo|legend=1| 23 6 -14 }}, [[ratio]]: 6 115 295 232 / 6 103 515 625), a [[5-limit]] comma of about 3 [[cent]]s. It is the amount by which seven just chromatic semitones of [[25/24]] fall short of a just perfect fourth of [[4/3]], or in other words (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;.<br /> <br /> == Vishnu ==<br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}<br /> : mapping generators: ~78125/55296, ~25/24<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~78125/55296 = 599.9771{{c}}, ~25/24 = 71.1405{{c}}<br /> : [[error map]]: {{val| -0.046 -0.030 +0.150 }}<br /> * [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1482{{c}}<br /> : error map: {{val| 0.000 +0.007 +0.242 }}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}<br /> <br /> [[Badness]] (Sintel): 0.731<br /> <br /> === Overview to extensions ===<br /> The second comma in the comma list defines which 7-limit family member we are looking at. Septimal vishnu (118 &amp; 152) adds [[4375/4374]]. Narayana (84 &amp; 118) adds [[65625/65536]]. Vishnean (16 &amp; 50) adds [[126/125]]. There is also an unnamed 50 &amp; 84 temperament, which tempers out [[225/224]]. These all use the same generators as classical vishnu. <br /> <br /> Quarvish (68 &amp; 270) adds [[2401/2400]], splitting the generator in four. Decavish adds [[420175/419904]], with a 1/10-octave period. <br /> <br /> == Septimal vishnu ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 29360128/29296875<br /> <br /> {{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~10125/7168 = 599.9486{{c}}, ~25/24 = 71.1014{{c}}<br /> : [[error map]]: {{val| -0.103 +0.129 +0.125 -0.092 }}<br /> * [[CWE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1106{{c}}<br /> : error map: {{val| 0.000 +0.271 +0.354 +0.081 }}<br /> <br /> {{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}<br /> <br /> [[Badness]] (Sintel): 1.06<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9549{{c}}, ~25/24 = 71.0994{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1077{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502 }}<br /> <br /> Badness (Sintel): 0.469<br /> <br /> ==== Acyuta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9475{{c}}, ~25/24 = 71.0947{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1028{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}<br /> <br /> Badness (Sintel): 0.653<br /> <br /> ==== Ananta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}<br /> <br /> Optimal tuning: <br /> * WE: ~99/70 = 599.9940{{c}}, ~25/24 = 71.1163{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1170{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}<br /> <br /> Badness (Sintel): 0.978<br /> <br /> == Narayana ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 65625/65536, 321489/320000<br /> <br /> {{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~567/400 = 600.1141{{c}}, ~25/24 = 71.2783{{c}}<br /> : [[error map]]: {{val| +0.228 -0.447 +0.422 -0.362 }}<br /> * [[CWE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2659{{c}}<br /> : error map: {{val| 0.000 -0.816 -0.111 -0.976 }}<br /> <br /> {{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}<br /> <br /> [[Badness]] (Sintel): 2.39<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 8019/8000, 65625/65536<br /> <br /> Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 600.0992{{c}}, ~25/24 = 71.2593{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2501{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}<br /> <br /> Badness (Sintel): 1.52<br /> <br /> == Vishnean ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 540225/524288<br /> <br /> {{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~735/512 = 600.8754{{c}}, ~25/24 = 71.8834{{c}}<br /> : [[error map]]: {{val| +1.751 -1.637 +2.413 -5.031 }}<br /> * [[CWE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.7141{{c}}<br /> : error map: {{val| 0.000 -3.954 -1.456 -10.255 }}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}<br /> <br /> [[Badness]] (Sintel): 4.08<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 385/384, 1350/1331<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}<br /> <br /> Optimal tunings: <br /> * WE: ~63/44 = 600.7144{{c}}, ~25/24 = 72.0091{{c}}<br /> * CWE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.8588{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Sintel): 2.38<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 105/104, 126/125, 144/143, 847/845<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}<br /> <br /> Optimal tunings: <br /> * WE: ~55/39 = 600.5983{{c}}, ~25/24 = 71.9975{{c}}<br /> * CWE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.8699{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Sintel): 1.68<br /> <br /> == Quarvish ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 2401/2400, 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}<br /> : mapping generators: ~78125/55296, ~110592/109375<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~78125/55296 = 599.9874{{c}}, ~110592/109375 = 17.7862{{c}}<br /> : [[error map]]: {{val| -0.025 -0.020 +0.189 -0.123 }}<br /> * [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~110592/109375 = 17.7873{{c}}<br /> : error map: {{val| 0.000 +0.002 +0.239 -0.060 }}<br /> <br /> {{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> [[Badness]] (Sintel): 1.14<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 2401/2400, 9801/9800, 172032/171875<br /> <br /> Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9884{{c}}, ~99/98 = 17.7865{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~99/98 = 17.7870{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> Badness (Sintel): 0.657<br /> <br /> == Decavish ==<br /> Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 &amp; 270 }} temperament. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 420175/419904, 2202927104/2197265625<br /> <br /> {{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}<br /> : mapping generators: ~15/14, ~54/49<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~15/14 = 119.9957{{c}}, ~54/49 = 168.8645{{c}} (~36/35 = 48.8689{{c}})<br /> : [[error map]]: {{val| -0.043 +0.071 +0.197 -0.242 }}<br /> * [[CWE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8658{{c}} (~36/35 = 48.8658{{c}})<br /> : error map: {{val| 0.000 +0.106 +0.284 -0.168 }}<br /> <br /> {{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}<br /> <br /> [[Badness]] (Sintel): 2.90<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 41503/41472, 172032/171875<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~15/14 = 119.9997{{c}}, ~54/49 = 168.8587{{c}} (~36/35 = 48.8590{{c}})<br /> * CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8589{{c}} (~36/35 = 48.8589{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}<br /> <br /> Badness (Sintel): 1.22<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}<br /> <br /> Optimal tunings: <br /> * WE: ~15/14 = 120.0037{{c}}, ~54/49 = 168.8537{{c}} (~36/35 = 48.8500{{c}})<br /> * CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8506{{c}} (~36/35 = 48.8506{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, …, 220, 270, 590, 860, 1130 }}<br /> <br /> Badness (Sintel): 0.905<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Vishnu family| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_family&diff=232430 Vishnu family 2026-06-19T10:05:16Z <p>FloraC: Switch to Sintel&#039;s badness, WE &amp; CWE tunings</p> <hr /> <div>{{Technical data page}}<br /> The '''vishnu family''' [[tempering out|tempers out]] the [[vishnu comma]] ({{monzo|legend=1| 23 6 -14 }}, [[ratio]]: 6 115 295 232 / 6 103 515 625), a [[5-limit]] comma of about 3 [[cent]]s. It is the amount by which seven just chromatic semitones of [[25/24]] fall short of a just perfect fourth of [[4/3]], or in other words (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;.<br /> <br /> == Vishnu ==<br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}<br /> : mapping generators: ~78125/55296, ~25/24<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~78125/55296 = 599.9771{{c}}, ~25/24 = 71.1405{{c}}<br /> : [[error map]]: {{val| -0.046 -0.030 +0.150 }}<br /> * [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1482{{c}}<br /> : error map: {{val| 0.000 +0.007 +0.242 }}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}<br /> <br /> [[Badness]] (Sintel): 0.731<br /> <br /> == Septimal vishnu ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 29360128/29296875<br /> <br /> {{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~10125/7168 = 599.9486{{c}}, ~25/24 = 71.1014{{c}}<br /> : [[error map]]: {{val| -0.103 +0.129 +0.125 -0.092 }}<br /> * [[CWE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1106{{c}}<br /> : error map: {{val| 0.000 +0.271 +0.354 +0.081 }}<br /> <br /> {{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}<br /> <br /> [[Badness]] (Sintel): 1.06<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9549{{c}}, ~25/24 = 71.0994{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1077{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502 }}<br /> <br /> Badness (Sintel): 0.469<br /> <br /> ==== Ananta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}<br /> <br /> Optimal tuning: <br /> * WE: ~99/70 = 599.9940{{c}}, ~25/24 = 71.1163{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1170{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}<br /> <br /> Badness (Sintel): 0.978<br /> <br /> ==== Acyuta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9475{{c}}, ~25/24 = 71.0947{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1028{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}<br /> <br /> Badness (Sintel): 0.653<br /> <br /> == Vishnean ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 540225/524288<br /> <br /> {{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~735/512 = 600.8754{{c}}, ~25/24 = 71.8834{{c}}<br /> : [[error map]]: {{val| +1.751 -1.637 +2.413 -5.031 }}<br /> * [[CWE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.7141{{c}}<br /> : error map: {{val| 0.000 -3.954 -1.456 -10.255 }}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}<br /> <br /> [[Badness]] (Sintel): 4.08<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 385/384, 1350/1331<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}<br /> <br /> Optimal tunings: <br /> * WE: ~63/44 = 600.7144{{c}}, ~25/24 = 72.0091{{c}}<br /> * CWE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.8588{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Sintel): 2.38<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 105/104, 126/125, 144/143, 847/845<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}<br /> <br /> Optimal tunings: <br /> * WE: ~55/39 = 600.5983{{c}}, ~25/24 = 71.9975{{c}}<br /> * CWE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.8699{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Sintel): 1.68<br /> <br /> == Narayana ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 65625/65536, 321489/320000<br /> <br /> {{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~567/400 = 600.1141{{c}}, ~25/24 = 71.2783{{c}}<br /> : [[error map]]: {{val| +0.228 -0.447 +0.422 -0.362 }}<br /> * [[CWE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2659{{c}}<br /> : error map: {{val| 0.000 -0.816 -0.111 -0.976 }}<br /> <br /> {{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}<br /> <br /> [[Badness]] (Sintel): 2.39<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 8019/8000, 65625/65536<br /> <br /> Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 600.0992{{c}}, ~25/24 = 71.2593{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2501{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}<br /> <br /> Badness (Sintel): 1.52<br /> <br /> == Quarvish ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 2401/2400, 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}<br /> : mapping generators: ~78125/55296, ~110592/109375<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~78125/55296 = 599.9874{{c}}, ~110592/109375 = 17.7862{{c}}<br /> : [[error map]]: {{val| -0.025 -0.020 +0.189 -0.123 }}<br /> * [[CWE]]: ~78125/55296 = 600.0000{{c}}, ~110592/109375 = 17.7873{{c}}<br /> : error map: {{val| 0.000 +0.002 +0.239 -0.060 }}<br /> <br /> {{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> [[Badness]] (Sintel): 1.14<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 2401/2400, 9801/9800, 172032/171875<br /> <br /> Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}<br /> <br /> Optimal tunings: <br /> * WE: ~99/70 = 599.9884{{c}}, ~99/98 = 17.7865{{c}}<br /> * CWE: ~99/70 = 600.0000{{c}}, ~99/98 = 17.7870{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> Badness (Sintel): 0.657<br /> <br /> == Decavish ==<br /> Decavish tempers out the [[wizma]] as well as the [[linus comma]], and may be described as the {{nowrap| 50 &amp; 270 }} temperament. <br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 420175/419904, 2202927104/2197265625<br /> <br /> {{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}<br /> : mapping generators: ~15/14, ~54/49<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~15/14 = 119.9957{{c}}, ~54/49 = 168.8645{{c}} (~36/35 = 48.8689{{c}})<br /> : [[error map]]: {{val| -0.043 +0.071 +0.197 -0.242 }}<br /> * [[CWE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8658{{c}} (~36/35 = 48.8658{{c}})<br /> : error map: {{val| 0.000 +0.106 +0.284 -0.168 }}<br /> <br /> {{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}<br /> <br /> [[Badness]] (Sintel): 2.90<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 41503/41472, 172032/171875<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~15/14 = 119.9997{{c}}, ~54/49 = 168.8587{{c}} (~36/35 = 48.8590{{c}})<br /> * CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8589{{c}} (~36/35 = 48.8589{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}<br /> <br /> Badness (Sintel): 1.22<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}<br /> <br /> Optimal tunings: <br /> * WE: ~15/14 = 120.0037{{c}}, ~54/49 = 168.8537{{c}} (~36/35 = 48.8500{{c}})<br /> * CWE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8506{{c}} (~36/35 = 48.8506{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, …, 220, 270, 590, 860, 1130 }}<br /> <br /> Badness (Sintel): 0.905<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Vishnu family| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=Temperament_naming&diff=232421 Temperament naming 2026-06-18T19:49:19Z <p>FloraC: Put editorial contents in notes</p> <hr /> <div>Regular temperament names come in two types: common names and systematic names. Common names takes a diversity of sources. Systematic names are rigorously derived from an algorithm. This article focuses on common names. <br /> <br /> == Temperament and comma naming conventions ==<br /> === State of the art ===<br /> A temperament name should be a common noun (thus written in lowercase), ideally consisting of a single word. This contrasts scales of a temperament, e.g. Machine[6], as well as concrete scales, e.g. Centaur. This convention of naming temperaments was first proposed in 2012&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_105566.html Yahoo! Tuning Group | ''Naming Convention Suggestion'']&lt;/ref&gt;. <br /> <br /> Below are explained some notable features of naming which might otherwise be confusing to beginners of RTT. <br /> <br /> ==== Use of a name for a temperament and its extensions ====<br /> A name can be shared by a temperament as well as its [[strong extension]]s. For example, meantone was defined in the 5-, 7-, and 11-limit, each temperament in the higher limit being a strong extension to the ones in the lower limit. The reason is sometimes you get the higher-limit intervals &quot;for free&quot; when using the lower-limit temperament, in which case we consider extending the temperament this way the ''canonical extension''. Whether an extension is canonical or not depends on a lot of factors, but in general: <br /> * Only the best and most obvious extension is canonical; <br /> * If a temperament does not have an obvious extension, or has multiple competing extensions, none of them is canonical; <br /> * [[Weak extension]]s are never canonical since their structures are very different.<br /> <br /> ==== Use of a related pair of names for a comma and its associated temperament ====<br /> With a few exceptions, a name of a comma implies an eponymous temperament that tempers out the comma alone and vice versa, in which case we consider it an official common name. A description, or descriptive name, is an alternative, typically longer, term that conveys some additional information at the cost of lacking in uniqueness. For example, 225/224 is named the ''marvel comma'', and tempering it out results in the marvel temperament. Meanwhile, it has a descriptive name ''septimal kleisma'' that perhaps dates back to earlier times. <br /> <br /> ==== Use of a related pair of names for prime-limit and subgroup temperaments ====<br /> It is often useful to investigate the implied full-prime-limit temperament as well as the subgroup temperaments for a comma, especially in the higher limits where there is a shift of interest towards the subgroups. The following practice was established around 2022–2023 when many higher-limit commas were getting named: if a comma is named the &quot;''X''-isma&quot;, then the temperament which tempers out the ''X''-isma in the minimal [[prime subgroup]] containing that comma should be named &quot;''X''-ic&quot; and the temperament which tempers out the ''X''-isma in the minimal [[prime limit]] containing that comma should be named &quot;''X-''ismic&quot;. However, that was not the only pattern in use. Below are tabulated all the widely observed and established patterns, known as ''declensions''. <br /> <br /> {| class=&quot;wikitable center-all&quot; style=&quot;margin: auto;&quot;<br /> |+ Comma–temperament name patterns<br /> |-<br /> ! # !! Short name !! Prime-limit temp. !! Prime-subgroup temp. !! Long name<br /> |-<br /> | 0 || -sma || -smic || -∅ || -∅ comma<br /> |-<br /> | 1 || -isma || -ismic || -ic || -ic comma<br /> |-<br /> | 2 || -ia || -ic || -ian || -ic comma<br /> |-<br /> | 3 || -on || -onic || -y || -y comma<br /> |}<br /> <br /> A comma page should ideally always include a mention of both the minimal-prime-subgroup and full-prime-limit temperaments. The temperaments and obvious and/or strong extensions may be discussed either there or on linked-to dedicated pages. <br /> <br /> === Contemporary rules ===<br /> It has become evident over time that there is a need to formalize when it is or is not okay to propose and accept names or renames of temperaments and commas, especially as more users contribute and offer input and as those users inevitably become more out-of-sync in their preferences. There is a repeated pattern of wasted energy and effort, that many may find demotivating, when conflict inevitably emerges out of a lack of clear ground rules. Therefore it is important to make clear a set of rules which wiki editors can defer to in cases of such conflicts that feel as though they have reached an impasse.<br /> <br /> Conventions for naming commas/temperaments:<br /> * The name should follow the state of the art, given above. <br /> * The name should have something to do with the comma/temperament. This is a rule that is often assumed implicitly without mention.<br /> * Stronger than the above, the name should ideally have a wealth of reasonings supporting its association (ideally ''uniquely'', within reason) with the comma/temperament in question.<br /> * The name should not cause potential confusion/ambiguity with other names. Note that an important exception to this rule is that closely related temperaments may have highly similar names; this is not uncommon.<br /> * The name's complexity should loosely reflect the complexity of the comma/temperament, so that very simple names are not exhausted for very complex commas/temperaments, which would later cause issues if one of those names found a simpler and more elegant comma/temperament to be associated with (see also the section on conventions for renaming). Note that &quot;simple&quot; here does not mean low-accuracy, nor high-accuracy, but rather simple in the conceptual sense; roughly how easy would it be for someone to rediscover this comma/temperament, assuming the rediscoverer has no particular interest in the comma/temperament in question? &quot;Elegant&quot; is meant as similar in meaning to &quot;simple&quot; but more in the direction of a potential subjective appraisal of a comma/temperament for unique properties it has.<br /> * The name must not be offensive, where &quot;offensive&quot; is defined as referring to topics that quite a few would deem controversial and/or where the name is NSFW (not-safe-for-work).<br /> * The name has a fair amount of consensus (e.g. several people in favour versus 2 against). This is not to be interpreted as iron democratic rule but rather as a significant indicator of a good name, along with other reasons detailed.<br /> <br /> Most important of the above points are those on: not being NSFW/inappropriate, lack of ambiguity, compliance with existing naming conventions, and consensus.<br /> <br /> It should not come as a surprise to anyone that good reasons for renaming commas/temperaments mostly mirror conventions for renaming them:<br /> <br /> Strong reasons for renaming a comma and/or temperament are:<br /> * The name is inconsistent with the state of the art. <br /> * The name causes significant confusion/ambiguity with other names. Note that an important exception to this rule is that closely related temperaments/commas/scales may have highly similar names; this is not uncommon. <br /> * The name can be deemed to be offensive, where offensive is defined as referring to topics that quite a few would deem controversial and/or where the name is NSFW (not-safe-for-work).<br /> * The name change proposal has a fair amount of consensus (e.g. several people in favour versus 2 against). This is not to be interpreted as iron democratic rule but rather as a significant indicator of a good name, along with other reasons detailed.<br /> <br /> Weaker but still good and standard reasons for renaming a comma and/or temperament include:<br /> * The name is simpler but not so simple as to be absurd and implicatory of many alternate candidates.<br /> * The name has reasoning behind it that identifies it as appropriate at least insofar as it identifies the comma as unique within reason.<br /> * The previous name is fairly new (within the last year).<br /> <br /> Therefore, if one finds oneself at an impasse, refer to this work in progress section and see how many bullet points are in favour of a name or rename. With that said, every rename proposal must have at least one ''strong reason''. The only time it is acceptable for it not to is if the previous name has very little or no usage and the rename does not cause friction (e.g. the recent proposer wants to change the name and there are no objections).<br /> <br /> If there are external references (outside of the wiki) beyond the mere proposal of the name, previous names may stay on the wiki for historical purposes, but should be moved out of the spotlights (lead section, infobox, etc.) to avoid the potential interpretation that these names are equally common/standard. It is important to note however that ''if'' there is nothing particularly wrong with the old name, then it is ''standard and common'' to let the old name coexist with the new name with the spirit that people can use whatever name they prefer.<br /> <br /> If, however, a name has received enough usage outside the wiki that a rename would be ''significantly'' inconvenient and confusing and/or if there is a very large amount of usage on the wiki so that many people may have seen and remembered the previous name, the previous name should be mentioned in passing towards the beginning of the page for clarity / to avoid confusion and for historical purposes. The only exception to this rule is if the name is NSFW, in which case it should be at the very least moved out of the spotlights if not removed entirely.<br /> <br /> This summary of conventions aims to be comprehensive but not exhaustive. Minor reasons may be included if they are abstract in nature rather than overly specific in application.<br /> <br /> {{Note| If you feel something is missing that many would agree on being added and which you do not believe would be controversial to add, please add it. If you feel something should be added but are unsure about how it may be taken, please take to this page's [[Talk:Temperament naming|talk page]], add your reasonings/arguments and await responses and some form of consensus first. Be patient, this full process may take weeks! And as always, do your best to remain objective, professional and respectful. }}<br /> <br /> == Temperament name examples ==<br /> {{Note| This is a closed list. Please explain temperament names in the temperament's dedicated article or catalog page. }}<br /> <br /> ; [[Alphatricot]]<br /> : Origin: Paul Erlich (2002)<br /> : Meaning: First named as ''tricot'', but later renamed to ''alphatricot'' following the specifications of [[ploidacot]]. The interval class of 3 is divided into three equal parts, hence &quot;tri-&quot;. The specific interval being divided is 3/1, which is an octave above 3/2, hence &quot;alpha-&quot;. See the temperament's dedicated page for sources. <br /> <br /> ; [[Amity]]<br /> : Origin: Gene Ward Smith (2001–2002)<br /> : Meaning: A restructuring of the phrase ''acute minor third'', as the ideal generator for amity is between a minor third and neutral third. See the temperament's dedicate page for sources. <br /> <br /> ; [[Augmented (temperament)|Augmented]]<br /> : Origin: Paul Erlich and Carl Lumma (2002)<br /> : Meaning: Augmented gets its name from its 1/3-octave period, corresponding to an augmented triad.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_34327#34708 Yahoo! Tuning Groups | ''new equal temperament 5-limit error lattices''] - &quot;i think carl and i just came to the consensus here that … the [temperament] you're calling 'diesic' should be called 'augmented'. besides the reasons already given … the period of the 'augmented' linear temperament is 1/3 octave (thus outlining an augmented triad).&quot; —Paul Erlich&lt;/ref&gt;<br /> <br /> ; [[Ammonite]]<br /> : Origin: Keenan Pepper (2011)<br /> : Meaning: Keenan Pepper suggested it was a good name of a weird spiral-shaped animal, for a temperament in the porcupine family (like nautilus). <br /> <br /> ; [[A-team]]<br /> : Origin: Igliashon Jones (2011)<br /> : Meaning: A pun on ''eighteen'', since the 2.9.21 subgroup of A-Team is nearly optimal in 18edo.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18559.html#18563 Yahoo! Tuning Group | ''1029'']&lt;/ref&gt;<br /> <br /> ; [[Augene]]<br /> : Originally ''tripletone'', in analogy with ''twintone'', but when ''twintone'' was renamed ''pajara'' Paul Erlich suggested it should be augene, after augmented and Gene Smith.<br /> <br /> ; [[Avila]]<br /> : Origin: Mike Battaglia, Ron Sword, Ryan Avella (2011)<br /> : Meaning: Originally discovered by Ryan by accident while he was reading the mapping for Mavila temperament incorrectly. It is the original spelling of Ryan's surname.<br /> <br /> ; [[Beatles]]<br /> : Origin: Gene Ward Smith (2003)<br /> : Meaning: Named for the 19\64 generator, since 1964 is the year the Beatlemania swept the world.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5279.html#5299 Yahoo! Tuning Group | ''Poptimal generators'']&lt;/ref&gt;<br /> <br /> ; [[Blackwood]]<br /> : Origin: Gene Ward Smith and Paul Erlich (2002)&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_4554.html Yahoo! Tuning Group | ''Modified best 5-limit geometric list'']&lt;/ref&gt;&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5080.html Yahoo! Tuning Group | ''Ultimate 5-limit comma list'']&lt;/ref&gt;<br /> : Meaning: Named after Easley Blackwood's 10-out-of-15 maximally even scale. <br /> <br /> ; [[Breed (temperament)|Breed]]<br /> : Origin: Gene Ward Smith (2004)<br /> : Named after [[Graham Breed]]. See [[breedsma]] for sources.<br /> <br /> ; [[Catakleismic]]<br /> : Meaning: The ''cata-'' prefix means ''down'', and the catakleismic generator is very slightly down from the hanson generator, a temperament called ''kleismic'' until Paul Erlich decided the name must and shall be changed.<br /> <br /> ; [[Catler]]<br /> : Named for [[Jon Catler]].<br /> <br /> ; [[Dicot]]<br /> : Meaning: 3/2 is divided into 2 equal parts, hence ''di-''. Not sure why ''-cot''. ''-Cot'' has been suggested to originate from ''cotyledon'', the name for the embryo of a plant seed.<br /> <br /> ; [[Diminished (temperament)|Diminished]]<br /> : Origin: Paul Erlich and Carl Lumma (2002)<br /> : Meaning: Diminished gets its name from its 1/4-octave period, corresponding to a diminished seventh chord.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_34327#34708 Yahoo! Tuning Groups | ''new equal temperament 5-limit error lattices''] - &quot;i think carl and i just came to the consensus here that this should be called 'diminished', and the one you're calling 'diesic' should be called 'augmented'. besides the reasons already given, the period of the 'diminished' linear temperament is 1/4 octave (thus outlining a diminished seventh chord)&quot; —Paul Erlich&lt;/ref&gt;<br /> : This naming was not immediate, however. Paul initially proposed the name ''octo-diminished''&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_1997#1998 Yahoo! Tuning Group | ''The four before meantone'']&lt;/ref&gt;, which appears to be a reference to {{w|Olivier Messiaen}}'s {{w|Mode of limited transposition #Messiaen's list|2nd mode of limited transposition}}, which is also known as the octatonic or ''diminished'' scale; this scale also divides the octave into four equal parts.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064#2068 Yahoo! Tuning Group | ''Kleismic &amp; co'' - &quot;Paul [Erlich] suggested 'Octo-diminished', since it can be done very well by the 64-et.&quot; —Gene Ward Smith]&lt;/ref&gt; but soon switched to sometimes using ''diminished''&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2009#2027 Yahoo! Tuning Group | ''Meantone &amp; co'']&lt;/ref&gt; and sometimes ''octatonic'', the latter of which was adopted by Joseph Monzo.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3433#3464 Yahoo! Tuning Group | ''some output from Graham's cgi''] - &quot;I think [Joseph] Monz[o] and Paul [Erlich] have been calling it octatonic.&quot; —Carl Lumma&lt;/ref&gt; Meanwhile, Gene proposed ''igor'' as a reference to {{w|Igor Stravinksy}}'s association with this scale,&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_3433#3455 Yahoo! Tuning Group | ''some output from Graham's cgi''] - &quot;It's a Paul [Erlich] favorite, since it is associated to the octatonic scale of jazz and Stravinsky. We could call it igor, I suppose.&quot; —Gene Ward Smith&lt;/ref&gt; but this did not catch on. Eventually ''octatonic'' was rejected for being too generic,&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_35256#35262 Yahoo! Tuning Group | ''Octatonic temperament''] - &quot;I'm not sure 'octatonic' is a good name for the temperament. There must be other temperaments whose basic scale has 8 notes. Isn't this what folks are calling the 'diminished' temperament on tuning-math?&quot; —Dave Keenan&lt;/ref&gt; while ''diminished'' was held to convey the 1/4-octave structure of the temperament better,&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_35256#35264 Yahoo! Tuning Group | ''Octatonic temperament''] - &quot;I guess I need a name for this system that doesn't imply there's ''only'' eight notes in the tuning. And 'diminished' does suggest the 1/4-octave framework of the scale, so it's a better name than 'octatonic'.&quot; —Herman Miller&lt;/ref&gt; and so ''diminished'' came to predominate. <br /> : Confusingly, in {{w|Jean-Philippe Rameau}}'s {{w|Treatise on Harmony}} from 1722, he called [[2048/2025]] the ''diminished comma''. This has been displaced by the modern name for 2048/2025, the ''diaschisma'', which gives its name to the diaschismic temperament, from [[Hermann von Helmholtz]] in 1875.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_62661#62683 Yahoo! Tuning Groups | ''Diaschisma article'']&lt;/ref&gt; The interval [[648/625]], the modern ''diminished comma'' by virtue of it being the one diminished temperament makes vanish, has been called the ''major diesis'' or ''greater diesis'',&lt;ref&gt;[[Wikipedia: Diesis]]&lt;/ref&gt; and so ''major diesic'' was also proposed as a name for this temperament.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2064#2067 Yahoo! Tuning Groups | ''Kleismic &amp; co'']&lt;/ref&gt; This would have gone along with [[128/125]] being the ''(minor/lesser) diesis'' and thus ''minor diesic'' temperament. Despite this not working out this way (due in part to too many things being named using ''diesis''), in the end ''diminished'' and ''augmented'' still came out as an opposing pair. <br /> <br /> ; [[Dominant (temperament)|Dominant]]<br /> : Meaning: It is meantone which calls the dominant seventh chord a 4:5:6:7. It is one of the least complex 7-limit extensions of meantone.<br /> <br /> ; [[Doublewide]]<br /> : Named after a type of mobile home.<br /> <br /> ; [[Ennealimmal]]<br /> : Origin: Gene Ward Smith (2001)<br /> : Meaning: Ennealimmal has a 1/9-octave period, hence ''ennea-''; the period is very close to the large limma, [[27/25]], hence ''limmal''.<br /> <br /> ; [[Ervsec]]<br /> {{Todo|research|inline=1|comment=Find out what this is.}}<br /> : A name derived from a scale discovered by Erv Wilson and George Secor in the 80's while George was visiting Erv.<br /> <br /> ; [[Father]]<br /> : Origin: 2000s?<br /> : Meaning: A combination of the words ''fourth'' and ''third''. This is meant to represent the unification of perfect fourths and major thirds in Father temperament.<br /> <br /> ; [[Flattone]]<br /> : Origin: Gene Ward Smith<br /> : Meaning: A variant of meantone in which the whole tone is flatter than in septimal meantone.<br /> <br /> ; [[Glacial]]<br /> : Origin: Igliashon Jones, Mike Battaglia (2012)<br /> : Meaning: ''Glacial'' sounds like ''Igliashon''.<br /> <br /> ; [[Godzilla]]<br /> : Origin: Gene Ward Smith<br /> : Meaning: Named after a Japanese fictional monster; part of the daikaiju series of names for temperaments with an approximate 8/7 as generator.<br /> <br /> ; [[Gravity]]<br /> : Origin: Mike Battaglia (2011)<br /> : Named after its 40/27 grave fifth generator. See [[graviton]] for sources.<br /> <br /> ; [[Hanson]]<br /> : Larry Hanson's 34-edo guitar (9\34 generator)<br /> <br /> ; [[Harry]]<br /> : Derived from a theory that you might be able to play the music of Harry Partch in it without driving him nuts so long as you did not say that was what you were doing.<br /> <br /> ; [[Hedgehog]]<br /> : So named because it is in the ''porcupine'' family, but different.<br /> <br /> ; [[Heinz]]<br /> : Named after the fact that 26\57 is a possible generator, and the words &quot;57 varieties&quot; are found on the bottle labels of a popular brand of ketchup called ''Heinz'', so the connection is based on the presence of the number 57. It does not seem to be related in any way to [[Heinz Bohlen]].<br /> <br /> ; [[Helmholtz (temperament)|Helmholtz]]<br /> : So named because [[Hermann von Helmholtz]] proposed 1/8-schisma flattened fifths.<br /> <br /> ; [[Injera]]<br /> : Origin: Paul Erlich<br /> : Meaning: Named after an Ethiopian flatbread because 26edo represents it well, and the Ethiopian alphabet has 26 consonants.<br /> <br /> ; [[Jamesbond]]<br /> : Named from the fact that, because it shares the 5-limit of 7et and maps 7 to one generator, the wedgie is {{multival| 0 0 7 … }}<br /> <br /> ; [[Keemun]]<br /> : Origin: Herman Miller (2006)<br /> : Meaning: Name of a variety of tea which could fit into the same space as &quot;keenan&quot; and replace it. <br /> : This temperament was discovered by [[Dave Keenan]], so an earlier proposed name was ''keenan''. As he did for the comma now known as the [[Keenanisma #Etymology|''keenanisma'']], Dave Keenan resisted the temperament being named after him, and preferred descriptive names to eponymous ones because they would be more useful. Unfortunately, by the time Dave's preference reached [[Paul Erlich]], Paul had already begun to use the name ''keenan'' in a series of diagrams, and so renaming it to something descriptive such as ''minorthirds'' at this point would require an inordinate amount of reordering busywork. Due to this, the effort to rename the temperament continued, but with the additional constraint that the name could not alter its alphabetical ordering with respect to its nearest neighboring temperaments in Paul's diagrams. The name chosen in the end, ''keemun'', was suggested by [[Herman Miller|Herman &quot;Teamouse&quot; Miller]] as a reference to {{w|Keemun}}, a Chinese black tea with a winey and fruity taste, designated as a China Famous Tea. <br /> : Although this name did not satisfy Dave's request for descriptiveness, it fulfilled the ultimate goal of distinguishing itself from the name ''kleismic'', thereby ending the unfortunate practice of calling this temperament, a 7-limit extension of hanson with a much lower accuracy, by ''kleismic'' also. See the temperament's dedicated page for sources.<br /> <br /> ; [[Mabila]]<br /> : Origin: Gene Ward Smith, Ryan Avella (2011)<br /> : Meaning: Named after mavila temperament due to their similar tunings and scale structure.<br /> <br /> ; [[Machine]]<br /> : Origin: Mike Battaglia (2011)&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_96074.html Yahoo! Tuning Group | ''Ridiculously awesome 6&amp;11 2.3.7.11.13 subgroup temperament'']&lt;/ref&gt;<br /> : Meaning: Because it sounded like a 4:7:9:11 machine.<br /> <br /> ; [[Magic]]<br /> : Origin: Graham Breed<br /> : Meaning: Graham named it ''magic'' by analogy with miracle; he was listening to the Fleetwood Mac song ''You Make Loving Fun'' that uses the word ''miracle'' at the time. Later he coined the backronym ''multiple approximations generated iteratively and consistently'' also by analogy with miracle.<br /> <br /> ; [[Marvel]]<br /> : Origin: Gene Ward Smith (2003)<br /> : Meaning: Marvel was discovered while investigating slendric temperament, which at the time was called ''wonder'', and so ''marvel'' was introduced as an implicit variation on that name; along with miracle, then, there were now three temperaments with names conveying extraordinary goodness, so this began to constitute a temperament naming theme. See the temperament's dedicated page for sources.<br /> <br /> ; [[Mavila]]<br /> : Origin: Erv Wilson (1989)<br /> : Meaning: Named after the Chopi village of Mavila in Mozambique, known for their use near-equal heptatonic scales. Nobody can agree on how to pronounce this word. See the temperament's dedicated page for sources.<br /> <br /> ; [[Meantone]]<br /> : Origin: really really old<br /> : Meaning: Named so because it maps the major whole tone (9/8) and the minor whole tone (10/9) to the same interval, which is near the average of the two tones in ideal tunings.<br /> <br /> ; [[Migration]]<br /> : Meaning: A temperament closely related to mohajira, which means &quot;migrating&quot;.<br /> <br /> ; [[Miracle]]<br /> : Origin: Paul Erlich (May 2001?)<br /> : Double meaning: It is a miracle that this scale is so accurate! And it is an acronym ''Multiple Integer Ratios Approximated Consistently, Linearly and Evenly''.<br /> <br /> ; [[Mohajira]]<br /> : Origin: Jacques Dudon<br /> : Meaning: from Arabic مهاجرة ''muhājirah'' which roughly means &quot;migrating&quot;.<br /> <br /> ; [[Mothra]]<br /> : Origin: Gene Ward Smith<br /> : Meaning: Named after a Japanese fictional monster: a daikaiju name for a temperament with ~8/7 generator. Mothra has defeated Godzilla more times than any other daikaiju; the musical meaning of this fact is at best speculative.<br /> <br /> ; [[Myna]]<br /> : Myna is related to starling, the 126/125 planar temperament, and a myna is a member of the starling family (Sturnidae). Myna is also a play on minor third, the generator.<br /> <br /> ; [[Negri]]<br /> : Origin: Paul Erlich (2001)<br /> : Meaning: Named after John Negri's 10-out-of-19 maximally even scale. See the temperament's dedicated page for sources.<br /> <br /> ; [[Octacot]]<br /> : Meaning: 3/2 is divided into 8 equal parts, therefore ''octa-''.<br /> <br /> ; [[Orgone]]<br /> : Origin: Andrew Heathwaite (2010)<br /> : Meaning: An analogy between Wilhelm Reich's proposal for an invisible, ephemeral creative energy and the subtleties of the higher harmonics 7 and 11. Superkleismic can be viewed as orgone extended to the full 11-limit.<br /> <br /> ; [[Orwell]]<br /> : Origin: Gene Ward Smith (2001)<br /> : Meaning: Named after George Orwell's book 1984, because of the generator of 19\84.<br /> <br /> ; [[Pajara]]<br /> : Origin: Originally (up to 2001) ''paultone'' and then ''twintone'', in analogy with meantone, but Paul Erlich did not like this and suggested pajara, after &quot;Paul, John, and Ara&quot;, the three people jamming at his house at some random point in time.<br /> <br /> ; [[Porcupine]]<br /> : Origin: Herman Miller (1999)<br /> : Meaning: Named after Herman Miller's ''Mizarian Porcupine Overture'' in 15edo.<br /> <br /> ; [[Quadritikleismic]]<br /> : Has a kleismic generator, so that (6/5)&lt;sup&gt;6&lt;/sup&gt; = 3, and four periods per octave, therefore ''quadri-''.<br /> <br /> ; [[Rodan]]<br /> : Origin: Gene Ward Smith<br /> : Meaning: Named after a Japanese fictional monster. A daikaiju name, from the 8/7 generator.<br /> <br /> ; [[Semaphore]]<br /> : Meaning: semi-fourth, i.e. half of a 4/3.<br /> <br /> ; [[Semisept]]<br /> : Meaning: semi-(septimal major sixth), i.e. half of a 12/7.&lt;ref&gt;Evidence for this interpretation can be found here, though the writer does not confirm it: [https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_16972#16979 Yahoo! Tuning Group | ''Complete Rank 2 Temperament Searches'']&lt;/ref&gt;<br /> <br /> ; [[Sensi]]<br /> : Originally ''semisixths'', but after it was decided that ''bi-'' or ''semi-'' should be half for periods and ''hemi-'' should be half for generators, that was contracted to ''sensi''.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_97722.html#97733 ''Temperament names''] &quot;The idea here is to use 'hemi' only when the generator is split in [two], not when the period is split in two.&quot; —Gene Ward Smith&lt;/ref&gt;<br /> : As for ''sensipent'', when Paul released his Middle Path paper, he introduced a naming pattern whereby certain&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_97783.html#98172 Yahoo! Tuning Group | ''A short recording of a semi-improvized 3D comma pump'' - &quot;The 'sept'/'pent' distinction was according to a rule I never agreed with. I think it was that the TOP tunings had to be the same for the name to be the same. Gene [Ward Smith] ignores it. I don't care much either way for established names, but I may have to keep &quot;Sensisept&quot; because it exists in a higher limit. I can see the rule makes some sense if we're talking about temperaments, as I understand them. The existence of the rule may indicate Paul [Erlich] was understanding temperaments [sic] a similar way. But as I understand temperament classes (which is similar to how others understand regular temperaments) the tuning is allowed to vary over a wide range. There are subjective rules I follow when I share names over different limits and we can talk about individual cases if you like. I don't have a fixed definition, or deterministic algorithm, for deciding if two things in different limits are the same, and I don't want one.&quot; —Graham Breed]&lt;/ref&gt; 7-limit extensions to 5-limit temperaments were required to have the same name, except for being suffixed with the numeric prefix ''-sept'' instead of the numeric prefix ''-pent''. This applied to three pairs of temperaments:<br /> :* ''diminished'', which became ''dimipent'' and ''dimisept'',<br /> :* ''sensi'', which became ''sensipent'' and ''sensisept'', and<br /> :* ''negri'', which became ''negripent'' and ''negrisept''.<br /> : This naming system was unpopular,&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10620#10640 Yahoo! Tuning Group | ''Gene's mail server''] - &quot;Anyway, since these names are so ugly, does ''anyone'' have suggestions for renaming them (Dimipent, Dimisept, Negripent, Negrisept, Sensipent, Sensisept) that preserves their approximate alphabetical location?&quot; —Paul Erlich&lt;/ref&gt;&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_12957 Yahoo! Tuning Group | ''98 named 7-limit temperaments''] - Shows that there was some support for the ''-sept'' prefix from Gene Ward Smith still at this time.&lt;/ref&gt; and did not catch on.&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104603#104603 Yahoo! Tuning Group | ''Subgroup temperament naming''] - &quot;The thing we're doing now is analogous to Paul [Erlich]'s having different names for 'negripent' and 'negrisept' and such, which also didn't catch on.&quot; —Mike Battaglia&lt;/ref&gt; In the case of diminished and negri, both the ''-pent'' and ''-sept'' suffixes fell out of use, and the modern convention of giving canonical extensions the exact same name (distinguishing them as necessary with ''septimal'', etc.) was adopted instead, so both the 5-limit and 7-limit were called ''diminished'' and ''negri'', respectively. For sensi, however, it became the name for the 7-limit temperament, while ''sensipent'' stuck as a name for the 5-limit temperament due to the temperaments' significantly higher accuracy. This originally 5-limit-specific name also became the name for its entire temperament family. <br /> <br /> ; [[Slendric]]<br /> : Named after [[slendro]], because a just tuning for slendro may be realized as {{dash|8/7, 8/7, 147/128, 8/7, 7/6}}, with [[1029/1024]] as the difference between [[8/7]] and [[147/128]].&lt;ref&gt;Miller, L. E., &amp; Lieberman, F. (1999). ''Lou Harrison and the American Gamelan''. American Music, 17(2), 146–178. https://doi.org/10.2307/3052712&lt;/ref&gt;<br /> <br /> ; [[Squares]]<br /> : Named from the fact that the wedgie is {{multival| 4 16 9 … }}, which is 2&lt;sup&gt;2&lt;/sup&gt;, 4&lt;sup&gt;2&lt;/sup&gt;, 3&lt;sup&gt;2&lt;/sup&gt;.<br /> <br /> ; [[Starling]]<br /> : Origin: Herman Miller (1999)<br /> : Meaning: Named after Herman Miller's Starling scale. See the temperament's dedicated page for sources. <br /> <br /> ; [[Srutal]]<br /> : A name proposed by Paul Erlich because the 22-tone mos looks a lot like the Indian Shruti scale.<br /> <br /> ; [[Superkleismic]]<br /> : The 6/5 generator is ~322 cents, sharper than the kleismic 6/5, hence ''super-''. Can be restricted to 2.7.11 (orgone) or 2.5/3.7.11 (magicaltet).<br /> <br /> ; [[Superpyth]]<br /> : Meaning: Fifths are sharper than the just ratio of 3/2, hence ''superpythagorean''. <br /> <br /> ; [[Tetracot]]<br /> : Meaning: 3/2 is divided into 4 equal parts, hence ''tetra-''. Not sure why ''-cot'' (see Dicot above).<br /> <br /> ; [[Triforce]]<br /> : Triforce has 3 periods per octave, hence tri-.<br /> <br /> ; [[Tritikleismic]]<br /> : Tritikleismic has a kleismic generator, so that (6/5)&lt;sup&gt;6&lt;/sup&gt; = 3, and 3 periods per octave (therefore tri-.)<br /> <br /> ; [[Valentine]]<br /> : Named for Robert C Valentine.<br /> <br /> ; [[Whitewood]]<br /> : Origin: Mike Battaglia (2010)<br /> : Meaning: Black keys are to Blackwood as white keys are to Whitewood. See the temperament's dedicated page for sources. <br /> <br /> ; [[Würschmidt]]<br /> : Named for physicist José Würschmidt.<br /> <br /> == See also ==<br /> * [[Systematic comma names explained]]<br /> * [[:Category:Commas by name]]<br /> * [[:Category:Temperament naming]]<br /> * [[Glossary]]<br /> * [[Acronyms]]<br /> <br /> == References ==<br /> <br /> [[Category:Temperament naming| ]] &lt;!-- main article --&gt;</div> FloraC https://en.xen.wiki/index.php?title=894edo&diff=232413 894edo 2026-06-18T15:19:12Z <p>FloraC: /* Theory */ correction</p> <hr /> <div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> == Theory ==<br /> 894edo is [[consistent]] to the [[17-odd-limit]], and except for [[19/13]], [[19/17]], [[25/13]], [[25/17]] and their [[octave complement]]s, it is consistent to the [[31-odd-limit]], thus making it a reasonable [[31-limit]] system. Its [[prime interval|primes]] [[5/1|5]], [[17/1|17]], [[19/1|19]], and [[23/1|23]] come from [[149edo]], its [[11/1|11]] from [[298edo]], and its [[7/1|7]] and [[13/1|13]] from [[447edo]]. <br /> <br /> As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]]; 250047/250000 ([[landscape comma]]) in the [[7-limit]]; [[9801/9800]], [[131072/130977]], [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]], 34398/34375 in the [[13-limit]]; [[1156/1155]], [[2431/2430]], [[2601/2600]], [[11016/11011]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[3250/3249]] in the [[19-limit]]; and [[1863/1862]], [[2300/2299]] among others in the [[23-limit]]. <br /> <br /> === Prime harmonics ===<br /> {{Harmonics in equal|894|columns=11}}<br /> {{Harmonics in equal|894|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 894edo (continued)}}<br /> <br /> === Subsets and supersets ===<br /> Since 894 factors into primes as {{nowrap| 2 × 3 × 149 }}, 894edo contains subset edos {{EDOs| 2, 3, 6, 149, 298, and 447 }}.<br /> <br /> == Regular temperament properties ==<br /> {| class=&quot;wikitable center-4 center-5 center-6&quot;<br /> |-<br /> ! rowspan=&quot;2&quot; | [[Subgroup]]<br /> ! rowspan=&quot;2&quot; | [[Comma list]]<br /> ! rowspan=&quot;2&quot; | [[Mapping]]<br /> ! rowspan=&quot;2&quot; | Optimal&lt;br&gt;8ve stretch (¢)<br /> ! colspan=&quot;2&quot; | Tuning error<br /> |-<br /> ! [[TE error|Absolute]] (¢)<br /> ! [[TE simple badness|Relative]] (%)<br /> |-<br /> | 2.3<br /> | {{Monzo| 1417 -894 }}<br /> | {{Mapping| 894 1417 }}<br /> | −0.0184<br /> | 0.0184<br /> | 1.37<br /> |-<br /> | 2.3.5<br /> | {{Monzo| 23 6 -14 }}, {{monzo| 93 -66 5 }}<br /> | {{Mapping| 894 1417 2076 }}<br /> | −0.0501<br /> | 0.0473<br /> | 3.52<br /> |-<br /> | 2.3.5.7<br /> | 250047/250000, 43046721/43025920, 134217728/133984375<br /> | {{Mapping| 894 1417 2076 2510 }}<br /> | −0.0644<br /> | 0.0479<br /> | 3.57<br /> |-<br /> | 2.3.5.7.11<br /> | 9801/9800, 131072/130977, 151263/151250, 1771875/1771561<br /> | {{Mapping| 894 1417 2076 2510 3093 }}<br /> | −0.0724<br /> | 0.0456<br /> | 3.40<br /> |-<br /> | 2.3.5.7.11.13<br /> | 1716/1715, 2080/2079, 4096/4095, 34398/34375, 1574640/1574573<br /> | {{Mapping| 894 1417 2076 2510 3093 3308 }}<br /> | −0.0486<br /> | 0.0675<br /> | 5.03<br /> |-<br /> | 2.3.5.7.11.13.17<br /> | 1156/1155, 1716/1715, 2080/2079, 2431/2430, 4096/4095, 34398/34375<br /> | {{Mapping| 894 1417 2076 2510 3093 3308 3654 }}<br /> | −0.0327<br /> | 0.0737<br /> | 5.49<br /> |-<br /> | 2.3.5.7.11.13.17.19<br /> | 1156/1155, 1521/1520, 1716/1715, 2080/2079, 2376/2375, 2431/2430, 3250/3249<br /> | {{Mapping| 894 1417 2076 2510 3093 3308 3654 3798 }}<br /> | −0.0425<br /> | 0.0737<br /> | 5.49<br /> |-<br /> | 2.3.5.7.11.13.17.19.23<br /> | 1156/1155, 1521/1520, 1716/1715, 1863/1862, 2080/2079, 2376/2375, 2431/2430, 3250/3249<br /> | {{Mapping| 894 1417 2076 2510 3093 3308 3654 3798 4044 }}<br /> | −0.0357<br /> | 0.0721<br /> | 5.37<br /> |}<br /> <br /> === Rank-2 temperaments ===<br /> {| class=&quot;wikitable center-all left-5&quot;<br /> |+ style=&quot;font-size: 105%;&quot; | Table of rank-2 temperaments by generator<br /> |-<br /> ! Periods&lt;br&gt;per 8ve<br /> ! Generator*<br /> ! Cents*<br /> ! Associated&lt;br&gt;ratio*<br /> ! Temperaments<br /> |-<br /> | 2<br /> | 53\894<br /> | 71.14<br /> | 25/24<br /> | [[Vishnu]] (5-limit)<br /> |}<br /> &lt;nowiki/&gt;* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct</div> FloraC https://en.xen.wiki/index.php?title=Tour_of_regular_temperaments&diff=232409 Tour of regular temperaments 2026-06-18T08:19:22Z <p>FloraC: Update</p> <hr /> <div>The following is a tour of many of the [[regular temperament]]s that contributors to this wiki have found notable. It is of course not meant to be comprehensive, and is not the result of a systematic search.<br /> <br /> == Rank-2 temperaments ==<br /> A rank-2 temperament maps all JI intervals within its [[JI subgroup]] to a 2-dimensional lattice. This lattice has two generators. The larger generator is called the period, as the temperament will repeat periodically at that interval. The period is usually the octave, or some unit fraction of the octave. If the period is a full octave, the temperament is said to be a '''linear temperament'''. The smaller generator, referred to as &quot;the&quot; generator, is stacked repeatedly to generate a scale within that period.<br /> <br /> A rank-2 temperament is defined by a period-generator mapping, a set of 2 vals, one val for the period and one for the generator. Each member of the JI subgroup is mapped to a period-generator pair.<br /> <br /> Rank-2 temperaments can be reduced to a related rank-1 temperament by tempering out an additional comma. For example, 5-limit meantone temperament, which is rank-2 (defined by tempering the syntonic comma 81/80 out of 3-dimensional 5-limit JI), can be reduced to 1-dimensional 12-ET by tempering out the Pythagorean comma.<br /> <br /> === Families defined by a 2.3 comma ===<br /> These are families defined by a 3-limit (color name: wa) comma. If only primes 2 and 3 are part of the [[subgroup]], the comma creates a rank-1 temperament, an [[edo]]. But if another prime such as 5 is present, the comma creates a rank-2 temperament. Since edos are discussed elsewhere, this section assumes the presence of at least one additional prime. The rank-2 temperament created consists of multiple &quot;copies&quot; of an edo. The edo copies can be thought of as being offset from one another by a small comma. This small comma is represented in the [[pergen]] by ^1. <br /> <br /> ; [[Limmic temperaments|Blackwood family]] (P8/5, ^1)<br /> : This family tempers out the [[limma]], {{monzo| 8 -5 }} (256/243). It equates 5 fifths with 3 octaves, which creates multiple copies of [[5edo]]. The fifth is ~720¢, quite sharp. The only member of this family is the [[blackwood]] temperament, which is 5-limit. Blackwood's edo copies are offset from one another by 5/4, or alternatively by 81/80. 5/4 is usually tempered sharp, perhaps ~400¢, to match the sharp fifth. Its color name is Sawati. <br /> <br /> ; [[Whitewood family]] (P8/7, ^1)<br /> : This family tempers out the apotome, {{monzo| -11 7 }} (2187/2048). It equates 7 fifths with 4 octaves, which creates multiple copies of [[7edo]]. The fifth is ~685¢, which is very flat. This family includes the [[whitewood]] temperament. Its color name is Lawati. <br /> <br /> ; [[Compton family]] (P8/12, ^1)<br /> : This tempers out the [[Pythagorean comma]], {{monzo| -19 12 }} (531441/524288). It equates 12 fifths with 7 octaves, which creates multiple copies of [[12edo]]. Temperaments in this family include [[compton]] and [[catler]]. In the 5-limit compton temperament, the edo copies are offset from one another by a justly tuned 5/4, or alternatively by a tempered 81/80. Several 12edo instruments slightly detuned from each other provide an easy way to make music with these temperaments. Its color name is Lalawati. <br /> <br /> ; [[Countercomp family]] (P8/41, ^1)<br /> : This family tempers out the [[41-comma|Pythagorean countercomma]], {{monzo| 65 -41 }}, which creates multiple copies of [[41edo]]. Its color name is Wa-41. <br /> <br /> ; [[Mercator family]] (P8/53, ^1)<br /> : This family tempers out the [[Mercator's comma]], {{monzo| -84 53 }}, which creates multiple copies of [[53edo]]. Its color name is Wa-53.<br /> <br /> === Families defined by a 2.3.5 comma ===<br /> These are families defined by a 5-limit (color name: ya) comma. As we go up in rank 2, the various 5-limit temperaments often break up as families of related temperaments, depending on how higher primes are mapped (or equivalently, on which higher limit commas are introduced.) The same comment applies to 7-limit temperaments and rank 3, etc. Members of families and their relationships can be classified by the [[normal lists|normal comma list]] of the various temperaments. Families include weak extensions as well as strong, in other words, the [[pergen]] shown here may change.<br /> <br /> ; [[Meantone family]] (P8, P5) <br /> : The meantone family tempers out [[81/80]], also called the syntonic comma. This comma manifests as the difference between a stack of four 3/2's (81/16, or (3/2)&lt;sup&gt;4&lt;/sup&gt;) and 5/1 harmonic (5/1, or 80/16). It is so named because it splits the major third into two equal sized tones, signifying that 9/8 and 10/9 are equated, with each tone being sized as a mean of the two tones. It has a flattened fifth or sharpened fourth as generator. Some meantone tunings are [[12edo|12-]], [[19edo|19-]], [[31edo|31-]], [[43edo|43-]], [[50edo|50-]], [[55edo|55-]] and [[81edo]]. Aside from tuning meantone as a subset of some equal division of the octave, some common rank-2 tunings include having a generator of 3/2 flattened by 1/3, 2/7, 1/4, 1/5 or 1/6 of the syntonic comma. Its color name is Guti. <br /> <br /> ; [[Schismatic family]] (P8, P5)<br /> : The schismatic family tempers out the schisma of {{monzo| -15 8 1 }} ([[32805/32768]]), which is the amount by which the Pythagorean comma exceeds the syntonic comma. The 5-limit version of the temperament is a [[microtemperament]] which flattens the fifth by a fraction of a schisma, but other members of the family are less accurate. As a 5-limit system, it is far more accurate than meantone but still with manageable complexity; whereas meantone equates four 3/2's with 5/1, schismatic equates eight 4/3's with 10/1, so that the Pythagorean diminished fourth of 8192/6561 is equated with 5/4. Tunings include [[12edo|12-]], [[29edo|29-]], [[41edo|41-]], [[53edo|53-]], and [[118edo]]. Its color name is Layoti. <br /> <br /> ; [[Mavila family]] (P8, P5)<br /> : This tempers out the mavila comma, {{monzo| -7 3 1 }} ([[135/128]]), also known as the major chroma or major limma. These temperaments are notable for having 3/2's tuned so flat that four of them stacked together and octave reduced leads you to 6/5 instead of 5/4, and one consequence of this is that it generates [[2L 5s]] (antidiatonic) scales. 5/4 is equated to 3 fourths minus 1 octave. Septimal mavila and armodue are some of the most notable temperaments associated with the mavila comma. Tunings include [[9edo|9-]], [[16edo|16-]], [[23edo|23-]], and [[25edo]]. Its color name is Layobiti. <br /> <br /> ; [[Father family]] (P8, P5)<br /> : This tempers out [[16/15]], the just diatonic semitone, and equates 5/4 with 4/3. Its color name is Gubiti. <br /> <br /> ; [[Diaschismic family]] (P8/2, P5)<br /> : The diaschismic family tempers out the [[diaschisma]], {{monzo| 11 -4 -2 }} (2048/2025), such that two classic major thirds and a [[81/64|Pythagorean major third]] stack to an octave (i.e. {{nowrap| (5/4)⋅(5/4)⋅(81/64) → 2/1 }}). It has a half-octave period of an approximate 45/32 or 64/45, and its generator is an approximate 3/2. 5/4 is equated to 3 periods minus 2 fifths. The major second ~9/8 is divided in half, with each half equated to ~16/15. Diaschismic tunings include [[12edo|12-]], [[22edo|22-]], [[34edo|34-]], [[46edo|46-]], [[56edo|56-]], [[58edo|58-]] and [[80edo]]. Its color name is Saguguti. An obvious 7-limit interpretation of the period is 7/5, which makes [[pajara]] temperament, where the intervals 50/49 and 64/63 are tempered out. [[22edo]] is an excellent pajara tuning.<br /> <br /> ; [[Bug family]] (P8, P4/2)<br /> : This low-accuracy family of temperaments tempers out [[27/25]], the large limma or bug comma. The generator is an approximate 6/5 or {{nowrap| 10/9 {{=}} ~250{{c}} }}, two of which make ~4/3. 5/4 is equated to 1 octave minus 3 generators. Its color name is Guguti. An obvious 7-limit interpretation of the generator is 7/6~8/7, which leads to semaphore or Zozoti.<br /> <br /> ; [[Immunity family]] (P8, P4/2)<br /> : This tempers out the immunity comma, {{monzo| 16 -13 2 }} (1638400/1594323). Its generator is {{nowrap| ~729/640 {{=}} ~247{{c}} }}, two of which make ~4/3. 5/4 is equated to 3 octaves minus 13 generators. Its color name is Sasa-yoyoti. An obvious 7-limit interpretation of the generator is 7/6~8/7, which leads to semaphore or Zozoti.<br /> <br /> ; [[Dicot family]] (P8, P5/2)<br /> : The dicot family is a low-accuracy family of temperaments which temper out the chromatic semitone, [[25/24]] (the difference between 5/4 and 6/5, or alternatively the difference between two 5/4's and 3/2 or between two 6/5's and 3/2). This temperament hence equates major and minor thirds, evening them out into a neutral-sized third of ~350¢ that is taken to approximate both. [[7edo]] makes for a &quot;good&quot; dicot tuning, although it is questionable whether this temperament bears any actual resemblance to 5-limit harmony. Two of the neutral dicot thirds span a 3/2. Tunings include 7edo, [[10edo]], and [[17edo]]. Its color name is Yoyoti. An obvious 2.3.11 interpretation of the generator is ~11/9, which leads to neutral or Luluti.<br /> <br /> ; [[Augmented family]] (P8/3, P5)<br /> : The augmented family tempers out the diesis of {{monzo| 7 0 -3 }} ([[128/125]]), the difference between three 5/4 major thirds and a 2/1 octave, and so identifies the major third with the third-octave. Hence it has the same 400-cent 5/4-approximations as [[12edo]], which is an excellent tuning for augmented. It is the temperament that results in what is commonly called the &quot;augmented scale&quot; ([[3L 3s]]) in common 12edo-based music theory, as well as what is commonly called &quot;[http://www.tcherepnin.com/alex/basic_elem1.htm#9step Tcherepnin's scale]&quot; ([[3L 6s]]). Its color name is Triguti. <br /> <br /> ; [[Misty family]] (P8/3, P5)<br /> : The misty family tempers out the [[misty comma]] of {{monzo| 26 -12 -3 }}, the difference between the [[Pythagorean comma]] and a stack of three [[schisma]]s. The period is ~512/405 and the generator is ~3/2 (or alternatively ~135/128). 5/4 is equated to 8 periods minus 4 fifths, thus 5/4 is split into 4 equal parts, each 2 periods minus a fifth. Its color name is Sasa-triguti. <br /> <br /> ; [[Porcupine family]] (P8, P4/3)<br /> : The porcupine family tempers out {{monzo| 1 -5 3 }} ([[250/243]]), the difference between three 10/9's (1000/729) and 4/3, known as the maximal diesis or porcupine comma. It subdivides the fourth into three equal parts, each taken as an approximated 10/9, of which two approximate 6/5. It also manifests itself as the difference between three 6/5's and 16/9, as the difference between 10/9 and 27/25, and as the difference between 81/80 and 25/24. 5/4 is equated to 1 octave minus 5 generators. Some porcupine temperaments include [[15edo|15-]], [[22edo|22-]], [[37edo|37-]], and [[59edo]]. Its color name is Triyoti. An important 7-limit extension also tempers out 64/63.<br /> <br /> ; [[Alphatricot family]] (P8, P11/3)<br /> : The alphatricot family tempers out the [[alphatricot comma]], {{monzo| 39 -29 3 }}. The generator is {{nowrap| ~59049/40960 ({{monzo| -13 10 -1 }}) {{=}} 633{{c}} }}, or its octave inverse {{nowrap| ~81920/59049 {{=}} 567{{c}} }}. Three of the former generators equals the third harmonic, ~3/1. 5/4 is equated to 29 of these generators octave-reduced. Its color name is Quadsa-triyoti. An obvious 7-limit interpretation of the generator is {{nowrap| 81/56 {{=}} 639{{c}} }}, a much simpler ratio which leads to the [[Tour of Regular Temperaments #Latriruti clan (P8, P11/3)|Latriruti clan]]. An obvious 13-limit interpretation is {{nowrap| 13/9 {{=}} 637¢ }}, an even simpler ratio implying the [[Tour of Regular Temperaments #Satrithoti clan (P8, P11/3)|Satrithoti clan]].<br /> <br /> ; [[Diminished family]] (P8/4, P5)<br /> : The diminished family tempers out the major diesis or diminished comma, {{monzo| 3 4 -4 }} or [[648/625]], the amount by which four 6/5 minor thirds exceed an octave, and so identifies the minor third with the quarter-octave. Hence it has the same 300-cent 6/5-approximations as [[12edo]]. 5/4 is equated to 1 fifth minus 1 period. Its color name is Quadguti. <br /> <br /> ; [[Undim family]] (P8/4, P5)<br /> : The undim family tempers out the [[undim comma]] of {{monzo| 41 -20 -4 }}, the difference between the Pythagorean comma and a stack of four schismas. Its color name is Trisa-quadguti. <br /> <br /> ; Negri family (P8, P4/4) <br /> : This tempers out the [[negri comma]], {{monzo| -14 3 4 }}. Its only member so far is [[negri]]. Its generator is ~16/15, four of which make ~4/3. 5/4 is equated to 3 generators. Its color name is Laquadyoti. <br /> <br /> ; [[Tetracot family]] (P8, P5/4)<br /> : The tetracot family is a much higher accuracy affair than the dicot family. Instead of taking two neutral thirds to reach 3/2, it takes four minor (10/9) whole tones. Four of these exceed 3/2 by {{monzo| 5 -9 4 }} (20000/19683), the minimal diesis or [[tetracot comma]]. 5/4 is equated to 9 generators minus an octave. [[7edo]] can also be considered a tetracot tuning, as can [[20edo]], [[27edo]], [[34edo]], and [[41edo]]. Its color name is Saquadyoti. <br /> <br /> ; [[Smate family]] (P8, P11/4)<br /> : This tempers out the [[symbolic comma]], {{monzo| 11 -1 -4 }} (2048/1875). Its generator is {{nowrap| ~5/4 {{=}} ~421{{c}} }}, four of which make ~8/3. Its color name is Saquadguti. <br /> <br /> ; [[Vulture family]] (P8, P12/4)<br /> : This tempers out the [[vulture comma]], {{monzo| 24 -21 4 }}. Its generator is {{nowrap| ~320/243 {{=}} ~475{{c}} }}, four of which make ~3/1. 5/4 is equated to 21 generators minus 8 octaves. Its color name is Sasa-quadyoti. An obvious 7-limit interpretation of the generator is 21/16, which makes buzzard or Saquadruti.<br /> <br /> ; [[Quintile family]] (P8/5, P5)<br /> : This tempers out the [[quintile comma]], 847288609443/838860800000 ({{monzo| -28 25 -5 }}). The period is ~59049/51200, and 5 periods make an octave. The generator is a fifth, or equivalently, 3/5 of an octave minus a fifth. This alternate generator is only about 18{{c}}, thus the scales have a very lopsided L/s ratio. 5/4 is equated to 2/5 of an octave minus 5 of these 18{{c}} generators. Its color name is Trila-quinguti. An obvious 7-limit interpretation of the generator is 8/7, which leads to Laquinzoti.<br /> <br /> ; [[Ripple family]] (P8, P4/5)<br /> : This tempers out the [[ripple comma]], 6561/6250 ({{monzo| -1 8 -5 }}), which equates a stack of four [[10/9]]'s with [[8/5]], and five of them with [[16/9]]. The generator is [[27/25]], two of which equals 10/9, three of which equals [[6/5]], and five of which equals [[4/3]]. 5/4 is equated to an octave minus 8 generators. As one might expect, [[12edo]] is about as accurate as it can be. Its color name is Quinguti. <br /> <br /> ; [[Passion family]] (P8, P4/5)<br /> : This tempers out the [[passion comma]], 262144/253125 ({{monzo| 18 -4 -5 }}), which equates a stack of four [[16/15]]'s with [[5/4]], and five of them with [[4/3]]. Its color name is Saquinguti. <br /> <br /> ; [[Quintaleap family]] (P8, P4/5)<br /> : This tempers out the [[quintaleap comma]], {{monzo| 37 -16 -5 }}. The generator is ~135/128, five of them gives ~4/3, and sixteen of them gives [[5/2]]. Its color name is Trisa-quinguti. An obvious 17-limit interpretation of the generator is ~18/17, which makes Saquinsoti.<br /> <br /> ; [[Quindromeda family]] (P8, P4/5)<br /> : This tempers out the [[quindromeda comma]], {{monzo| 56 -28 -5 }}. The generator is ~4428675/4194304, five of them gives ~4/3, and 28 of them gives the fifth harmonic, [[5/1]]. Its color name is Quinsa-quinguti. An obvious 17-limit interpretation of the generator is ~18/17, which makes Saquinsoti.<br /> <br /> ; [[Amity family]] (P8, P11/5)<br /> : This tempers out the [[amity comma]], 1600000/1594323 ({{monzo| 9 -13 5 }}). The generator is {{nowrap| 243/200 {{=}} ~339.5{{c}} }}, five of which make ~8/3. 5/4 is equated to 4 octaves minus 13 generators, or 2 fifths minus 3 generators. Its color name is Saquinyoti. An obvious 11-limit interpretation of the generator is 11/9, which makes Saquinloti. An obvious 13-limit interpretation of the generator is 39/32, which makes Lala-quinthoti.<br /> <br /> ; [[Magic family]] (P8, P12/5)<br /> : The magic family tempers out {{monzo| -10 -1 5 }} (3125/3072), known as the [[magic comma]] or small diesis, which is the difference between five 5/4's (3125/2048) and a 3/1. The generator is itself an approximate 5/4. The magic family includes [[16edo|16-]], [[19edo|19-]], [[22edo|22-]], [[25edo|25-]], and [[41edo]] among its possible tunings, with the last being near-optimal. Its color name is Laquinyoti. <br /> <br /> ; [[Fifive family]] (P8/2, P5/5)<br /> : This tempers out the [[fifive comma]], {{monzo| -1 -14 10 }} (9765625/9565938). The period is ~4374/3125 ({{monzo| 1 7 -5 }}), two of which make an octave. The generator is ~27/25, five of which make ~3/2. 5/4 is equated to 7 generators minus 1 period. Its color name is Saquinbiyoti. <br /> <br /> ; [[Quintosec family]] (P8/5, P5/2)<br /> : This tempers out the [[quintosec comma]], 140737488355328/140126044921875 ({{monzo| 47 -15 -10 }}). The period is ~524288/455625 ({{monzo| 19 -6 -4 }}), five of which equals an octave. The generator is ~16/15. A period plus a generator makes half a fifth. 5/4 is equated to 3 periods minus 3 generators. Its color name is Quadsa-quinbiguti. An obvious 7-limit interpretation of the period is 8/7. <br /> <br /> ; [[Trisedodge family]] (P8/5, P4/3)<br /> : This tempers out the [[trisedodge comma]], 30958682112/30517578125 ({{monzo| 19 10 -15 }}). The period is {{nowrap| ~144/125 {{=}} 240{{c}} }}. The generator is ~6/5. Six periods minus three generators equals ~4/3. 5/4 is equated to 2 generators minus 1 period. Its color name is Saquintriguti. An obvious 7-limit interpretation of the period is 8/7. <br /> <br /> ; Ampersand family (P8, P5/6) <br /> : This tempers out the [[ampersand comma]], 34171875/33554432 ({{monzo| -25 7 6 }}). Its only member is [[ampersand]]. The generator is ~16/15, of which six make ~3/2. 5/4 is equated to 1 octave minus 7 generators. Its color name is Lala-tribiyoti. If the generator is also equated to ~15/14, and three generators to ~11/9, one gets the [[miracle]] temperament.<br /> <br /> ; [[Kleismic family]] (P8, P12/6)<br /> : The kleismic family of temperaments tempers out the [[15625/15552|kleisma]], 15625/15552 ({{monzo| -6 -5 6 }}), which is the difference between six 6/5's and 3/1. It takes a slightly sharpened minor third as a generator, optimally tuned about 1.4 cents sharp. 5/4 is equated to 5 generators minus 1 octave. The kleismic family includes [[15edo|15-]], [[19edo|19-]], [[34edo|34-]], [[49edo|49-]], [[53edo|53-]], [[72edo|72-]], [[87edo|87-]] and [[140edo]] among its possible tunings. Its color name is Tribiyoti. <br /> <br /> ; [[Semicomma family|Orson or semicomma family]] (P8, P12/7)<br /> : The [[semicomma]] (also known as Fokker's comma), 2109375/2097152 ({{monzo| -21 3 7 }}), is tempered out by the members of the semicomma family. Its generator is ~75/64, seven of which equals ~3/1. 5/4 is equated to 1 octave minus 3 generators. Its color name is Lasepyoti. Its generator has a natural interpretation as ~7/6, leading to the [[orwell|orwell or Sepruti]] temperament.<br /> <br /> ; [[Wesley family]] (P8, ccP4/7)<br /> : This tempers out the [[wesley comma]], 78125/73728 ({{monzo| -13 -2 7 }}). The generator is {{nowrap| ~125/96 {{=}} ~412{{c}} }}. Seven generators equals a double-compound fourth of ~16/3. 5/4 is equated to 1 octave minus 2 generators. Its color name is Lasepyobiti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Lasepruti temperament. An obvious 3-limit interpretation of the generator is 81/64, implying [[29edo]]. <br /> <br /> ; [[Sensipent family]] (P8, ccP5/7)<br /> : The sensipent family tempers out the [[sensipent comma]], 78732/78125 ({{monzo| 2 9 -7 }}), also known as the medium semicomma. Its generator is {{nowrap| ~162/125 {{=}} ~443{{c}} }}. Seven generators equals a double-compound fifth of ~6/1. 5/4 is equated to 9 generators minus 3 octaves. Tunings include [[8edo]], [[19edo]], [[46edo]], and [[65edo]]. Its color name is Sepguti. An obvious 7-limit interpretation of the generator is 9/7, leading to the Sasepzoti temperament. <br /> <br /> ; [[Vishnu family]] (P8/2, P4/7)<br /> : This tempers out the [[vishnu comma]], {{monzo| 23 6 -14 }}, or the amount by which seven chromatic semitones (25/24) fall short of a perfect fourth (4/3), or (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;. The period is ~{{monzo| -11 -3 7 }} and the generator is ~25/24. 5/4 is equated to 1 period minus 3 generators. Its color name is Sasepbiguti. <br /> <br /> ; [[Unicorn family]] (P8, P4/8)<br /> : This tempers out the [[unicorn comma]], 1594323/1562500 ({{monzo| -2 13 -8 }}). The generator is {{nowrap| ~250/243 {{=}} ~62{{c}} }} and eight of them equal ~4/3. Its color name is Laquadbiguti. <br /> <br /> ; [[Würschmidt family]] (P8, ccP5/8)<br /> : The würschmidt family tempers out the [[würschmidt comma]], 393216/390625 ({{monzo| 17 1 -8 }}). Würschmidt itself has a generator of a major third, eight of which give a 6/1 (the 6th harmonic, or a double-compound perfect fifth); that is, {{nowrap| (5/4)&lt;sup&gt;8&lt;/sup&gt;⋅(393216/390625) {{=}} 6 }}. It tends to generate the same mos scales as the [[magic]] temperament, but is tuned slightly more accurately. Both [[31edo]] and [[34edo]] can be used as würschmidt tunings, as can [[65edo]], which is quite accurate. Its color name is Saquadbiguti. <br /> <br /> ; [[Escapade family]] (P8, P4/9)<br /> : This tempers out the [[escapade comma]], {{monzo| 32 -7 -9 }}, which is the difference between nine just major thirds and seven just fourths. The generator is {{monzo| -14 3 4 }} of ~55{{c}} and nine of them equal ~4/3. Seven of them equal ~5/4, thus two of them equal ~16/15. Its color name is Sasa-tritriguti. An obvious 11-limit interpretation of the generator is 33/32, leading to the Trisa-tritriluti temperament. <br /> <br /> ; [[Mabila family]] (P8, c4P4/10)<br /> : The mabila family tempers out the [[mabila comma]], {{monzo| 28 -3 -10 }} (268435456/263671875). The generator is {{nowrap| ~512/375 {{=}} ~530{{c}} }}, three generators equals ~5/2 and ten of them equals a quadruple-compound fourth of ~64/3. Its color name is Sasa-quinbiguti. An obvious 11-limit interpretation of the generator is ~15/11.<br /> <br /> ; [[Sycamore family]] (P8, P5/11)<br /> : The sycamore family tempers out the [[sycamore comma]], {{monzo| -16 -6 11 }} (48828125/47775744), which is the amount by which five stacked chromatic semitones, 25/24, exceed 6/5, and hence also the amount six exceeds 5/4. Eleven of these generators equals ~3/2. Its color name is Laleyoti. <br /> <br /> ; [[Quartonic family]] (P8, P4/11)<br /> : The quartonic family tempers out the [[quartonic comma]], {{monzo| 3 -18 11 }} (390625000/387420489). The generator is {{nowrap| ~250/243 {{=}} ~45{{c}} }}, seven generators equals ~6/5, and eleven generators equals ~4/3. Its color name is Saleyoti. An obvious 7-limit interpretation of the generator is ~36/35.<br /> <br /> ; [[Lafa family]] (P8, P12/12)<br /> : This tempers out the [[lafa comma]], {{monzo| 77 -31 -12 }}. The generator is {{nowrap| ~4982259375/4294967296 {{=}} ~258.6{{c}} }}. Twelve generators equals a twelfth (~3/1). 5/4 is equated to 7 octaves minus 31 generators. Its color name is Tribisa-quadtriguti. <br /> <br /> ; [[Ditonmic family]] (P8, c4P4/13)<br /> : This tempers out the [[ditonma]], {{monzo| -27 -2 13 }} (1220703125/1207959552). Thirteen ~{{monzo| -12 -1 6 }} generators of about 407{{c}} equals a quadruple-compound fourth. 5/4 is equated to 1 octave minus 2 generators. An obvious 3-limit interpretation of the generator is 81/64, which implies 53edo, which is a good tuning for this high-accuracy family of temperaments. Its color name is Lala-theyoti. <br /> <br /> ; [[Luna family]] (P8, ccP4/15)<br /> : This tempers out the [[luna comma]], {{monzo| 38 -2 -15 }} (274877906944/274658203125). The generator is ~{{monzo| 18 -1 -7 }} at ~193{{c}}. Two generators equals ~5/4, and fifteen generators equals a double-compound fourth of ~16/3. Its color name is Sasa-quintriguti. <br /> <br /> ; [[Vavoom family]] (P8, P12/17)<br /> : This tempers out the [[vavoom comma]], {{monzo| -68 18 17 }}. The generator is {{nowrap| ~16/15 {{=}} ~111.9{{c}} }}. Seventeen generators equals a twelfth (~3/1). 5/4 is equated to two octaves minus 18 generators. Its color name is Quinla-seyoti. <br /> <br /> ; [[Minortone family]] (P8, ccP5/17)<br /> : This tempers out the [[minortone comma]], {{monzo| -16 35 -17 }}. The head of the family is minortone, with a generator of a minor tone (~10/9). Seventeen generators equals a double-compound fifth (~6/1). 5/4 is equated to 35 generators minus 5 octaves. Its color name is Trila-seguti. <br /> <br /> ; [[Maja family]] (P8, c&lt;sup&gt;6&lt;/sup&gt;P4/17)<br /> : This tempers out the [[maja comma]], {{monzo| -3 -23 17 }} (762939453125/753145430616). The generator is {{nowrap| ~162/125 {{=}} ~453{{c}} }}. Seventeen generators equals a sextuple-compound fourth. 5/4 is equated to 9 octaves minus 23 generators. Its color name is Saseyoti. <br /> <br /> ; [[Maquila family]] (P8, c&lt;sup&gt;7&lt;/sup&gt;P5/17)<br /> : This tempers out the [[maquila comma]], {{monzo| 49 -6 -17 }} (562949953421312/556182861328125). The generator is {{nowrap| ~512/375 {{=}} ~535{{c}} }}. Seventeen generators equals a septuple-compound fifth. 5/4 is equated to 3 octaves minus 6 generators. Its color name is Trisa-seguti. An obvious 11-limit interpretation of the generator is 11/8, leading to the Lala-seloti temperament. However, Lala-seloti is not nearly as accurate as Trisa-seguti.<br /> <br /> ; [[Gammic family]] (P8, P5/20)<br /> : The gammic family tempers out the [[gammic comma]], {{monzo| -29 -11 20 }}. Nine generators of about 35{{c}} equals ~6/5, eleven equals ~5/4 and twenty equals ~3/2. 34edo is an obvious tuning. The head of the family is 5-limit gammic, whose generator chain is [[Carlos Gamma]]. Another member is the [[neptune]] temperament. Its color name is Laquinquadyoti. <br /> <br /> === Clans defined by a 2.3.7 comma ===<br /> These are defined by a no-5's 7-limit (color name: za) comma. See also [[subgroup temperaments]].<br /> <br /> If a 5-limit comma defines a family of rank-2 temperaments, then we might say a comma belonging to another [[subgroup]] of the 7-limit can define a clan. In particular we might say a triprime comma (one with exactly three primes in the factorization) can define a clan. We can modify the definition of [[normal lists|normal comma list]] for clans by changing the ordering of prime numbers, and using this to sort out clan relationships.<br /> <br /> ; [[Archytas clan]] (P8, P5)<br /> : This clan tempers out Archytas' comma, [[64/63]]. It equates 7/4 with 16/9. The clan consists of rank-2 temperaments, and should not be confused with the [[archytas family]] of rank-3 temperaments. Its color name is Ruti. Its best downward extension is [[superpyth]].<br /> <br /> ; [[Trienstonic clan]] (P8, P5)<br /> : This clan tempers out the septimal third-tone, [[28/27]], a low-accuracy temperament that equates 7/6 with 9/8, and 7/4 with 27/16. Its color name is Zoti. <br /> <br /> ; Harrison clan (P8, P5)<br /> : This clan tempers out [[Harrison's comma]], {{monzo| -13 10 0 -1 }} (59049/57344). It equates 7/4 to an augmented sixth. Its color name is Laruti. Its best downward extension is [[septimal meantone]]. <br /> <br /> ; [[Garischismic clan]] (P8, P5)<br /> : This clan tempers out the [[garischisma]], {{monzo| 25 -14 0 -1 }} (33554432/33480783). It equates 8/7 to two apotomes ({{monzo| -11 7 }}, 2187/2048) and 7/4 to a double-diminished octave {{monzo| 23 -14 }}. This clan includes [[vulture family #Vulture|vulture]], [[breedsmic temperaments #Newt|newt]], [[schismatic family #Garibaldi|garibaldi]], [[landscape microtemperaments #Sextile|sextile]], and [[canousmic temperaments #Satin|satin]]. Its color name is Sasaruti. <br /> <br /> ; Sasazoti clan (P8, P5)<br /> : This clan tempers out the [[leapfrog comma]], {{monzo| 21 -15 0 1 }} (14680064/14348907). It equates 7/6 to two apotomes and 7/4 to double augmented fifth. This clan includes [[aberschismic temperaments #Leapday|leapday]], [[sensamagic clan #Leapweek|leapweek]] and [[diaschismic family #Srutal|srutal]]. <br /> <br /> ; Laruruti clan (P8/2, P5)<br /> : This clan tempers out the Laruru comma, {{monzo| -7 8 0 -2 }} (6561/6272). Two ~81/56 periods equal an octave. The generator is ~3/2, and four generators minus three periods equals ~7/4. The major second ~9/8 is divided in half, with each half equated to ~28/27. See also the Diaschismic or Saguguti temperament and the Jubilismic or Biruyoti temperament.<br /> <br /> ; [[Semaphoresmic clan]] (P8, P4/2)<br /> : This clan tempers out the large septimal diesis, [[49/48]]. Its generator is ~8/7 or ~7/6. Its color name is Zozoti. Its best downward extension is [[godzilla]]. See also [[semaphore]]. <br /> <br /> ; Parahemif clan (P8, P5/2)<br /> : This clan tempers out the [[parahemif comma]], {{monzo| 15 -13 0 2 }} (1605632/1594323), and includes the [[hemif]] temperament and its strong extension [[hemififths]]. 7/4 is equated to 13 generators minus 3 octaves. Its color name is Sasa-zozoti. An obvious 11-limit interpretation of the ~351{{c}} generator is 11/9, leading to the Luluti temperament.<br /> <br /> ; Triruti clan (P8/3, P5)<br /> : This clan tempers out the Triru comma, {{monzo| -1 6 0 -3 }} (729/686), a low-accuracy temperament. Three ~9/7 periods equals an octave. The generator is ~3/2, and two generators minus a period equals ~7/4. An obvious 5-limit interpretation of the ~400{{c}} period is 5/4, leading to the [[augmented (temperament)|augmented]] temperament.<br /> <br /> ; [[Gamelismic clan]] (P8, P5/3)<br /> : This clan tempers out the [[gamelisma]], {{monzo| -10 1 0 3 }} (1029/1024). Three ~8/7 generators equals a fifth. 7/4 is equated to an octave minus a generator. Five generators is slightly flat of 2/1, making this a [[cluster temperament]]. Its color name is Latrizoti. See also Sawati and Lasepzoti.<br /> : A particularly noteworthy member of the gamelismic clan is miracle, but other members include valentine, unidec, mothra, rodan, and hemithirds. Miracle divides the fifth into 6 equal steps, thus it is a weak extension. Its 21-note scale called Blackjack and 31-note scale called Canasta have some useful properties. It is the most efficient 11-limit temperament for many purposes, with a tuning close to 72edo.<br /> <br /> ; Trizoti clan (P8, P5/3)<br /> : This clan tempers out the Trizo comma, {{monzo| -2 -4 0 3 }} (343/324), a low-accuracy temperament. Three ~7/6 generators equals a fifth, and four equal ~7/4. An obvious interpretation of the ~234{{c}} generator is 8/7, leading to the much more accurate gamelismic or Latrizoti temperament.<br /> <br /> ; Latriru clan (P8, P11/3)<br /> : This clan tempers out the [[lee comma]], {{monzo| -9 11 0 -3 }} (177147/175616). The generator is {{nowrap| ~112/81 {{=}} ~566{{c}} }}, and three such generators equals ~8/3. 7/4 is equated to 11 generators minus 5 octaves. Its color name is Latriruti. An obvious full 7-limit interpretation of the generator is 7/5, leading to the [[liese]] temperament, which is a weak extension of meantone.<br /> <br /> ; [[Stearnsmic clan]] (P8/2, P4/3)<br /> : This clan temper out the [[stearnsma]], {{monzo| 1 10 0 -6 }} (118098/117649). The period is {{nowrap| ~486/343 {{=}} ~600{{c}} }}. The generator is {{nowrap| ~9/7 {{=}} ~434{{c}} }}, or alternatively one period minus ~9/7, which equals {{nowrap| ~54/49 {{=}} ~166{{c}} }}. Three of these alternate generators equal ~4/3. 7/4 is equated to five ~9/7 generators minus an octave. Its color name is Latribiruti. Equating the ~54/49 generator to ~10/9 creates a weak extension of the [[porcupine]] temperament, as does equating the period to ~7/5.<br /> <br /> ; Skwaresmic clan (P8, P11/4)<br /> : This clan tempers out the [[skwaresma]], {{monzo| -3 9 0 -4 }} (19683/19208). its generator is ~9/7. Four generators equals ~8/3. 7/4 is equated to 4 octaves minus 9 generators. Its color name is Laquadruti. This clan includes as a strong extension the [[squares]] temperament, which is a weak extension of meantone. <br /> <br /> ; [[Buzzardsmic clan]] (P8, P12/4)<br /> : This clan tempers out the [[buzzardsma]], {{monzo| 16 -3 0 -4 }} (65536/64827). Its generator is ~21/16. Four generators makes ~3/1. 7/4 is equated to 2 octaves minus 3 generators. Its color name is Saquadruti. This clan includes as a strong extension the [[Vulture family #Septimal vulture|vulture]] temperament, which is in the vulture family. <br /> <br /> ; [[Cloudy clan]] (P8/5, P5)<br /> : This clan tempers out the [[cloudy comma]], {{monzo| -14 0 0 5 }} (16807/16384). It has a period of 1/5 octave, which represents ~8/7. The generator is ~3/2. Unlike the blackwood or Sawati family, ~3/2 is not equated with three-fifths of an octave, resulting in very small intervals. Its color name is Laquinzoti. <br /> <br /> ; Quinruti clan (P8, P5/5)<br /> : This clan tempers out the [[bleu comma]], {{monzo| 3 7 0 -5 }} (17496/16807). The ~54/49 generator is about 139{{c}}. Two of them equal ~7/6, three equal ~9/7, five equal ~3/2, and seven equal ~7/4. <br /> <br /> ; [[Septimagic clan]] (P8, P12/5)<br /> : This clan tempers out the [[septimagic comma]], {{monzo| 5 -12 0 5 }} (537824/531441). Its generator is {{nowrap| ~243/196 {{=}} ~380{{c}} }}. Five generators makes ~3/1. 7/4 is equated to 12 generators minus 3 octaves. An obvious 5-limit interpretation of the generator is 5/4, leading to the [[magic]] temperament, which is in the magic family. Its color name is Saquinzoti. <br /> <br /> ; Lasepzoti clan (P8, P11/7)<br /> : This clan tempers out the Lasepzo comma {{monzo| -18 -1 0 7 }} (823543/786432). Its generator is ~8/7. Six generators equals ~7/3, and seven generators equals ~8/3. Three generators is ~30{{c}} sharp of 3/2, and five generators is ~15{{c}} sharp of 2/1, making this a [[cluster temperament]]. See also Sawati and Latrizoti.<br /> <br /> ; Septiness clan (P8, P11/7)<br /> : This clan tempers out the [[septiness comma]] {{monzo| 26 -4 0 -7 }} (67108864/66706983). Its generator is ~147/128, four of them gives ~7/4, and seven of them gives ~8/3. Five generators is ~12.5¢ sharp of 2/1, making this a [[cluster temperament]]. Its color name is Sasasepruti. <br /> <br /> ; Sepruti clan (P8, P12/7)<br /> : This clan tempers out the Sepru comma, {{monzo| 7 8 0 -7 }} (839808/823543). Its generator is ~7/6. Seven generators equals ~3/1. 7/4 is equated to 8 generators minus 1 octave. This clan includes as a strong extension the [[orwell]] temperament, which is in the semicomma family.<br /> <br /> ; [[Septiennealimmal clan]] (P8/9, P5)<br /> : This clan tempers out the [[septimal ennealimma|septiennealimma]], {{monzo| -11 -9 0 9 }} (40353607/40310784). It has a period of 1/9 octave, which represents ~7/6. The generator is ~3/2. This clan includes a number of regular temperaments including [[enneaportent]], [[ennealimmal]], and [[novemkleismic]]. Its color name is Tritrizoti.<br /> <br /> === Clans defined by a 2.3.11 comma ===<br /> Color name: ila. See also [[subgroup temperaments]].<br /> <br /> ; Lulubiti clan (P8/2, P5) <br /> : This low-accuracy 2.3.11 clan tempers out the Alpharabian limma, [[128/121]]. Both 11/8 and 16/11 are equated to half-octave period. This clan includes as a strong extension the pajaric temperament, which is in the diaschismic family.<br /> <br /> ; [[Rastmic clan]] (P8, P5/2) <br /> : This 2.3.11 clan tempers out [[243/242]] ({{monzo| -1 5 0 0 -2 }}). Its generator is ~11/9. Two generators equals ~3/2. 11/8 is equated to 5 generators minus an octave. This clan includes as a strong extension the [[dicot]] temperament, which is in the dicot family. Its color name is Luluti. <br /> <br /> ; [[Nexus clan]] (P8/3, P4/2)<br /> : This 2.3.11 clan tempers out the [[nexus comma]] {{monzo| -16 -3 0 0 6 }}. Its 1/3-octave period is ~121/96 and its least-cents generator is ~12/11. A period plus a generator equals ~11/8. Six of these generators equals ~27/16. A period minus a generator equals ~1331/1152 or ~1536/1331. Two of these alternative generators equals ~4/3. Its color name is Tribiloti. <br /> <br /> ; Alphaxenic clan (P8/2, M2/4) <br /> : This 2.3.11 clan tempers out the [[Alpharabian comma]] {{monzo| -17 2 0 0 4 }}. Its half-octave period is ~363/256, and its generator is ~33/32. Four generators equals ~9/8. 3/2 is equated to a period plus 2 generators, and 11/8 is equated to a period minus a generator. This clan includes a strong extension to the comic or Saquadyobiti temperament, which is in the jubilismic clan. Its color name is Laquadloti. <br /> <br /> === Clans defined by a 2.3.13 comma ===<br /> Color name: tha. See also [[subgroup temperaments]].<br /> <br /> ; Thuthuti clan (P8, P5/2) <br /> : This 2.3.13 clan tempers out [[512/507]] ({{monzo| 9 -1 0 0 0 -2 }}). Its generator is ~16/13. Two generators equals ~3/2. 13/8 is equated to 1 octave minus 1 generator. This clan includes as a strong extension the [[dicot]] temperament, which is in the dicot family.<br /> <br /> ; Satrithoti clan (P8, P11/3) <br /> : This 2.3.13 clan tempers out the threedie, [[2197/2187]] ({{monzo| 0 -7 0 0 0 3 }}). Its generator is ~18/13, and three generators equals ~8/3. 13/8 is equated to 7 generators minus three octaves. This clan is related to the Latriruti clan.<br /> <br /> === Clans defined by a 2.5.7 comma ===<br /> These are defined by a no-3's 7-limit (color name: yaza nowa) comma. See also [[subgroup temperaments]]. The pergen's multigen (the second term, omitting any fraction) is always a no-3's 5-limit ratio such as 5/4, 8/5, 25/8, etc.<br /> <br /> ; [[Jubilismic clan]] (P8/2, M3)<br /> : This clan tempers out the jubilisma, [[50/49]], which is the difference between 10/7 and 7/5. The generator is the classical major third (~5/4). The half-octave period is ~7/5 or ~10/7. 7/4 is equated to 1 period plus 1 generator. Its color name is Biruyoti. <br /> <br /> ; [[Bapbo clan]] (P8, M3/2) <br /> : This clan tempers out the bapbo comma, [[256/245]]. The genarator is {{nowrap| ~8/7 {{=}} ~202{{c}} }} and two of them equals ~5/4. Its color name is Ruruguti Nowa. <br /> <br /> ; [[Hemimean clan]] (P8, M3/2)<br /> : This clan tempers out the [[hemimean comma]], {{monzo| 6 0 -5 2 }} (3136/3125). The generator is {{nowrap| ~28/25 {{=}} ~194{{c}} }}. Two generators equals the classical major third (~5/4), three of them equals ~7/5, and five of them equals ~7/4. Its color name is Zozoquinguti Nowa. <br /> <br /> ; Mabilismic clan (P8, cM3/3)<br /> : This clan tempers out the [[mabilisma]], {{monzo| -20 0 5 3 }} (1071875/1048576). The generator is {{nowrap| ~175/128 {{=}} ~527{{c}} }}. Three generators equals ~5/2 and five of them equals ~32/7. Its color name is Latrizo-aquiniyoti Nowa. <br /> <br /> ; Vorwell clan (P8, m6/3)<br /> : This clan tempers out the [[vorwell comma]] (named for being tempered in [[septimal vulture]] and [[orwell]]), {{monzo| 27 0 -8 -3 }} (134217728/133984375). The generator is {{nowrap| ~1024/875 {{=}} ~272{{c}} }}. Three generators equals ~8/5 and eight of them equals ~7/2. Its color name is Sasatriru-aquadbiguti Nowa. <br /> <br /> ; Rainy clan (P8, M3/5)<br /> : This clan tempers out the [[rainy comma]], {{monzo| -21 0 3 5 }} (2100875/2097152). The generator is {{nowrap| ~256/245 {{=}} ~77{{c}} }}. Three generators equals ~8/7 and five of them equals the classic major third (~5/4). Its color name is Quinzo-atriyoti Nowa.<br /> <br /> ; [[Llywelynsmic clan]] (P8, cM3/7)<br /> : This clan tempers out the [[llywelynsma]], {{monzo| 22 0 -1 -7 }} (4194304/4117715). The generator is {{nowrap| ~8/7 {{=}} ~227{{c}} }} and seven of them equals ~5/2. Its color name is Sasepru-aguti Nowa. <br /> <br /> ; [[Quince clan]] (P8, m6/7)<br /> : This clan tempers out the [[quince comma]], {{monzo| -15 0 -2 7 }} (823543/819200). The generator is {{nowrap| ~343/320 {{=}} ~116{{c}} }}. Two generators equals ~8/7, five generators equals ~7/5, and seven generators equals the classical minor sixth ~8/5. An obvious 5-limit interpretation of the generator is ~16/15, leading to the [[miracle]] temperament, which is in the gamelismic clan. Its color name is Lasepzo-aguguti Nowa. <br /> <br /> ; Exodia clan (P8, ccM3/8)<br /> : This clan tempers out the [[exodia comma]], {{monzo| -48 0 11 8 }}. The generator is {{nowrap| ~262144/214375 {{=}} ~348{{c}} }}. Eight generators equals ~5/1, 11 of them equals ~64/7, and 19 of them equals ~320/7 (five octaves above ~10/7). Its color name is Trila-quadbizo-aleyoti Nowa. <br /> <br /> ; Slither clan (P8, ccm6/9)<br /> : This clan tempers out the [[slither comma]], {{monzo| 16 0 4 -9 }} (40960000/40353607). The generator is {{nowrap| ~49/40 {{=}} ~357{{c}} }}. Four generators equals ~16/7, five of them equals ~14/5, and nine of them equals a double-compound minor sixth of ~32/5. Its color name is Satritriru-aquadyoti Nowa. <br /> <br /> === Clans defined by a 3.5.7 comma ===<br /> These are defined by a no-2's 7-limit (color name: yaza noca) comma. Any no-2's comma is a ratio of odd numbers. If no other commas are tempered out, It is a non-octave tuning, with a period of a perfect 12th or tritave, 3/1 (or some fraction of that). See also [[subgroup temperaments]]. The pergen's multigen (the second term, omitting any fraction) is always a no-2's 5-limit ratio such as 5/3, 9/5, 25/9, etc. In any no-2's subgroup, &quot;compound&quot; means increased by 3/1 not 2/1.<br /> <br /> ; Rutribiyoti Noca clan (P12, M6) <br /> : This 3.5.7 clan tempers out the [[arcturus comma]] {{monzo| 0 -7 6 -1 }} (15625/15309). Its only member so far is [[arcturus]]. The generator is the classical major sixth (~5/3), and six generators equals ~21/1.<br /> <br /> ; [[Sensamagic clan]] (P12, M6/2)<br /> : This 3.5.7 clan tempers out the [[sensamagic comma]] {{monzo| 0 -5 1 2 }} (245/243). The generator is ~9/7, and two generators equals the classic major sixth (~5/3). Its color name is Zozoyoti Noca. <br /> <br /> ; [[Gariboh clan]] (P12, M6/3)<br /> : This 3.5.7 clan tempers out the [[gariboh comma]] {{monzo| 0 -2 5 -3 }} (3125/3087). The generator is ~25/21, two generators equals ~7/5, and three generators equals the classical major sixth (~5/3). Its color name is Triru-aquinyoti Noca. <br /> <br /> ; [[Canopic clan]] (P12, cm7/5)<br /> : This 3.5.7 clan tempers out the [[canopic comma]], {{monzo| 0 3 4 -5 }} (16875/16807). The generator is ~7/5, four generators equals ~27/7, and five generators equals the classical compound minor seventh (~27/5). Its color name is Quinru-aquadyoti Noca. <br /> <br /> ; Sasepzo-atriguti Noca clan (P12, m7/7)<br /> : This 3.5.7 clan tempers out the [[procyon comma]] {{monzo| 0 -8 -3 7 }} (823543/820125). Its only member so far is [[procyon]]. The generator is ~49/45, three generators equals ~9/7, four equals ~7/5, and seven equals the classic minor seventh (~9/5).<br /> <br /> ; Satritrizo-aguguti Noca clan (P12, c&lt;sup&gt;3&lt;/sup&gt;M6/9)<br /> : This 3.5.7 clan tempers out the [[betelgeuse comma]] {{monzo| 0 -13 -2 9 }} (40353607/39858075). Its only member so far is [[betelgeuse]]. The generator is ~3645/2401, two generators equals ~7/3, and nine generators equals the classical triple-compound major sixth (~45/1).<br /> <br /> ; Saquadtrizo-asepguti Noca clan (P12, c&lt;sup&gt;5&lt;/sup&gt;m7/12)<br /> : This 3.5.7 clan tempers out the [[izar comma]] (also known as bapbo schismina), {{monzo| 0 -11 -7 12 }} (13841287201/13839609375). Its only member so far is [[izar]]. The generator is ~16807/10125, five generators give ~63/5, seven give ~243/7, and twelve give ~2187/5.<br /> <br /> === Temperaments defined by a 2.3.5.7 comma ===<br /> These are defined by a full 7-limit (color name: yaza) comma.<br /> <br /> ; [[Septisemi temperaments]]<br /> : These are very low complexity temperaments tempering out the minor septimal semitone, [[21/20]], and hence equating 5/3 with 7/4. Its color name is Zoguti. <br /> <br /> ; [[Greenwoodmic temperaments]]<br /> : These temper out the [[greenwoodma]], {{monzo| -3 4 1 -2 }} (405/392). Its color name is Ruruyoti. <br /> <br /> ; [[Keegic temperaments]]<br /> : Keegic rank-2 temperaments temper out the [[keega]], {{monzo| -3 1 -3 3 }} (1029/1000). Its color name is Trizoguti. <br /> <br /> ; [[Mint temperaments]]<br /> : Mint rank-2 temperaments temper out the septimal quartertone, [[36/35]], equating 7/6 with 6/5, and 5/4 with 9/7. Its color name is Ruguti. <br /> <br /> ; [[Avicennmic temperaments]]<br /> : These temper out the [[avicennma]], {{monzo| -9 1 2 1 }} (525/512), also known as Avicenna's enharmonic diesis. Its color name is Zoyoyoti. <br /> <br /> ; Sengic temperaments<br /> : Sengic rank-2 temperaments temper out the [[senga]], {{monzo| 1 -3 -2 3 }} (686/675). Its color name is Trizo-aguguti. <br /> <br /> ; [[Keemic temperaments]]<br /> : Keemic rank-2 temperaments temper out the [[keema]], {{monzo| -5 -3 3 1 }} (875/864). Its color name is Zotriyoti. <br /> <br /> ; Secanticorn temperaments<br /> : Secanticorn rank-2 temperaments temper out the [[secanticornisma]], {{monzo| -3 11 -5 -1 }} (177147/175000). Its color name is Laruquinguti. <br /> <br /> ; Nuwell temperaments<br /> : Nuwell rank-2 temperaments temper out the [[nuwell comma]], {{monzo| 1 5 1 -4 }} (2430/2401). Its color name is Quadru-ayoti. <br /> <br /> ; Mermismic temperaments<br /> : Mermismic rank-2 temperaments temper out the [[mermisma]], {{monzo| 5 -1 7 -7 }} (2500000/2470629). Its color name is Sepruyoti. <br /> <br /> ; Negricorn temperaments<br /> : Negricorn rank-2 temperaments temper out the [[negricorn comma]], {{monzo| 6 -5 -4 4 }} (153664/151875). Its color name is Saquadzoguti. <br /> <br /> ; Tolermic temperaments<br /> : These temper out the [[tolerma]], {{monzo| 10 -11 2 1 }} (179200/177147). Its color name is Sazoyoyoti. <br /> <br /> ; Valenwuer temperaments<br /> : Valenwuer rank-2 temperaments temper out the [[valenwuer comma]], {{monzo| 12 3 -6 -1 }} (110592/109375). Its color name is Sarutribiguti. <br /> <br /> ; [[Mirwomo temperaments]]<br /> : Mirwomo rank-2 temperaments temper out the [[mirwomo comma]], {{monzo| -15 3 2 2 }} (33075/32768). Its color name is Labizoyoti. <br /> <br /> ; Catasyc temperaments<br /> : Catasyc rank-2 temperaments temper out the [[catasyc comma]], {{monzo| -11 -3 8 -1 }} (390625/387072). Its color name is Laruquadbiyoti. <br /> <br /> ; Compass temperaments<br /> : Compass rank-2 temperaments temper out the [[compass comma]], {{monzo| -6 -2 10 -5 }} (9765625/9680832). Its color name is Quinruyoyoti. <br /> <br /> ; [[Sensibeta temperaments]]<br /> : Sensibeta rank-2 temperaments temper out the [[sensibeta comma]], {{monzo| -1 -12 5 3 }} (1071875/1062882). Its color name is Satrizo-aquinyoti. <br /> <br /> ; Trimyna temperaments<br /> : Trimyna rank-2 temperaments temper out the [[trimyna comma]], {{monzo| -4 1 -5 5 }} (50421/50000). Its color name is Quinzoguti. <br /> <br /> ; [[Starling temperaments]]<br /> : Starling rank-2 temperaments temper out the [[starling comma]] a.k.a. septimal semicomma, {{monzo| 1 2 -3 1 }} ([[126/125]]), the difference between three 6/5's plus one 7/6, and an octave. It includes myna, sensi, valentine, casablanca and nusecond temperaments, not to mention meantone, keemun, muggles and opossum. Its color name is Zotriguti. <br /> <br /> ; [[Octagar temperaments]]<br /> : Octagar rank-2 temperaments temper out the [[octagar comma]], {{monzo| 5 -4 3 -2 }} (4000/3969). Its color name is Rurutriyoti. <br /> <br /> ; [[Orwellismic temperaments]]<br /> : Orwellismic rank-2 temperaments temper out [[orwellisma]], {{monzo| 6 3 -1 -3 }} (1728/1715). Its color name is Triru-aguti. <br /> <br /> ; Mynaslendric temperaments<br /> : Mynaslendric rank-2 temperaments temper out the [[mynaslender comma]], {{monzo| 11 4 1 -7 }} (829440/823543). Its color name is Sepru-ayoti. <br /> <br /> ; [[Mistismic temperaments]]<br /> : Mistismic rank-2 temperaments temper out the [[mistisma]], {{monzo| 16 -6 -4 1 }} (458752/455625). Its color name is Sazoquadguti. <br /> <br /> ; [[Bronzismic temperaments]]<br /> : Bronzismic rank-2 temperaments temper out the [[bronzisma]], {{monzo| 21 -5 -2 -3 }} (2097152/2083725). Its color name is Satriru-aguguti. <br /> <br /> ; [[Varunismic temperaments]]<br /> : Varunismic rank-2 temperaments temper out the [[varunisma]], {{monzo| -9 8 -4 2 }} (321489/320000). Its color name is Labizoguguti. <br /> <br /> ; [[Marvel temperaments]]<br /> : Marvel rank-2 temperaments temper out the [[marvel comma]], {{monzo| -5 2 2 -1 }} (225/224). It includes wizard, tritonic, septimin, slender, triton, escapist and marv, not to mention negri, sharpie, pelogic, meantone, miracle, magic, pajara, orwell, catakleismic, garibaldi, august and compton. Its color name is Ruyoyoti. <br /> <br /> ; Dimcomp temperaments<br /> : Dimcomp rank-2 temperaments temper out the [[dimcomp comma]], {{monzo| -1 -4 8 -4 }} (390625/388962). Its color name is Quadruyoyoti. <br /> <br /> ; [[Cataharry temperaments]]<br /> : Cataharry rank-2 temperaments temper out the [[cataharry comma]], {{monzo| -4 9 -2 -2 }} (19683/19600). Its color name is Labiruguti. <br /> <br /> ; [[Canousmic temperaments]]<br /> : Canousmic rank-2 temperaments temper out the [[canousma]], {{monzo| 4 -14 3 4 }} (4802000/4782969). Its color name is Saquadzo-atriyoti. <br /> <br /> ; [[Triwellismic temperaments]]<br /> : Triwellismic rank-2 temperaments temper out the [[triwellisma]], {{monzo| 1 -1 -7 6 }} (235298/234375). Its color name is Tribizo-asepguti. <br /> <br /> ; [[Hemimage temperaments]]<br /> : Hemimage rank-2 temperaments temper out the [[hemimage comma]], {{monzo| 5 -7 -1 3 }} (10976/10935). Its color name is Satrizo-aguti. <br /> <br /> ; [[Aberschismic temperaments]]<br /> : Aberschismic rank-2 temperaments temper out the [[aberschisma]], {{monzo| 10 -6 1 -1 }} (5120/5103). Its color name is Saruyoti. <br /> <br /> ; [[Parkleiness temperaments]]<br /> : Parkleiness rank-2 temperaments temper out the [[parkleiness comma]], {{monzo| 7 7 -9 1 }} (1959552/1953125). Its color name is Zotritriguti. <br /> <br /> ; [[Porwell temperaments]]<br /> : Porwell rank-2 temperaments temper out the [[porwell comma]], {{monzo| 11 1 -3 -2 }} (6144/6125). Its color name is Sarurutriguti. <br /> <br /> ; [[Cartoonismic temperaments]]<br /> : Cartoonismic rank-2 temperaments temper out the [[cartoonisma]], {{monzo| 12 -3 -14 9 }} (165288374272/164794921875). Its color name is Satritrizo-asepbiguti. <br /> <br /> ; [[Hemfiness temperaments]]<br /> : Hemfiness rank-2 temperaments temper out the [[hemfiness comma]], {{monzo| 15 -5 3 -5 }} (4096000/4084101). Its color name is Saquinru-atriyoti. <br /> <br /> ; [[Hewuermera temperaments]]<br /> : Hewuermera rank-2 temperaments temper out the [[hewuermera comma]], {{monzo| 16 2 -1 -6 }} (589824/588245). Its color name is Satribiru-aguti. <br /> <br /> ; [[Lokismic temperaments]]<br /> : Lokismic rank-2 temperaments temper out the [[lokisma]], {{monzo| 21 -8 -6 2 }} (102760448/102515625). Its color name is Sasa-bizotriguti. <br /> <br /> ; Decovulture temperaments<br /> : Decovulture rank-2 temperaments temper out the [[decovulture comma]], {{monzo| 26 -7 -4 -2 }} (67108864/66976875). Its color name is Sasabiruguguti. <br /> <br /> ; Pontiqak temperaments<br /> : Pontiqak rank-2 temperaments temper out the [[pontiqak comma]], {{monzo| -17 -6 9 2 }} (95703125/95551488). Its color name is Lazozotritriyoti. <br /> <br /> ; [[Mitonismic temperaments]]<br /> : Mitonismic rank-2 temperaments temper out the [[mitonisma]], {{monzo| -20 7 -1 4 }} (5250987/5242880). Its color name is Laquadzo-aguti. <br /> <br /> ; [[Horwell temperaments]]<br /> : Horwell rank-2 temperaments temper out the [[horwell comma]], {{monzo| -16 1 5 1 }} (65625/65536). Its color name is Lazoquinyoti. <br /> <br /> ; Neptunismic temperaments<br /> : Neptunismic rank-2 temperaments temper out the [[neptunisma]], {{monzo| -12 -5 11 -2 }} (48828125/48771072). Its color name is Laruruleyoti. <br /> <br /> ; [[Metric microtemperaments]]<br /> : Metric rank-2 temperaments temper out the [[meter]], {{monzo| -11 2 7 -3 }} (703125/702464). Its color name is Latriru-asepyoti. <br /> <br /> ; [[Wizmic microtemperaments]]<br /> : Wizmic rank-2 temperaments temper out the [[wizma]], {{monzo| -6 -8 2 5 }} (420175/419904). Its color name is Quinzo-ayoyoti. <br /> <br /> ; [[Supermatertismic temperaments]]<br /> : Supermatertismic rank-2 temperaments temper out the [[supermatertisma]], {{monzo| -6 3 9 -7 }} (52734375/52706752). Its color name is Lasepru-atritriyoti. <br /> <br /> ; [[Breedsmic temperaments]]<br /> : Breedsmic rank-2 temperaments temper out the [[breedsma]], {{monzo| -5 -1 -2 4 }} (2401/2400). Its color name is Bizozoguti. <br /> <br /> ; Supermasesquartismic temperaments<br /> : Supermasesquartismic rank-2 temperaments temper out the [[supermasesquartisma]], {{monzo| -5 10 5 -8 }} (184528125/184473632). Its color name is Laquadbiru-aquinyoti. <br /> <br /> ; [[Ragismic microtemperaments]]<br /> : Ragismic rank-2 temperaments temper out the [[ragisma]], {{monzo| -1 -7 4 1 }} (4375/4374). Its color name is Zoquadyoti. <br /> <br /> ; Akjaysmic temperaments<br /> : Akjaysmic rank-2 temperaments temper out the [[akjaysma]], {{monzo| 47 -7 -7 -7 }}. These have a period of 1/7 octave, and five periods equals ~105/64. Unlike the whitewood or Lawati family, ~3/2 is not equated with 4/7 of an octave, resulting in small intervals. Its color name is Trisa-sepruguti. <br /> <br /> ; [[Landscape microtemperaments]]<br /> : Landscape rank-2 temperaments temper out the [[landscape comma]], {{monzo| -4 6 -6 3 }} (250047/250000). These have a period of 1/3 octave, but ~5/4 is not equated with a period, resulting in small intervals. Its color name is Trizoguguti.<br /> <br /> == Rank-3 temperaments ==<br /> Even less familiar than rank-2 temperaments are the [[rank-3 temperament]]s, generated by a set of three intervals. Since these temperaments may be mapped in many different ways, it is more common to identify rank-3 temperaments by the commas they temper out. They can also be identified by pergen. The third generator in a rank-3 pergen is usually a comma, but sometimes it is some fraction of a 5-limit or 7-limit interval.<br /> <br /> === Families defined by a 2.3.5 comma ===<br /> Every 5-limit (color name: ya) comma defines a rank-3 family, thus every comma in the list of rank-2 2.3.5 families could be included here. If nothing else is tempered out, the prime subgroup is assumed to be 2.3.5.7, and we have a 7-limit (color name: yaza) temperament in which one of the generators is ~7/1. This generator can be reduced to ~7/4, which can be reduced further to ~64/63. Hence in all the pergens below, the ^1 or /1 generator is ~64/63. An additional 7-limit or 11-limit comma creates an 11-limit (color name: yazala) temperament, and so forth. All these examples are 7-limit:<br /> <br /> ; [[Didymus rank-3 family]] (P8, P5, ^1)<br /> : These are the rank-3 temperaments tempering out the didymus or meantone comma, 81/80. Its color name is Guti. <br /> <br /> ; [[Diaschismic rank-3 family]] (P8/2, P5, /1)<br /> : These are the rank-3 temperaments tempering out the diaschisma, {{monzo| 11 -4 -2 }} (2048/2025). The half-octave period is ~45/32. Its color name is Saguguti. <br /> <br /> ; [[Porcupine rank-3 family]] (P8, P4/3, /1)<br /> : These are the rank-3 temperaments tempering out the porcupine comma a.k.a. maximal diesis, {{monzo| 1 -5 3 }} (250/243). In the pergen, P4/3 is ~10/9. Its color name is Triyoti. <br /> <br /> ; [[Kleismic rank-3 family]] (P8, P12/6, /1)<br /> : These are the rank-3 temperaments tempering out the kleisma, {{monzo| -6 -5 6 }} (15625/15552). In the pergen, P12/6 is ~6/5. Its color name is Tribiyoti. <br /> <br /> === Families defined by a 2.3.7 comma ===<br /> Every no-5's 7-limit (color name: za) comma defines a rank-3 family, thus every comma in the list of rank-2 2.3.7 families could be included here. If nothing else is tempered out, the prime subgroup is assumed to be 2.3.5.7, and we have a 7-limit (color name: yaza) temperament in which one of the generators is ~5/1. This generator can be reduced to ~5/4, which may be reduced further to ~81/80. Hence in all the pergens below, {{nowrap| ^1 {{=}} ~81/80 }}. An additional 5-limit or 11-limit comma creates a 11-limit (color name: yazala) temperament, and so forth. All these examples are 7-limit:<br /> <br /> ; [[Archytas family]] (P8, P5, ^1)<br /> : Archytas temperament tempers out 64/63. This comma equates every 7-limit interval to some 3-limit interval. If 81/80 were tempered out too, the otonal tetrad 4:5:6:7 would be identified with the dominant seventh chord. Its color name is Ruti. <br /> <br /> ; [[Garischismic family]] (P8, P5, ^1)<br /> : A garischismic temperament is one which tempers out the garischisma, {{monzo| 25 -14 0 -1 }} (33554432/33480783). Its color name is Sasaruti. <br /> <br /> ; Laruruti clan (P8/2, P5)<br /> : This clan tempers out the Laruru comma, {{monzo| -7 8 0 -2 }} (6561/6272). Two ~81/56 periods equal an octave. The generator is ~3/2, and four generators minus three periods equals ~7/4. The major second ~9/8 is divided in half, with each half equated to ~28/27. See also the diaschismic or Saguguti temperament and the jubilismic or Biruyoti temperament.<br /> <br /> ; [[Semaphoresmic family]] (P8, P4/2, ^1)<br /> : Semaphoresmic temperament tempers out 49/48 and thereby identifies the septimal minor third 7/6 with the septimal whole tone 8/7. It also splits the fourth into two of these intervals; hence the name, which sounds like ''semi-fourth''. See also [[semaphore]]. Its color name is Zozoti. <br /> <br /> ; [[Gamelismic family]] (P8, P5/3, ^1)<br /> : Not to be confused with the gamelismic clan of rank-2 temperaments, the gamelismic family are those rank-3 temperaments which temper out the gamelisma, {{monzo| -10 1 0 3 }} (1029/1024). In the pergen, P5/3 is ~8/7. Its color name is Latrizoti. <br /> <br /> ; Stearnsmic family (P8/2, P4/3, ^1)<br /> : Stearnsmic temperaments temper out the stearnsma, {{monzo| 1 10 0 -6 }} (118098/117649). In the pergen, P8/2 is ~343/243 and P4/3 is ~54/49. Its color name is Latribiruti. <br /> <br /> === Families defined by a 2.3.5.7 comma ===<br /> Color name: yaza. <br /> <br /> ; [[Marvel family]] (P8, P5, ^1)<br /> : The head of the marvel family is marvel, which tempers out the [[marvel comma]], {{monzo| -5 2 2 -1 }} (225/224). It divides 8/7 into two 16/15's, or equivalently, two 15/14's. It has a number of 11-limit children, including unidecimal marvel, prodigy, minerva and spectacle. <br /> : The marvel comma equates every 7-limit interval to some 5-limit interval, therefore the generators are the same as for 5-limit JI: 2/1, 3/1 and 5/1. These may be reduced to 2/1, 3/2 and 5/4, and 5/4 may be reduced further to 81/80. Hence in the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Ruyoyoti. <br /> <br /> ; [[Starling family]] (P8, P5, ^1)<br /> : Starling tempers out the [[starling comma]] a.k.a. septimal semicomma, {{monzo| 1 2 -3 1 }} (126/125), the difference between three 6/5's plus one 7/6, and an octave. It divides 10/7 into two 6/5's. Like marvel, it has the same generators as 5-limit JI. An excellent tuning for starling is [[77edo]], but 31, 46 or 58 also work nicely. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Zotriguti. <br /> <br /> ; [[Sensamagic family]] (P8, P5, ^1)<br /> : These temper out {{monzo| 0 -5 1 2 }} (245/243), which divides 16/15 into two 28/27's. In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Zozoyoti. <br /> <br /> ; Greenwoodmic family (P8, P5, ^1)<br /> : These temper out the greenwoodma, {{monzo| -3 4 1 -2 }} (405/392), which divides 10/9 into two 15/14's. In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Ruruyoti. <br /> <br /> ; Avicennmic family (P8, P5, ^1)<br /> : These temper out the avicennma, {{monzo| -9 1 2 1 }} (525/512), which divides 7/6 into two 16/15's. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Lazoyoyoti. <br /> <br /> ; [[Keemic family]] (P8, P5, ^1)<br /> : These temper out the keema, {{monzo| -5 -3 3 1 }} (875/864), which divides 15/14 into two 25/24's. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Zotriyoti. <br /> <br /> ; [[Orwellismic family]] (P8, P5, ^1)<br /> : These temper out the orwellisma, {{monzo| 6 3 -1 -3 }} (1728/1715). In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Triru-aguti. <br /> <br /> ; [[Nuwell family]] (P8, P5, ^1)<br /> : These temper out the nuwell comma, {{monzo| 1 5 1 -4 }} (2430/2401). In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Quadru-ayoti. <br /> <br /> ; [[Ragismic family]] (P8, P5, ^1)<br /> : The 7-limit rank-3 microtemperament which tempers out the ragisma, {{monzo| -1 -7 4 1 }} (4375/4374), extends to various higher-limit rank-3 temperaments such as thor. These are not by any means all microtemperaments, but those which are not highly accurate are probably best discussed under another heading. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Zoquadyoti. <br /> <br /> ; [[Aberschismic family]] (P8, P5, ^1)<br /> : The aberschismic family of rank-3 temperaments tempers out the aberschisma, {{monzo| 10 -6 1 -1 }} (5120/5103), which divides 10/7 into three 9/8's. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Saruyoti. <br /> <br /> ; [[Horwell family]] (P8, P5, ^1)<br /> : The horwell family of rank-3 temperaments tempers out the horwell comma, {{monzo| -16 1 5 1 }} (65625/65536). In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Lazoquinyoti. <br /> <br /> ; [[Hemimage family]] (P8, P5, ^1)<br /> : The hemimage family of rank-3 temperaments tempers out the hemimage comma, {{monzo| 5 -7 -1 3 }} (10976/10935), which divides 10/9 into three 28/27's. In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Satrizo-aguti. <br /> <br /> ; [[Mint family]] (P8, P5, ^1)<br /> : The mint temperament is a low-complexity, high-error temperament, tempering out the septimal quartertone 36/35, equating 7/6 with 6/5, and 5/4 with 9/7. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }} or ~64/63. Its color name is Ruguti. <br /> <br /> ; Septisemi family (P8, P5, ^1)<br /> : These are very low-accuracy temperaments tempering out the minor septimal semitone, [[21/20]], and hence equating 5/3 with 7/4. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Zoguti. <br /> <br /> ; [[Jubilismic family]] (P8/2, P5, ^1)<br /> : Jubilismic temperament tempers out 50/49 and thereby equates the two septimal tritones, 7/5 and 10/7. This is the half-octave period. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Biruyoti. <br /> <br /> ; [[Cataharry family]] (P8, P4/2, ^1)<br /> : Cataharry temperaments temper out the cataharry comma, {{monzo| -4 9 -2 -2 }} (19683/19600). In the pergen, half a fourth is ~81/70, and {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Labiruguti. <br /> <br /> ; [[Breed family]] (P8, P5/2, ^1)<br /> : Breed is a 7-limit microtemperament which tempers out {{monzo| -5 -1 -2 4 }} (2401/2400). While it is so accurate it hardly matters what is used to temper it, or whether it is even tempered at all, 2749edo will certainly do the trick. Breed has generators of 2/1, a 49/40-cum-60/49 neutral third, and ~64/63. Its color name is Bizozoguti. <br /> <br /> ; [[Sengic family]] (P8, P5, vm3/2)<br /> : These temper out the senga, {{monzo| 1 -3 -2 3 }} (686/675). One generator is ~15/14, two give ~7/6 (the downminor third in the pergen), and three give ~6/5. Its color name is Trizo-aguguti. <br /> <br /> ; [[Porwell family]] (P8, P5, ^m3/2)<br /> : The porwell family of rank-3 temperaments tempers out the porwell comma, {{monzo| 11 1 -3 -2 }} (6144/6125). Two ~35/32 generators equal the pergen's upminor third of ~6/5. Its color name is Sarurutriguti. <br /> <br /> ; [[Octagar family]] (P8, P5, ^m6/2)<br /> : The octagar family of rank-3 temperaments tempers out the octagar comma, {{monzo| 5 -4 3 -2 }} (4000/3969). Two ~80/63 generators equal the pergen's upminor sixth of ~8/5. Its color name is Rurutriyoti. <br /> <br /> ; [[Hemimean family]] (P8, P5, vM3/2)<br /> : The hemimean family of rank-3 temperaments tempers out the hemimean comma, {{monzo| 6 0 -5 2 }} (3136/3125). Two ~28/25 generators equal the pergen's downmajor third of ~5/4. Its color name is Zozoquinguti. <br /> <br /> ; Wizmic family (P8, P5, vm7/2)<br /> : A wizmic temperament is one which tempers out the wizma, {{monzo| -6 -8 2 5 }}, 420175/419904. Two ~324/245 generators equal the pergen's downminor seventh of ~7/4. Its color name is Quinzo-ayoyoti. <br /> <br /> ; [[Landscape family]] (P8/3, P5, ^1) <br /> : The 7-limit rank-3 microtemperament which tempers out the landscape comma, {{monzo| -4 6 -6 3 }} (250047/250000), extends to various higher-limit rank-3 temperaments such as tyr and odin. In the pergen, the 1/3-octave period is ~63/50, and {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Trizoguguti. <br /> <br /> ; [[Gariboh family]] (P8, P5, vM6/3)<br /> : The gariboh family of rank-3 temperaments tempers out the gariboh comma, {{monzo| 0 -2 5 -3 }} (3125/3087). Three ~25/21 generators equal the pergen's downmajor sixth of ~5/3. Its color name is Triru-aquinyoti. <br /> <br /> ; [[Canou family]] (P8, P5, vm6/3)<br /> : The canou family of rank-3 temperaments tempers out the canousma, {{monzo| 4 -14 3 4 }} (4802000/4782969). Three ~81/70 generators equal the pergen's downminor sixth of ~14/9. Its color name is Saquadzo-atriyoti. <br /> <br /> ; [[Dimcomp family]] (P8/4, P5, ^1) <br /> : The dimcomp family of rank-3 temperaments tempers out the dimcomp comma, {{monzo| -1 -4 8 -4 }} (390625/388962). In the pergen, the 1/4-octave period is ~25/21, and {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Quadruyoyoti. <br /> <br /> ; [[Canopic family]] (P8, P5, c^M7/4)<br /> : The canopic family of rank-3 temperaments tempers out the canopic comma, {{monzo| 0 3 4 -5 }} (16875/16807). Four ~7/5 generators equal the pergen's compound upmajor seventh of ~27/7. Its color name is Quinru-aquadyoti. <br /> <br /> === Temperaments defined by an 11-limit comma ===<br /> ; [[Ptolemismic clan]] (P8, P5, ^1)<br /> : These temper out the [[ptolemisma]], {{monzo| 2 -2 2 0 -1 }} (100/99). 11/8 is equated to 25/18, which is an octave minus two 6/5's. Since 25/18 is a 5-limit interval, every 2.3.5.11 interval is equated to a 5-limit interval, and both the pergen and the lattice are identical to that of 5-limit JI. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }}. Its color name is Luyoyoti. <br /> <br /> ; [[Biyatismic clan]] (P8, P5, ^1)<br /> : These temper out the [[biyatisma]], {{monzo| -3 -1 -1 0 2 }} (121/120). 5/4 is equated to 121/96, which is two 11/8's minus a 3/2 fifth. Since 121/96 is an ila (11-limit no-fives no-sevens) interval, every 2.3.5.11 interval is equated to an ila interval, and both the pergen and the lattice are identical to that of ila JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Lologuti. <br /> <br /> ; [[Valinorsmic clan]] <br /> : These temper out the [[valinorsma]], {{monzo| 4 0 -2 -1 1 }} (176/175). To be a rank-3 temperament, either an additional comma must vanish or the prime subgroup must omit prime 3. Thus no assumptions can be made about the pergen. Its color name is Loruguguti. <br /> <br /> ; [[Rastmic rank-3 clan]]<br /> : These temper out the [[rastma]], {{monzo| 1 5 0 0 -2 }} (243/242). In the corresponding [[#Clans defined by a 2.3.11 comma|2.3.11 rank-2 temperament]], the pergen is (P8, P5/2). Its color name is Luluti. <br /> <br /> ; [[Pentacircle clan]] (P8, P5, ^1)<br /> : These temper out the [[pentacircle comma]], {{monzo| 7 -4 0 1 -1 }} (896/891). The interval between 11/8 and 7/4 is equated to 81/64. Since that is a 3-limit interval, every 2.3.11 interval is equated to a 2.3.7 interval and vice versa, and both the pergen and the lattice are identical to that of either 2.3.7 JI or 2.3.11 JI. In the pergen, ^1 is either ~64/63 or ~33/32 or ~729/704. Its color name is Saluzoti. <br /> <br /> ; [[Moctdelismic clan]] <br /> : These temper out the [[moctdelisma]], {{monzo| -2 0 3 -3 1 }} (1375/1372). To be a rank-3 temperament, either an additional comma must vanish or the prime subgroup must omit prime 3. Thus no assumptions can be made about the pergen. Its color name is Lotriruyoti.<br /> <br /> ; [[Wizardharry clan]] (P8, P4/3, ^1)<br /> : These temper out the [[4000/3993|wizardharry comma]], {{monzo| 5 -1 3 0 -3 }} (4000/3993), and split the fourth in three. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Triluyoti. <br /> <br /> ; [[Semicanousmic clan]] (P8, P5, ^1)<br /> : These temper out the [[semicanousma]], {{monzo| -2 -6 -1 0 4 }} (14641/14580). 5/4 is equated to a 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Quadlo-aguti. <br /> <br /> ; [[Semiporwellismic clan]] (P8, P5, ^1)<br /> : These temper out the [[semiporwellisma]], {{monzo| 14 -3 -1 0 -2 }} (16384/16335). 5/4 is equated to an 2.3.11 (color name: ila) interval, thus every 2.3.5.11 interval is equated to a 2.3.11 interval, and both the pergen and the lattice are identical to that of 2.3.11-subgroup JI. In the pergen, ^1 is either ~33/32 or ~729/704. Its color name is Saluluguti. <br /> <br /> ; [[Olympic clan]] (P8, P5, ^1)<br /> : These temper out the [[olympia]], {{monzo| 17 -5 0 -2 -1 }} (131072/130977). 11/8 is equated with a 2.3.7 interval, and thus every 2.3.7.11 interval is equated with a 2.3.7 interval. In the pergen, {{nowrap| ^1 {{=}} ~64/63 }}. Its color name is Salururuti. <br /> <br /> ; [[Alphaxenic rank-3 clan]]<br /> : These temper out the [[Alpharabian comma]], {{monzo| -17 2 0 0 4 }} (131769/131072). In the corresponding [[#Clans defined by a 2.3.11 comma|2.3.11 rank-2 temperament]], the pergen is (P8/2, M2/4). Its color name is Laquadloti. <br /> <br /> ; [[Keenanismic temperaments]]<br /> : These temper out the [[keenanisma]], {{monzo| -7 -1 1 1 1 }} (385/384). Its color name is Lozoyoti. <br /> <br /> ; [[Werckismic temperaments]]<br /> : These temper out the [[werckisma]], {{monzo| -3 2 -1 2 -1 }} (441/440). Its color name is Luzozoguti. <br /> <br /> ; [[Swetismic temperaments]]<br /> : These temper out the [[swetisma]], {{monzo| 2 3 1 -2 -1 }} (540/539). Its color name is Lururuyoti. <br /> <br /> ; [[Lehmerismic temperaments]]<br /> : These temper out the [[lehmerisma]], {{monzo| -4 -3 2 -1 2 }} (3025/3024). Its color name is Loloruyoyoti. <br /> <br /> ; [[Kalismic temperaments]]<br /> : These temper out the [[kalisma]], {{monzo| -3 4 -2 -2 2 }} (9801/9800). Its color name is Biloruguti.<br /> <br /> == Rank-4 temperaments ==<br /> {{Main| Catalog of rank-4 temperaments }}<br /> <br /> Even less explored than rank-3 temperaments are rank-4 temperaments. In fact, unless one counts 7-limit JI they do not seem to have been explored at all. However, they could be used; for example [[hobbit]] scales can be constructed for them.<br /> <br /> ; [[Keenanismic family]] (P8, P5, ^1, /1)<br /> : These temper out the keenanisma, {{monzo| -7 -1 1 1 1 }} (385/384). In the pergen, ^1 could be either ~81/80 or ~64/63, and /1 could be either ~64/63 (if ^1 is not), ~33/32 or ~729/704. Its color name is Lozoyoti. <br /> <br /> ; Werckismic family (P8, P5, ^1, /1)<br /> : These temper out the werckisma, {{monzo| -3 2 -1 2 -1 }} (441/440). 11/8 is equated to {{monzo| -6 2 -1 2 }} and 5/4 is equated to {{monzo| -5 2 0 2 -1 }}, thus the lattice can be thought of as either 7-limit JI or no-5's 11-limit JI. In the pergen, ^1 is ~64/63, and /1 is either ~81/80, ~33/32 or ~729/704. Its color name is Luzozoguti. <br /> <br /> ; Swetismic family (P8, P5, ^1, /1)<br /> : These temper out the swetisma, {{monzo| 2 3 1 -2 -1 }} (540/539). 11/8 is equated to {{monzo| -1 3 1 -2 }} (135/98) and 5/4 is equated to {{monzo| -4 -3 0 2 1 }}, thus the lattice can be thought of as either 7-limit JI or no-5's 11-limit JI. In the pergen, ^1 is ~64/63, and /1 can be either ~81/80, ~33/32 or ~729/704. Its color name is Lururuyoti. <br /> <br /> ; Lehmerismic family (P8, P5, ^1, /1)<br /> : These temper out the lehmerisma, {{monzo| -4 -3 2 -1 2 }} (3025/3024). Since 7/4 is equated to a no-7's 11-limit (color name: yala) interval, both the pergen and the lattice are identical to that of no-7's 11-limit JI. In the pergen, {{nowrap| ^1 {{=}} ~81/80 }} and /1 is either ~33/32 or ~729/704. Its color name is Loloruyoyoti. <br /> <br /> ; Kalismic family (P8/2, P5, ^1, /1)<br /> : These temper out the kalisma, {{monzo| -3 4 -2 -2 2 }} (9801/9800). The octave is split into two ~99/70 periods. In the pergen, ^1 could be either ~81/80 or ~64/63, and /1 could be either ~64/63 (if ^1 is not), ~33/32 or ~729/704. Its color name is Biloruguti. <br /> <br /> == Subgroup temperaments ==<br /> {{Main| Subgroup temperaments }}<br /> <br /> A wide-open field. These are regular temperaments of various ranks which temper [[just intonation subgroups]].<br /> <br /> == Commatic realms ==<br /> By a ''commatic realm'' is meant the whole collection of regular temperaments of various ranks and for [[subgroup]]s (including full [[prime limit]]s) tempering out a given comma. For some commas, looking at the full commatic realm seems the best approach to discussing associated temperaments.<br /> <br /> ; [[The Biosphere]]<br /> : The Biosphere is the name given to the commatic realm of the [[13-limit]] comma 91/90. Its color name is Thozoguti. <br /> <br /> ; [[Marveltwin]]<br /> : This is the commatic realm of the 13-limit comma 325/324, the [[marveltwin comma]]. Its color name is Thoyoyoti. <br /> <br /> ; [[The Archipelago]]<br /> : The Archipelago is a name which has been given to the commatic realm of the 13-limit comma 676/675 ({{monzo| 2 -3 -2 0 0 2 }}), the [[island comma]]. Its color name is Bithoguti. <br /> <br /> ; [[The Jacobins]]<br /> : This is the commatic realm of the 13-limit comma 6656/6655, the [[jacobin comma]]. Its color name is Thotrilu-aguti. <br /> <br /> ; [[Orgonia]]<br /> : This is the commatic realm of the 11-limit comma 65536/65219 ({{monzo| 16 0 0 -2 -3 }}), the [[orgonisma]]. Its color name is Satrilu-aruruti. <br /> <br /> ; [[The Nexus]]<br /> : This is the commatic realm of the 11-limit comma 1771561/1769472 ({{monzo| -16 -3 0 0 6 }}), the [[nexus comma]]. Its color name is Tribiloti. <br /> <br /> ; [[The Quartercache]]<br /> : This is the commatic realm of the 11-limit comma 117440512/117406179 ({{monzo| 24 -6 0 1 -5 }}), the [[quartisma]]. Its color name is Saquinlu-azoti. <br /> <br /> == Miscellaneous other temperaments ==<br /> ; [[Limmic temperaments]]<br /> : Various subgroup temperaments all tempering out the limma, 256/243.<br /> <br /> ; [[Fractional-octave temperaments]]<br /> : These temperaments all have a fractional-octave period.<br /> <br /> ; [[Miscellaneous 5-limit temperaments]]<br /> : High in badness, but worth cataloging for one reason or another.<br /> <br /> ; [[Miscellaneous 7-limit temperaments]]<br /> : Various rank-3 temperaments which are high in badness.<br /> <br /> ; [[Low harmonic entropy linear temperaments]]<br /> : Temperaments where the average [[harmonic entropy]] of their intervals is low in a particular scale size range.<br /> <br /> ; [[Turkish maqam music temperaments]]<br /> : Various theoretical solutions have been put forward for the vexing problem of how to indicate and define the tuning of Turkish [[Arabic, Turkish, Persian music|makam (maqam) music]] in a systematic way. This includes, in effect, certain linear temperaments.<br /> <br /> ; [[Very low accuracy temperaments]]<br /> : All hope abandon ye who enter here.<br /> <br /> ; [[Very high accuracy temperaments]]<br /> : Microtemperaments which do not fit in elsewhere.<br /> <br /> ; Middle Path tables<br /> : Tables of temperaments where {{nowrap| complexity/7.65 + damage/10 &lt; 1 }}. Useful for beginners looking for a list of a manageable number of temperaments, which approximate harmonious intervals accurately with a manageable number of notes.<br /> :: [[Middle Path table of 5-limit rank-2 temperaments]]<br /> :: [[Middle Path table of 7-limit rank-2 temperaments]]<br /> :: [[Middle Path table of 11-limit rank-2 temperaments]]<br /> <br /> == Maps of temperaments ==<br /> * [[Map of rank-2 temperaments]], sorted by generator size<br /> ** [[Catalog of 7-limit rank-2 temperaments]]<br /> ** [[Catalog of 11-limit rank-2 temperaments]]<br /> ** [[Catalog of 13-limit rank-2 temperaments]]<br /> * [[Catalog of 11-limit rank-3 temperaments]]<br /> * [[List of rank-2 temperaments by generator and period]]<br /> * [[List of rank-2 temperaments supported by EDOs]]<br /> * [[Rank-2 temperaments by mapping of 3]]<br /> * [[Temperaments for MOS shapes]]<br /> <br /> == Temperament nomenclature ==<br /> * [[Temperament naming]]<br /> <br /> == External links ==<br /> * [http://www.huygens-fokker.org/docs/lintemps.html List of temperaments] in [http://www.huygens-fokker.org/scala Scala] with ready to use values<br /> <br /> [[Category:Lists of temperaments]] &lt;!-- main article --&gt;</div> FloraC https://en.xen.wiki/index.php?title=Enneadeca&diff=232408 Enneadeca 2026-06-18T08:13:49Z <p>FloraC: - trivially supporting edos</p> <hr /> <div>{{Infobox Interval<br /> | Monzo = -14 -19 19<br /> | Name = enneadeca<br /> | Color name = y&lt;sup&gt;19&lt;/sup&gt;-4, Neyo comma<br /> | Comma = yes<br /> }}<br /> The '''enneadeca''' ({{monzo|legend=1| -14 -19 19 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] of 2.816 [[cent]]s. It is the amount by which nineteen [[6/5|classical minor thirds]] fall short of five [[2/1|octaves]], that is, 2&lt;sup&gt;5&lt;/sup&gt;/(6/5)&lt;sup&gt;19&lt;/sup&gt;. <br /> <br /> == Temperament ==<br /> [[Tempering out]] the enneadeca leads to the 5-limit [[enneadecal]] temperament, [[support]]ed by equal divisions divisible by 19 such as [[152edo]], [[171edo]], and [[190edo]]. <br /> <br /> == Etymology ==<br /> This comma was named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''enneadecal''&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic &amp; co'']&lt;/ref&gt;, for the temperament has 19 periods per octave. The comma was at one point dubbed ''enneadecima''&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']&lt;/ref&gt;, though it was ''enneadeca'' that stuck. <br /> <br /> == See also ==<br /> * [[Septimal enneadeca]]<br /> <br /> == References ==<br /> <br /> [[Category:Enneadecal]]<br /> [[Category:Commas named for their periods per equave]]</div> FloraC https://en.xen.wiki/index.php?title=Unnoticeable_comma&diff=232407 Unnoticeable comma 2026-06-18T08:12:33Z <p>FloraC: /* List of commas, by prime limit */ less absurdities</p> <hr /> <div>'''Unnoticeable commas''' are very small intervals. These [[comma]]s are called &quot;unnoticeable&quot; because, being equal to or less than 3.5{{cent}}, they are smaller than the average peak [[just-noticeable difference]] (JND) of human pitch perception, as illustrated by the research of [[Aaron Andrew Hunt]]&lt;ref&gt;[http://musictheory.zentral.zone/huntsystem2.html#2 H-Pi Instruments | ''Hunt System Scale §The JND'']&lt;/ref&gt;. It is improbable that even a trained listener would be able to notice these intervals, and as such they are a prime target for psychoacoustically informed [[microtempering]]. (However, a considerably larger comma can be unnoticeable in an [[adaptive just intonation|adaptive]] tuning context. Instead of one large pitch shift of the entire comma, there can be many small pitch shifts of a fraction of a comma, one per chord change. Given this, a noticeable 3-limit comma that arguably deserves inclusion is the [[mercator comma]], corresponding to using [[53edo]] for the circle of fifths.) In [[Sagittal notation]], intervals in the smaller part of this category are [[schismina]]s, and intervals in the larger part of this category are [[schisma (interval region)|schismas]]&lt;ref&gt;[https://sagittal.org/sagittal.pdf ''Sagittal – A Microtonal Notation System''] by [[George Secor|George D. Secor]] and [[Dave Keenan|David C. Keenan]]&lt;/ref&gt;. <br /> <br /> For commas over 100{{c}} in size, see [[Large comma]]; for commas in between 30–100{{c}} in size, see [[Medium comma]]; and for commas between 3.5–30{{c}} in size, see [[Small comma]].<br /> <br /> Due to the wide range of sizes, cents values here and on the other commas pages are listed to 5 significant digits, instead of to a fixed number of decimal places as is the [[conventions|convention]] elsewhere on the wiki.<br /> <br /> The commas might be numerous, but there is no need to memorize all the names. For pretty much all use cases, it is perfectly acceptable to just refer to a comma by the monzo or ratio, whichever is simpler. <br /> <br /> == List of commas, by prime limit ==<br /> === 3-limit commas ===<br /> {{See also| Table of 3-limit commas }}<br /> <br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[Qian's large comma]]<br /> | 359wama<br /> | 359wM<br /> | &lt;abbr title=&quot;1934329451767021421190980423006270754962252499447372679942534652297789463068718331568475476554301659845788554312924531179306109686817232569946089263295619210341718686733067/1932268761508629172347675945465993672149463664853217499328617625725759571144780212268096883290961288981231808015751088588682539330521493827871454336733540374348490407411712&quot;&gt;(344 digits)&lt;/abbr&gt;<br /> | {{Monzo| -569 359 }}<br /> | 1.8453<br /> | Chen Yingshi (2009)<br /> |-<br /> | [[Qian's small comma]], sasktel comma<br /> | 306wama<br /> | 306wM<br /> | &lt;abbr title=&quot;99895953610111751404211111353381321783955140565279076827493022708011895642232499843849795298031743077114461795885011932654335221737225129801285632/99793888233710926097676673961542382339552034110870991187709058567130998942396826836880350287497238272034603157195937657211050782186192219658614729&quot;&gt;(292 digits)&lt;/abbr&gt;<br /> | {{Monzo| 485 -306 }}<br /> | 1.7697<br /> | Chen Yingshi (2009) for ''Qian's small comma''<br /> |-<br /> | [[Satanic comma]]<br /> | 665wama<br /> | 665wM<br /> | &lt;abbr title=&quot;193034257116813465350415306746516837350333763798962117430788985740786485136987943002905988649011085058426719117038711696606024631330152759176330399379617346789616335692978372064681236597226671488585092334981423081811727458166457361300251189808300631437024118571790058070714566731059066970852059271394655662607817543843/193025830561934107162947985381047541665608072055952185017491682078771915023799273387871154500424503798663213600460826789274033295999330021731389427128542432710187362934652673115221889249890533772697227171395058697282798274445240687006095271729621464100656563293799180557568945517759802372156455525060659659679134121984&quot;&gt;(636 digits)&lt;/abbr&gt;<br /> | {{Monzo| -1054 665 }}<br /> | 0.075575<br /> | [[Marc Jones]] (1990)<br /> |-<br /> | 15601-comma<br /> | 15601wama<br /> | 15601wM<br /> | (14888 digits)<br /> | {{Monzo| 24727 -15601 }}<br /> | 0.031499<br /> | <br /> |-<br /> | 31867-comma<br /> | 31867wama<br /> | 31867wM<br /> | (30410 digits)<br /> | {{Monzo| -50508 31867 }}<br /> | 0.012577<br /> | <br /> |-<br /> | [[Archangelic comma]]<br /> | 190537wama<br /> | 190537wM<br /> | (181820 digits)<br /> | {{monzo| 301994 -190537 }}<br /> | 0.00011162<br /> | [[Dawson Berry]] (2022)<br /> |}<br /> <br /> === 5-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[Dodifo comma]]<br /> | Quadla-sepquinyoma<br /> | 4L35yM<br /> | &lt;abbr title=&quot;2910383045673370361328125 / 2904698108822600835661824&quot;&gt;(50 digits)&lt;/abbr&gt;<br /> | {{Monzo| -67 -9 35 }}<br /> | 3.3850<br /> | [[Petr Pařízek]] (2011)<br /> |-<br /> | [[Vishnu comma]], semisuper comma<br /> | Sasepbiguma<br /> | s14gM<br /> | 6115295232 / 6103515625<br /> | {{Monzo| 23 6 -14 }}<br /> | 3.3380<br /> | [[Gene Ward Smith]] (2001), for ''semisuper comma''<br /> |-<br /> | [[Enneadeca]]<br /> | Neyoma<br /> | 19yM<br /> | 19073486328125 / &lt;br&gt;19042491875328<br /> | {{Monzo| -14 -19 19 }}<br /> | 2.8155<br /> | [[Gene Ward Smith]] (2001)<br /> |-<br /> | [[Vavoom comma]]<br /> | Quinla-seyoma<br /> | 5L17yM<br /> | &lt;abbr title=&quot;295578376007080078125 / 295147905179352825856&quot;&gt;(42 digits)&lt;/abbr&gt;<br /> | {{Monzo| -68 18 17 }}<br /> | 2.5232<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Alphatricot comma]]<br /> | Quadsa-triyoma<br /> | 4s3yM<br /> | 68719476736000 / &lt;br&gt;68630377364883<br /> | {{Monzo| 39 -29 3 }}<br /> | 2.2461<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Schisma]]<br /> | Layoma<br /> | LyM<br /> | 32805 / 32768<br /> | {{Monzo| -15 8 1 }}<br /> | 1.9537<br /> | [[Hermann von Helmholtz]], [[Alexander Ellis]] (1875)<br /> |-<br /> | [[Aluminium comma]]<br /> | Sepsa-theguma<br /> | 7s13gM<br /> | &lt;abbr title=&quot;4951760157141521099596496896 / 4946966739525117513427734375&quot;&gt;(56 digits)&lt;/abbr&gt;<br /> | {{Monzo| 92 -39 -13 }}<br /> | 1.6767<br /> | [[Eliora]] (2023)<br /> |-<br /> | [[Counterschisma]]<br /> | Tribilaguma<br /> | 6LgM<br /> | &lt;abbr title=&quot;2954312706550833698643 / 2951479051793528258560&quot;&gt;(44 digits)&lt;/abbr&gt;<br /> | {{Monzo| -69 45 -1 }}<br /> | 1.6613<br /> | [[Gene Ward Smith]] (2003)<br /> |-<br /> | [[Neon comma]]<br /> | Laquinquinbiguma<br /> | L50gM<br /> | &lt;abbr title=&quot;88900702359186211632409599176343552 / 88817841970012523233890533447265625&quot;&gt;(70 digits)&lt;/abbr&gt;<br /> | {{monzo| 21 60 -50 }}<br /> | 1.6144<br /> | [[Eliora]] (2024)<br /> |-<br /> | [[Septendecima]]<br /> | Lala-sebiyoma<br /> | LL34yM<br /> | &lt;abbr title=&quot;582076609134674072265625 / 581595589965365114830848&quot;&gt;(48 digits)&lt;/abbr&gt;<br /> | {{Monzo| -52 -17 34 }}<br /> | 1.4313<br /> | <br /> |-<br /> | [[Luna comma]], hemithirds comma<br /> | Sasa-quintriguma<br /> | ss15gM<br /> | 274877906944 / &lt;br&gt;274658203125<br /> | {{Monzo| 38 -2 -15 }}<br /> | 1.3843<br /> | [[Gene Ward Smith]] (2002)<br /> |-<br /> | [[Minortone comma]]<br /> | Trila-seguma<br /> | 3L17gM<br /> | &lt;abbr title=&quot;50031545098999707 / 50000000000000000&quot;&gt;(34 digits)&lt;/abbr&gt;<br /> | {{Monzo| -16 35 -17 }}<br /> | 1.0919<br /> | [[Gene Ward Smith]] (2002)<br /> |-<br /> | [[Ennealimma]]<br /> | Satritribiyoma<br /> | s18yM<br /> | 7629394531250 / &lt;br&gt;7625597484987<br /> | {{Monzo| 1 -27 18 }}<br /> | 0.86183<br /> | [[Paul Erlich]], [[Gene Ward Smith]] (2001)<br /> |-<br /> | [[Astro comma]]<br /> | Tribisa-thiweguma<br /> | 6s31gM<br /> | &lt;abbr title=&quot;2475880078570760549798248448 / 2474715001881122589111328125&quot;&gt;(56 digits)&lt;/abbr&gt;<br /> | {{Monzo| 91 -12 -31 }}<br /> | 0.81486<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Gaster comma]]<br /> | Quadbila-neguma<br /> | 8L19gM<br /> | &lt;abbr title=&quot;22528399544939174411840147874772641 / 22517998136852480000000000000000000&quot;&gt;(70 digits)&lt;/abbr&gt;<br /> | {{Monzo| -70 72 -19 }}<br /> | 0.79950<br /> | [[Xenllium]] (2022)<br /> |-<br /> | [[Niobium comma]]<br /> |<br /> |<br /> |<br /> | {{Monzo| -875 492 41 }}<br /> | 0.72269<br /> | [[Eliora]] (2023)<br /> |-<br /> | [[Kwazy comma]]<br /> | Quadla-quadquadyoma<br /> | 4L16yM<br /> | &lt;abbr title=&quot;9010162353515625 / 9007199254740992&quot;&gt;(32 digits)&lt;/abbr&gt;<br /> | {{Monzo| -53 10 16 }}<br /> | 0.56943<br /> | [[Paul Erlich]], [[Gene Ward Smith]] (2002)<br /> |-<br /> | [[Whoosh comma]]<br /> | Saletriguma<br /> | s33gM<br /> | &lt;abbr title=&quot;116450459770592056836096 / 116415321826934814453125&quot;&gt;(48 digits)&lt;/abbr&gt;<br /> | {{Monzo| 37 25 -33 }}<br /> | 0.52246<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Egads comma]]<br /> | Setriyoma<br /> | 51yM<br /> | &lt;abbr title=&quot;444089209850062616169452667236328125 / 444002166576103304796646509039845376&quot;&gt;(72 digits)&lt;/abbr&gt;<br /> | {{Monzo| -36 -52 51 }}<br /> | 0.33936<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Monzisma]]<br /> | Quinsa-yoyoma<br /> | 5syyM<br /> | &lt;abbr title=&quot;450359962737049600 / 450283905890997363&quot;&gt;(36 digits)&lt;/abbr&gt;<br /> | {{Monzo| 54 -37 2 }}<br /> | 0.29240<br /> | [[Margo Schulter]] (2001)<br /> |-<br /> | [[Fortune comma]]<br /> | Tritrila-sepbiyoma<br /> | 9L14yM<br /> | &lt;abbr title=&quot;162285243890121480027996826171875 / 162259276829213363391578010288128&quot;&gt;(66 digits)&lt;/abbr&gt;<br /> | {{Monzo| -107 47 14 }}<br /> | 0.27703<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Gross comma]]<br /> | Quinbisa-foseguma<br /> | 10s47gM<br /> | &lt;abbr title=&quot;22300745198530623141535718272648361505980416 / 22297583945629639856633730232715606689453125&quot;&gt;(88 digits)&lt;/abbr&gt;<br /> | {{Monzo| 144 -22 -47 }}<br /> | 0.24543<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Senior comma]]<br /> | Quadla-sepquinguma<br /> | 4L35gM<br /> | &lt;abbr title=&quot;381520424476945831628649898809 / 381469726562500000000000000000&quot;&gt;(60 digits)&lt;/abbr&gt;<br /> | {{Monzo| -17 62 -35 }}<br /> | 0.23007<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | [[Counterquectisma]], deltapion comma<br /> | Quintritrilayoma<br /> | 45LyM<br /> |<br /> | {{Monzo| -500 314 1 }}<br /> | 0.18399<br /> | [[Eliora]] (2023)<br /> |-<br /> | [[Septarium comma]]<br /> | Sasepquadtriguma<br /> | s84gM<br /> | &lt;abbr title=&quot;51704256436926231056548749215693807357721577836111615492096 / 51698788284564229679463043254372678347863256931304931640625&quot;&gt;(118 digits)&lt;/abbr&gt;<br /> | {{Monzo| 73 77 -84 }}<br /> | 0.18310<br /> | [[Xenllium]] (2026)<br /> |-<br /> | [[Quectisma]]<br /> | <br /> | <br /> |<br /> | {{Monzo| 554 -351 1 }}<br /> | 0.10841<br /> | [[User:CompactStar|CompactStar]] (2023)<br /> |-<br /> | Raider comma<br /> | Tritrisa-thiseyoma<br /> | 9s37yM<br /> | &lt;abbr title=&quot;171798691840000000000000000000000000000000000000 / 171792506910670443678820376588540424234035840667&quot;&gt;(96 digits)&lt;/abbr&gt;<br /> | {{Monzo| 71 -99 37 }}<br /> | 0.062327<br /> | [[Gene Ward Smith]] (2002)<br /> |-<br /> | Pirate comma<br /> | Quinla-sepsepyoma<br /> | 5L49yM<br /> | &lt;abbr title=&quot;17763568394002504646778106689453125 / 17763086495282268024161967871623168&quot;&gt;(70 digits)&lt;/abbr&gt;<br /> | {{Monzo| -90 -15 49 }}<br /> | 0.046966<br /> | [[Paul Erlich]] (2002)<br /> |-<br /> | Viking comma<br /> | Nela-siweyoma<br /> | 19L61yM<br /> | <br /> | {{Monzo| -251 69 61 }}<br /> | 0.031605<br /> | [[Gene Ward Smith]] (2002)<br /> |-<br /> | [[Kirnberger's atom]]<br /> | Sepbisa-quadtriguma<br /> | 14s12gM<br /> | &lt;abbr title=&quot;2923003274661805836407369665432566039311865085952 / 2922977339492680612451840826835216578535400390625&quot;&gt;(98 digits)&lt;/abbr&gt;<br /> | {{Monzo| 161 -84 -12 }}<br /> | 0.015361<br /> | <br /> |-<br /> | Selenia<br /> |<br /> |<br /> | <br /> | {{Monzo| -433 -137 280 }}<br /> | 0.0047636<br /> | <br /> |-<br /> | Titania<br /> |<br /> |<br /> | <br /> | {{Monzo| 2746 -521 -827 }}<br /> | 0.0031829<br /> | <br /> |-<br /> | Quark<br /> |<br /> |<br /> | <br /> | {{Monzo| -573 237 85 }}<br /> | 8.8361 × 10&lt;sup&gt;-4&lt;/sup&gt;<br /> | <br /> |-<br /> | Scamp<br /> |<br /> |<br /> | <br /> | {{Monzo| -5836 4293 -417 }}<br /> | 3.3472 × 10&lt;sup&gt;-5&lt;/sup&gt;<br /> | <br /> |-<br /> | Rover<br /> |<br /> |<br /> | <br /> | {{Monzo| 1634 1502 -1729 }}<br /> | 2.7513 × 10&lt;sup&gt;-5&lt;/sup&gt;<br /> | <br /> |-<br /> | Rascal<br /> |<br /> |<br /> | <br /> | {{Monzo| -7470 2791 1312 }}<br /> | 5.9596 × 10&lt;sup&gt;-6&lt;/sup&gt;<br /> | <br /> |}<br /> <br /> === 7-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[Decovulture comma]]<br /> | Sasa-biruguguma<br /> | ss2rggM<br /> | 67108864 / 66976875<br /> | {{Monzo| 26 -7 -4 -2 }}<br /> | 3.4083<br /> | [[User:Xenllium|Xenllium]] (2021)<br /> |-<br /> | [[Rainy comma]]<br /> | Laquinzo-atriyoma<br /> | L5za3yM<br /> | 2100875/2097152<br /> | {{Monzo| -21 0 3 5 }}<br /> | 3.0706<br /> | [[User:Flirora|+merlan #flirora]] (2020)<br /> |-<br /> | [[Pontiqak comma]]<br /> | Lazozotritriyoma<br /> | Lzz9yM<br /> | 95703125 / 95551488<br /> | {{Monzo| -17 -6 9 2 }}<br /> | 2.7452<br /> | [[User:Xenllium|Xenllium]] (2021)<br /> |-<br /> | [[Pessoalisma]]<br /> | Sasa-tribiru-aguguma<br /> | ss6raggM<br /> | 2147483648 / 2144153025<br /> | {{Monzo| 31 -6 -2 -6 }}<br /> | 2.6871<br /> | [[Dawson Berry]] (2023)<br /> |-<br /> | [[Mitonisma]]<br /> | Laquadzo-aguma<br /> | L4zagM<br /> | 5250987/5242880<br /> | {{Monzo| -20 7 -1 4 }}<br /> | 2.6749<br /> | [[User:Xenllium|Xenllium]] (2021)<br /> |-<br /> | [[Horwell comma]]<br /> | Lazoquinyoma<br /> | Lz5yM<br /> | 65625/65536<br /> | {{Monzo| -16 1 5 1 }}<br /> | 2.3495<br /> | [[Gene Ward Smith]] (2005)<br /> |-<br /> | [[Forge comma]]<br /> | Lala-trizo-aquinguma<br /> | LL3za5gM<br /> | 1640558367 / 1638400000<br /> | {{Monzo| -19 14 -5 3 }}<br /> | 2.2792<br /> | [[Dawson Berry]] (2022)<br /> |-<br /> | [[109-7-comma]]<br /> |<br /> |<br /> |<br /> | {{Monzo| -306 0 0 109 }}<br /> | 2.0238<br /> | <br /> |-<br /> | [[Neptunisma]]<br /> | Laruruleyoma<br /> | Lrr11yM<br /> | 48828125 / 48771072<br /> | {{monzo| -12 -5 11 -2 }}<br /> | 2.0240<br /> | [[User:Xenllium|Xenllium]] (2021)<br /> |-<br /> | [[Slendroschisma]], slendric schisma<br /> | Sasa-quinbiruma<br /> | ss10rM<br /> | 68719476736 / 68641485507<br /> | {{monzo| 36 -5 0 -10 }}<br /> | 1.9659<br /> | [[User:Xenllium|Xenllium]] (2024), &lt;br&gt;modified by [[Flora Canou]] (2025)<br /> |-<br /> | [[Septimal ennealimma]]<br /> | Tritrizoma<br /> | 9zM<br /> | 40353607 / 40310784<br /> | {{Monzo| -11 -9 0 9 }}<br /> | 1.8382<br /> | [[Eliora]] (2021)<br /> |-<br /> | [[Meter]]<br /> | Latriru-asepyoma<br /> | L3ra7yM<br /> | 703125/702464<br /> | {{Monzo| -11 2 7 -3 }}<br /> | 1.6283<br /> | <br /> |-<br /> | [[Scheme comma]]<br /> | Lala-rutriguma<br /> | LLr3gM<br /> | 14348907 / 14336000<br /> | {{Monzo| -14 15 -3 -1}}<br /> | 1.5580<br /> | [[User:Jerdle|Jerdle]] (2021)<br /> |-<br /> | [[Breeze comma]]<br /> | Laquadru-atriyoma<br /> | L4ra3yM<br /> | 2460375 / 2458624<br /> | {{Monzo| -10 9 3 -4 }}<br /> | 1.2325<br /> | [[Tristan Bay]] (2024)<br /> |-<br /> | [[Wizma]]<br /> | Quinzo-ayoyoma<br /> | 5zayyM<br /> | 420175/419904<br /> | {{Monzo| -6 -8 2 5 }}<br /> | 1.1170<br /> | <br /> |-<br /> | [[Supermatertisma]]<br /> | Lasepru-atritriyoma<br /> | L7ra9yM<br /> | 52734375 / 52706752<br /> | {{Monzo| -6 3 9 -7 }}<br /> | 0.90708<br /> | [[User:Xenllium|Xenllium]] (2021)<br /> |-<br /> | [[Trienstonisma]]<br /> | Laquinru-aguma<br /> | L5ragM<br /> | 43046721 / 43025920<br /> | {{monzo| -9 16 -1 -5 }}<br /> | 0.83677<br /> | [[User:Xenllium|Xenllium]] (2021)<br /> |-<br /> | [[2401/2400|Breedsma]]<br /> | Bizozoguma<br /> | 2zzgM<br /> | 2401/2400<br /> | {{monzo| -5 -1 -2 4 }}<br /> | 0.72120<br /> | [[Gene Ward Smith]] (2004)<br /> |-<br /> | [[Gariatom]]<br /> | Quintrila-tribizoma<br /> | 15L6zM<br /> | <br /> | {{monzo| -169 96 0 6 }}<br /> | 0.63552<br /> | [[Tristan Bay]] (2023)<br /> |-<br /> | 171-9/7-comma<br /> | Quadtribisa-netritrizoma<br /> | 24s171zM<br /> | <br /> | {{monzo| 62 -342 0 171 }}<br /> | 0.61971<br /> | <br /> |-<br /> | [[Supermasesquartisma]]<br /> | Laquadbiru-aquinyoma<br /> | L8ra5yM<br /> | 184528125 / 184473632<br /> | {{monzo| -5 10 5 -8 }}<br /> | 0.51133<br /> | [[User:Xenllium|Xenllium]] (2021)<br /> |-<br /> | 571-7-comma<br /> | <br /> |<br /> | <br /> | {{monzo| 1603 0 0 -571 }}<br /> | 0.40741<br /> | <br /> |-<br /> | [[Ragisma]]<br /> | Zoquadyoma<br /> | z4yM<br /> | 4375/4374<br /> | {{Monzo| -1 -7 4 1 }}<br /> | 0.39576<br /> | <br /> |-<br /> | [[Septiruthenia]], septimal ruthenia<br /> | Nela-lequadzoma<br /> | 19L44zM<br /> | <br /> | {{Monzo| -263 88 0 44 }}<br /> | 0.37996<br /> | [[Eliora]] (2022)<br /> |-<br /> | [[Akjaysma]]<br /> | Trisa-sepruguma<br /> | 3s7rgM<br /> | 140737488355328 / &lt;br&gt;140710042265625<br /> | {{Monzo| 47 -7 -7 -7 }}<br /> | 0.33765<br /> | [[Aaron Krister Johnson]] (2011)<br /> |-<br /> | [[Landscape comma]]<br /> | Trizoguguma<br /> | 3zggM<br /> | 250047/250000<br /> | {{Monzo| -4 6 -6 3 }}<br /> | 0.32544<br /> | [[Yahya Abdal-Aziz]] (2005)<br /> |-<br /> | [[Izar comma]], bapbo schismina<br /> | Saquadtrizo-asepguma<br /> | s12za7gM<br /> | 13841287201 / &lt;br&gt;13839609375<br /> | {{Monzo| 0 -11 -7 12 }}<br /> | 0.20987<br /> | <br /> |-<br /> | [[Nanisma]]<br /> | Quinbisaruma<br /> | 10srM<br /> | &lt;abbr title=&quot;649037107316853453566312041152512 / 648966242035284859600333477874109&quot;&gt;(66 digits)&lt;/abbr&gt;<br /> | {{Monzo| 109 -67 0 -1 }}<br /> | 0.18904<br /> | [[Margo Schulter]] (2002)<br /> |-<br /> | laleruyo (171&amp;1547&amp;3125)<br /> | Laleruyoma<br /> | L11ryM<br /> | 3955078125 / 3954653486<br /> | {{Monzo| -1 4 11 -11 }}<br /> | 0.18588<br /> | <br /> |-<br /> | 87-fold starling comma<br /> | Twenetrizotriguma<br /> | <br /> | <br /> | {{Monzo| 86 174 -261 87 }}<br /> | 0.14469<br /> | <br /> |-<br /> | [[Revopentisma]]<br /> | Sasa-neruma<br /> | ss19rM<br /> | &lt;abbr title=&quot;11399736556781568 / 11398895185373143&quot;&gt;(34 digits)&lt;/abbr&gt;<br /> | {{Monzo| 47 4 0 -19 }}<br /> | 0.12778<br /> | [[Eliora]] (2023)<br /> |-<br /> | [[Starscape comma]]<br /> | Latritriru-ayoma<br /> | L9rayM<br /> | 645700815 / 645657712<br /> | {{Monzo| -4 17 1 -9 }}<br /> | 0.11557<br /> | <br /> |-<br /> | [[Nommisma]]<br /> | Quinla-zoyoyoma<br /> | 5LzzyM<br /> | &lt;abbr title=&quot;36030948116563575 / 36028797018963968&quot;&gt;(34 digits)&lt;/abbr&gt;<br /> | {{Monzo| -55 30 2 1 }}<br /> | 0.10336<br /> | [[Flora Canou]] (2023)<br /> |-<br /> | [[Euzenius comma]]<br /> | Sabiruquinyoma<br /> | s2r5yM<br /> | 78125000 / 78121827<br /> | {{Monzo| 3 -13 10 -2 }}<br /> | 0.070314<br /> | <br /> |-<br /> | [[Exodia comma]]<br /> | Trila-quadbizo-aleyoma<br /> | 3L8za11yM<br /> | 281484423828125 / 281474976710656<br /> | {{Monzo| -48 0 11 8 }}<br /> | 0.058104<br /> | <br /> |-<br /> | [[Septrongisma]]<br /> | Lala-sepru-atritriguma<br /> | LL7ra9gM<br /> | 205891132094649 / 205885750000000<br /> | {{Monzo| -7 30 -9 -7 }}<br /> | 0.045256<br /> | [[User:Xenllium|Xenllium]] (2026)<br /> |-<br /> | 171&amp;1547&amp;4973 comma<br /> | Satwethezo-atritribiguma<br /> | s23za18gM<br /> | &lt;abbr title=&quot;54737494680161832686 / 54736736297607421875&quot;&gt;(40 digits)&lt;/abbr&gt;<br /> | {{Monzo| 1 -15 -18 23 }}<br /> | 0.023986<br /> | <br /> |-<br /> | [[Technologisma]]<br /> | Trisa-quinbiru-aguma<br /> | 3s10ragM<br /> | &lt;abbr title=&quot;2251799813685248 / 2251783932057135&quot;&gt;(32 digits)&lt;/abbr&gt;<br /> | {{Monzo| 51 -13 -1 -10 }}<br /> | 0.012210<br /> | [[User:Godtone|Godtone]] (2024)<br /> |-<br /> | Termite<br /> | Satritribiru-athiseyoma<br /> | s18ra37yM<br /> | &lt;abbr title=&quot;37252902984619140625000000000 / 37252879910233655318543787489&quot;&gt;(58 digits)&lt;/abbr&gt;<br /> | {{Monzo| 9 -28 37 -18 }}<br /> | 0.0010723<br /> | <br /> |-<br /> | Neutrino<br /> |<br /> |<br /> | <br /> | {{Monzo| 1889 -2145 138 424 }}<br /> | 1.6361 × 10&lt;sup&gt;-10&lt;/sup&gt;<br /> | <br /> |}<br /> <br /> === 11-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[Lifthrasirsma]]<br /> | Sasa-biluguma<br /> | ss2(1ug)M<br /> | 536870912 / 535869675<br /> | {{Monzo| 29 -11 -2 0 -2 }}<br /> | 3.2317<br /> | [[Flora Canou]] (2023)<br /> |-<br /> | [[540/539|Swetisma]]<br /> | Lururuyoma<br /> | 1urryM<br /> | 540/539<br /> | {{Monzo| 2 3 1 -2 -1 }}<br /> | 3.2090<br /> | [[Manuel Op de Coul]] (2004)<br /> |-<br /> | [[Anthill comma]]<br /> | Satrilo-ayoyoma<br /> | s3(1o)yyM<br /> | 532400/531441<br /> | {{Monzo| 4 -12 2 0 3 }}<br /> | 3.1212<br /> | [[Budjarn Lambeth]] (2024)<br /> |-<br /> | [[4000/3993|Wizardharry comma]], pine comma<br /> | Triluyoma<br /> | 3(1uy)M<br /> | 4000/3993<br /> | {{Monzo| 5 -1 3 0 -3 }}<br /> | 3.0323<br /> | [[User:Godtone|Godtone]] (2023) for ''pine comma''<br /> |-<br /> | 23-11/7-comma<br /> | Twetheluzoma<br /> | 23(1uz)M<br /> | &lt;abbr title=&quot;896819112839771466727424 / 895430243255237372246531&quot;&gt;(48 digits)&lt;/abbr&gt;<br /> | {{Monzo| 15 0 0 23 -23 }}<br /> | 2.6832<br /> | <br /> |-<br /> | [[Symbiotic comma]]<br /> | Salozoma<br /> | s1ozM<br /> | 19712/19683<br /> | {{Monzo| 8 -9 0 1 1 }}<br /> | 2.5488<br /> | [[Dawson Berry]] (2020)<br /> |-<br /> | [[5632/5625|Vishdel comma]]<br /> | Saloquadguma<br /> | s1o4gM<br /> | 5632/5625<br /> | {{Monzo| 9 -2 -4 0 1 }}<br /> | 2.1531<br /> | <br /> |-<br /> | [[Nexus comma]], nexisma<br /> | Tribiloma<br /> | 6(1o)M<br /> | 1771561/1769472<br /> | {{Monzo| -16 -3 0 0 6 }}<br /> | 2.0427<br /> | [[Dawson Berry]] (2020)<br /> |-<br /> | [[Reef comma]]<br /> | Salubizoguma<br /> | s1u2zgM<br /> | 200704/200475<br /> | {{Monzo| 12 -6 -2 2 -1 }}<br /> | 1.9764<br /> | [[Dawson Berry]] (2022)<br /> |-<br /> | [[41503/41472|Argyria]], tinge<br /> | Lolotrizoma<br /> | 1oo3zM<br /> | 41503/41472<br /> | {{Monzo| -9 -4 0 3 2 }}<br /> | 1.2936<br /> | [[Gayle Young]] (2018) and [[Todd Harrop]] (2020) for ''tinge'' &lt;br&gt;[[Lériendil]] (2024) for ''argyria''<br /> |-<br /> | [[Alpharabian schisma]]<br /> | Trisa-tritriloma<br /> | 3s9(1o)M<br /> | 618121839509504 / 617673396283947<br /> | {{Monzo| 18 -31 0 0 9 }}<br /> | 1.2565<br /> | [[Dawson Berry]] (2024)<br /> |-<br /> | [[Olympia]]<br /> | Salururuma<br /> | s1urrM<br /> | 131072/130977<br /> | {{Monzo| 17 -5 0 -2 -1 }}<br /> | 1.2552<br /> | [[Flora Canou]] (2021)<br /> |-<br /> | [[37-11-comma]], 11-cycle schisma<br /> | Quinsa-thiseluma<br /> | 5s37(1u)M<br /> | &lt;abbr title=&quot;340282366920938463463374607431768211456 / 340039485861577398992406882305761986971&quot;&gt;(78 digits)&lt;/abbr&gt;<br /> | {{Monzo| 128 0 0 0 -37 }}<br /> | 1.2361<br /> | <br /> |-<br /> | [[Seascape comma]], undecimal hemifourths comma<br /> | Bilozoguguma<br /> | 2(1ozgg)M<br /> | 160083/160000<br /> | {{Monzo| -8 3 -4 2 2 }}<br /> | 0.89784<br /> | [[User:Tristanbay|Tristan Bay]] (2024) for ''seascape comma''<br /> |-<br /> | [[Sesdecal comma]]<br /> | Laquadlu-asepyoma<br /> | L4(1u)7yM<br /> | 234375/234256<br /> | {{Monzo| -4 1 7 0 -4 }}<br /> | 0.87923<br /> | <br /> |-<br /> | [[Triagnoshenisma]]<br /> | Trila-trilo-aguma<br /> | 3L3(1o)gM<br /> | 171885556953 / 171798691840<br /> | {{Monzo| -35 17 -1 0 3 }}<br /> | 0.87513<br /> | [[Dawson Berry]], [[User:Frostburn|Frostburn]] (2024) <br /> |-<br /> | [[Frameshift comma]]<br /> | Quadla-triluma<br /> | 4L3(1u)M<br /> | 22876792454961 / &lt;br&gt;22866405883904<br /> | {{Monzo| -34 28 0 0 -3 }}<br /> | 0.78620<br /> | [[Dawson Berry]] (2021)<br /> |-<br /> | [[Chrysia]]<br /> | Quadlo-atriruma<br /> | 4(1o)3rM<br /> | 43923/43904<br /> | {{Monzo| -7 1 0 -3 4 }}<br /> | 0.74905<br /> | [[VIxen]] (2025)<br /> |-<br /> | [[Sossmarvel comma]]<br /> | Trila-lusepruyoyoma<br /> | 3L1u7ryyM<br /> | &lt;abbr title=&quot;9730975341796875 / 9726998192586752&quot;&gt;(32 digits)&lt;/abbr&gt;<br /> | {{Monzo| -30 13 14 -7 -1 }}<br /> | 0.70772<br /> | [[Dawson Berry]] (2022)<br /> |-<br /> | [[3025/3024|Lehmerisma]]<br /> | Loloruyoyoma<br /> | 1ooryyM<br /> | 3025/3024<br /> | {{Monzo| -4 -3 2 -1 2 }}<br /> | 0.57240<br /> | [[Gene Ward Smith]] (2004)<br /> |-<br /> | [[Ptolemi-nicema]]<br /> | Quinbisa-twethetriluyoyoma<br /> | 10s69(1uyy)M<br /> | <br /> | {{Monzo| 137 -138 138 0 -69 }}<br /> | 0.56437<br /> | [[User:Eliora|Eliora]] (2023)<br /> |-<br /> | [[Elysia]]<br /> | Bilutrizoma<br /> | 2(1u3z)M<br /> | 117649/117612<br /> | {{Monzo| -2 -5 0 6 -2 }}<br /> | 0.54455<br /> | [[Lériendil]] (2024)<br /> |-<br /> | [[Quartisma]]<br /> | Saquinlu-azoma<br /> | s5(1u)zM<br /> | 117440512 / 117406179<br /> | {{Monzo| 24 -6 0 1 -5 }}<br /> | 0.50619<br /> | [[Dawson Berry]] (2020)<br /> |-<br /> | [[9801/9800|Kalisma]], Gauss' comma<br /> | Biloruguma<br /> | 2(1org)M<br /> | 9801/9800<br /> | {{Monzo| -3 4 -2 -2 2 }}<br /> | 0.17665<br /> | [[Margo Schulter]] (2000)&lt;br&gt;[[Gene Ward Smith]] (2004) for ''Gauss' comma''<br /> |-<br /> | [[151263/151250|Odiheim comma]]<br /> | Luluquinzo-aquadguma<br /> | 1uu5za4gM<br /> | 151263/151250<br /> | {{Monzo| -1 2 -4 5 -2 }}<br /> | 0.14879<br /> | <br /> |-<br /> | [[Countercentisma]]<br /> | <br /> | <br /> | (3776 digits)<br /> | {{Monzo| -1 -3300 2700 0 -300 }}<br /> | 0.14187<br /> | [[User:CompactStar|CompactStar]] (2024)<br /> |-<br /> | [[Spoob]]<br /> | Tribiluzozoguma<br /> | 6(1uzzg)M<br /> | 27682574402 / 27680640625<br /> | {{Monzo| 1 0 -6 12 -6 }}<br /> | 0.12094<br /> | [[User:Eliora|Eliora]] (2023)<br /> |-<br /> | [[Luxma]]<br /> | Saquinlu-aquadguma<br /> | s5(1u)4gM<br /> | 100663296/100656875<br /> | {{Monzo|25 1 -4 0 -5}}<br /> | 0.11043<br /> | [[User:Tristanbay|Tristan Bay]] (2026)<br /> |-<br /> | [[Syntonoschisma]]<br /> | Trisa-lusepyoma<br /> | 3s1u7yM<br /> | 83886080000000 / &lt;br&gt;83881572334857<br /> | {{Monzo|30 -27 7 0 -1}}<br /> | 0.093031<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Parimo]]<br /> | Satribilo-aguma<br /> | s6(1o)gM<br /> | 1771561/1771470<br /> | {{Monzo|-1 -11 -1 0 6}}<br /> | 0.088931<br /> | <br /> |-<br /> | Parisma<br /> | Laquadlu-aruruguma<br /> | L4(1u)rrgM<br /> | 14348907 / 14348180<br /> | {{Monzo|-2 15 -1 -2 -4}}<br /> | 0.087717<br /> | <br /> |-<br /> | [[Blare comma]]<br /> | Laquadquadlo-aquadtrizoma<br /> | L16(1o)12zM<br /> | &lt;abbr title=&quot;636003407850068828189211361 / 635974777627126753067532288&quot;&gt;(54 digits)&lt;/abbr&gt;<br /> | {{Monzo|-51 -24 0 12 16}}<br /> | 0.077935<br /> | [[User:Akselai|Akselai]] (2024)<br /> |-<br /> | Ultimo<br /> | Quadlo-asepru-ayoyoma<br /> | 4(1o)7rayyM<br /> | 3294225/3294172<br /> | {{Monzo|-2 2 2 -7 4}}<br /> | 0.027854<br /> | <br /> |-<br /> | Parismina<br /> | Sasa-quinbilo-azozoma<br /> | ss10(1o)zzM<br /> | 2541867610898 / &lt;br&gt;2541865828329<br /> | {{Monzo|1 -26 0 2 10}}<br /> | 0.0012141<br /> | <br /> |}<br /> <br /> === 13-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[Wilschisma]]<br /> | Sathoyoma<br /> | s3oyM<br /> | 532480/531441<br /> | {{Monzo| 13 -12 1 0 0 1 }}<br /> | 3.3814<br /> | [[Flora Canou]] (2021)<br /> |-<br /> | Bean<br /> | Sathuquinluma<br /> | s3u5(1u)M<br /> | 2097152/2093663<br /> | {{Monzo| 21 0 0 0 -5 -1 }}<br /> | 2.8826<br /> | <br /> |-<br /> | [[625/624|Tunbarsma]]<br /> | Thuquadyoma<br /> | 3u4yM<br /> | 625/624<br /> | {{Monzo| -4 -1 4 0 0 -1 }}<br /> | 2.7722<br /> | <br /> |-<br /> | [[Fifthless mohohomma]]<br /> | Thuthululuyoma<br /> | 3uu1uuyM<br /> | 20480/20449<br /> | {{Monzo| 12 0 1 0 -2 -2 }}<br /> | 2.6225<br /> | [[User:原井玉葱郎|Misohito Nakai]] (2025)<br /> |-<br /> | [[676/675|Island comma]]<br /> | Bithoguma<br /> | 2(3og)M<br /> | 676/675<br /> | {{Monzo| 2 -3 -2 0 0 2 }}<br /> | 2.5629<br /> | [[Mike Battaglia]] (2011)<br /> |-<br /> | [[729/728|Squbema]]<br /> | Lathuruma<br /> | L3urM<br /> | 729/728<br /> | {{Monzo| -3 6 0 -1 0 -1 }}<br /> | 2.3764<br /> | <br /> |-<br /> | [[2200/2197|Petrma]]<br /> | Trithu-aloyoyoma<br /> | 3(3u)1oyyM<br /> | 2200/2197<br /> | {{Monzo| 3 0 2 0 1 -3 }}<br /> | 2.3624<br /> | <br /> |-<br /> | [[Tridecimal eighth-octave comma]]<br /> | Thotrilo-aguma<br /> | 3o3(1o)gM<br /> | 17303/17280<br /> | {{Monzo| -7 -3 -1 0 3 1 }}<br /> | 2.3028<br /> | [[Budjarn Lambeth]] (2024)<br /> |-<br /> | [[Sinarabian comma]]<br /> | Lathotriluma<br /> | L3o3(1u)M<br /> | 85293/85184<br /> | {{Monzo| -6 8 0 0 -3 1 }}<br /> | 2.2138<br /> | [[Dawson Berry]] (2025)<br /> |-<br /> | [[1575/1573|Nicola]]<br /> | Thululuzoyoyoma<br /> | 3u1uuzyyM<br /> | 1575/1573<br /> | {{Monzo| 0 2 2 1 -2 -1 }}<br /> | 2.1998<br /> | <br /> |-<br /> | [[Eufalesma]]<br /> | <br /> | <br /> | 35035/34992<br /> | {{Monzo| -4 -7 1 2 1 1 }}<br /> | 2.1261<br /> | [[Eufalesio]] (2026)<br /> |-<br /> | [[Navicular comma]]<br /> | Trithu-aluzoma<br /> | 3(3u)1uzM<br /> | 24192/24167<br /> | {{Monzo| 7 3 0 1 -1 -3 }}<br /> | 1.7900<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1001/1000|Sinbadma]]<br /> | Tholozotriguma<br /> | 3o1oz3gM<br /> | 1001/1000<br /> | {{Monzo| -3 0 -3 1 1 1 }}<br /> | 1.7303<br /> | <br /> |-<br /> | [[4459/4455|Tristanisma]]<br /> | Tholutrizo-aguma<br /> | 3o1u3zagM<br /> | 4459/4455<br /> | {{Monzo| 0 -4 -1 3 -1 1}}<br /> | 1.5537<br /> | [[User:Tristanbay|Tristan Bay]] (2024)<br /> |-<br /> | [[Tridecapyth comma]]<br /> | Trisathoma<br /> | 3s3oM<br /> | 3489660928 / 3486784401<br /> | {{Monzo| 28 -20 0 0 0 1 }}<br /> | 1.4276<br /> | [[Dawson Berry]] (2021)<br /> |-<br /> | [[Cantonisma]]<br /> | Trithoru-ayoma<br /> | 3(3or)yM<br /> | 10985/10976<br /> | {{Monzo| -5 0 1 -3 0 3 }}<br /> | 1.4190<br /> | [[Margo Schulter]] (2013)<br /> |-<br /> | [[Punctisma]]<br /> | Sathutrizoguma<br /> | s3u3zgM<br /> | 43904/43875<br /> | {{Monzo| 7 -3 -3 3 0 -1 }}<br /> | 1.1439<br /> | [[User:Jerdle|Jerdle]], [[Dawson Berry]] (2023)<br /> |-<br /> | [[Neguschisma]]<br /> | Lala-thulozoma<br /> | LL3u1ozM<br /> | 13640319 / 13631488<br /> | {{Monzo| -20 11 0 1 1 -1 }}<br /> | 1.1212<br /> | [[User:Tristanbay|Tristan Bay]] (2024)<br /> |-<br /> | [[1716/1715|Lummic comma]]<br /> | Tholotriru-aguma<br /> | 3o1o3ragM<br /> | 1716/1715<br /> | {{Monzo| 2 1 -1 -3 1 1 }}<br /> | 1.0092<br /> | <br /> |-<br /> | [[Pseudovishnuzma]]<br /> | Sasa-thozosepbiguma<br /> | ss3oz14gM<br /> | 6106906624 / 6103515625<br /> | {{Monzo| 26 0 -14 1 0 1 }}<br /> | 0.96157<br /> | [[User:Eliora|Eliora]] (2023)<br /> |-<br /> | [[Sercloreminisma]]<br /> | Bithuthuzo-aguma<br /> | 2(3uuz)gM<br /> | 142884/142805<br /> | {{Monzo| 2 6 -1 2 0 -4 }}<br /> | 0.95746<br /> | [[Francium]] (2024)<br /> |-<br /> | [[2080/2079|Ibnsinma, sinaisma]]<br /> | Tholuruyoma<br /> | 3o1uryM<br /> | 2080/2079<br /> | {{Monzo| 5 -3 1 -1 -1 1 }}<br /> | 0.83252<br /> | [[Margo Schulter]], [[Gene Ward Smith]] (2012) &lt;br&gt;[[Flora Canou]] (2023)<br /> |-<br /> | [[Phaotic comma]], phaotisma<br /> | Sathotriyoma<br /> | s3u3yM<br /> | 256000/255879<br /> | {{Monzo| 11 -9 3 0 0 -1 }}<br /> | 0.81847<br /> | [[Dawson Berry]] (2021)<br /> |-<br /> | [[Kuragesma]]<br /> | Tritho-aquadlu-ayoma<br /> | 3(3o)4(1u)gM<br /> | 43940/43923<br /> | {{Monzo| 2 -1 1 0 -4 3 }}<br /> | 0.66993<br /> | [[User:原井玉葱郎|Misohito Nakai]] (2025)<br /> |-<br /> | [[Barbadisma]]<br /> | Quadla-thuyoma<br /> | 4L3uyM<br /> | 114383962274805 / 114349209288704<br /> | {{Monzo| -43 28 1 0 0 -1 }}<br /> | 0.52608<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[4096/4095|Minisma]]<br /> | Sathuruguma<br /> | s3urgM<br /> | 4096/4095<br /> | {{Monzo| 12 -2 -1 -1 0 -1 }}<br /> | 0.42272<br /> | [[Flora Canou]] (2026)<br /> |-<br /> | [[4225/4224|Leprechaun comma]]<br /> | Thotholuyoyoma<br /> | 3oo1uyyM<br /> | 4225/4224<br /> | {{Monzo| -7 -1 2 0 -1 2 }}<br /> | 0.40981<br /> | [[Margo Schulter]] (2012)<br /> |-<br /> | [[6656/6655|Jacobin comma]]<br /> | Thotrilu-aguma<br /> | 3o3(1u)gM<br /> | 6656/6655<br /> | {{Monzo| 9 0 -1 0 -3 1 }}<br /> | 0.26012<br /> | [[Gene Ward Smith]] (2014)<br /> |-<br /> | [[Catasma]]<br /> | Latrithuyoyoma<br /> | L3(3uyy)M<br /> | 140625/140608<br /> | {{Monzo| -6 2 6 0 0 -3 }}<br /> | 0.20930<br /> | [[Tristan Bay]] (2023)<br /> |-<br /> | [[492128/492075|13^3⋅7/25 schismina]]<br /> | Satritho-azoguguma<br /> | s3(3o)zggM<br /> | 492128/492075<br /> | {{Monzo| 5 -9 -2 1 0 3 }}<br /> | 0.18646<br /> | <br /> |-<br /> | [[Harmonisma]]<br /> | Thuthutrilo-aruma<br /> | 3uu3(1o)rM<br /> | 10648/10647<br /> | {{Monzo| 3 -2 0 -1 3 -2 }}<br /> | 0.16260<br /> | [[Margo Schulter]] (2002)<br /> |-<br /> | [[Pentonisma]]<br /> | Saquinthuzoguma<br /> | s5(3uzg)M<br /> | 281974669312 / 281950621875<br /> | {{Monzo| 24 -5 -5 5 0 -5 }}<br /> | 0.14765<br /> | [[User:Xenllium|Xenllium]] (2022)<br /> |-<br /> | [[Pontigailimma]]<br /> | Thururuquinguma<br /> | 3urr5gM<br /> | 1990656/1990625<br /> | {{Monzo| 13 5 -5 -2 0 -1 }}<br /> | 0.026960<br /> | [[User:Recentlymaterialized|Recentlymaterialized]] (2024)<br /> |-<br /> | [[Grossmisma]]<br /> | septholo-azoguma<br /> | 7(3o1o)zgM<br /> | &lt;abbr title=&quot;8559537565427849 / 8559456430325760&quot;&gt;(32 digits)&lt;/abbr&gt;<br /> | {{Monzo| -30 -13 -1 1 7 7 }}<br /> | 0.016410<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Chalmersia]]<br /> | Lathotholuruguguma<br /> | L3oo1urggM<br /> | 123201/123200<br /> | {{Monzo| -6 6 -2 -1 -1 2 }}<br /> | 0.01405<br /> | [[Gene Ward Smith]] (2003)<br /> |-<br /> | [[Lanasma]]<br /> | Trila-septrithu-aquinquadbizoma<br /> | 3L21(3u)40zM<br /> | &lt;abbr title=&quot;6366805760909027985741435139224001 / 6366804434232663711262864979263488&quot;&gt;(68 digits)&lt;/abbr&gt;<br /> | {{Monzo| -33 -1 0 40 0 -21 }}<br /> | 3.6074 × 10&lt;sup&gt;-4&lt;/sup&gt;<br /> | [[User:Angekallikoita|Ange]] (2025)<br /> |}<br /> <br /> === 17-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[Quinticular comma]]<br /> | Saquinsoma<br /> | s5(17o)M<br /> | 1419857/1417176<br /> | {{Monzo| -3 -11 0 0 0 0 5 }}<br /> | 3.2720<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[561/560|Monardisma]]<br /> | Soloruguma<br /> | 17o1orgM<br /> | 561/560<br /> | {{Monzo| -4 1 -1 -1 1 0 1 }}<br /> | 3.0887<br /> | [[Scott Dakota]] (2023)<br /> |-<br /> | [[595/594|Dakotisma]]<br /> | Soluzoyoma<br /> | 17o1uzyM<br /> | 595/594<br /> | {{Monzo| -1 -3 1 1 -1 0 1 }}<br /> | 2.9121<br /> | [[Praveen Venkataramana]] (2022)<br /> |-<br /> | [[715/714|September comma]]<br /> | Sutholoruyoma<br /> | 17u3o1oryM<br /> | 715/714<br /> | {{Monzo| -1 -1 1 -1 1 1 -1 }}<br /> | 2.4230<br /> | [[Scott Dakota]] (2021)<br /> |-<br /> | [[833/832|Horizma, horizon comma]]<br /> | Sothuzozoma<br /> | 17o3uzzM<br /> | 833/832<br /> | {{Monzo| -6 0 0 2 0 -1 1 }}<br /> | 2.0796<br /> | [[User:Jerdle|Jerdle]] (2021)<br /> |-<br /> | [[936/935|Ainisma, ainic comma]]<br /> | Sutholuguma<br /> | 17u3o1ugM<br /> | 936/935<br /> | {{Monzo| 3 2 -1 0 -1 1 -1 }}<br /> | 1.8506<br /> | [[Dawson Berry]] (2020)<br /> |-<br /> | [[2025/2023|Fidesma]]<br /> | Susuruyoyoma<br /> | 17uuryyM<br /> | 2025/2023<br /> | {{Monzo| 0 4 2 -1 0 0 -2 }}<br /> | 1.7107<br /> | [[Dawson Berry]] (2023)<br /> |-<br /> | [[1089/1088|Twosquare comma]]<br /> | Suloloma<br /> | 17u1ooM<br /> | 1089/1088<br /> | {{Monzo| -6 2 0 0 2 0 -1 }}<br /> | 1.5905<br /> | [[User:Kaiveran|Kaiveran]] (2018)<br /> |-<br /> | [[1156/1155|Quadrantonisma]]<br /> | Sosoluruguma<br /> | 17oo1urgM<br /> | 1156/1155<br /> | {{Monzo| 2 -1 -1 -1 -1 0 2 }}<br /> | 1.4983<br /> | [[Flora Canou]] (2023)<br /> |-<br /> | [[1225/1224|Noellisma]]<br /> | Subizoyoma<br /> | 17u2zyM<br /> | 1225/1224<br /> | {{Monzo| -3 -2 2 2 0 0 -1 }}<br /> | 1.4138<br /> | [[Flora Canou]] (2022)<br /> |-<br /> | [[1275/1274|Cimbrisma]]<br /> | Sothubiruyoma<br /> | 17o3u2ryM<br /> | 1275/1274<br /> | {{Monzo| -1 1 2 -2 0 -1 1 }}<br /> | 1.3584<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[1701/1700|Palingenetic comma, palingenesis]]<br /> | Suzoguguma<br /> | 17uzggM<br /> | 1701/1700<br /> | {{Monzo| -2 5 -2 1 0 0 -1 }}<br /> | 1.0181<br /> | [[Dawson Berry]] (2021)<br /> |-<br /> | [[Laser comma]]<br /> | Lasorutriyoma<br /> | L17or3yM<br /> | 57375/57344<br /> | {{Monzo| -13 3 3 -1 0 0 1 }}<br /> | 0.93564<br /> | [[User:Jerdle|Jerdle]] (2023)<br /> |-<br /> | [[2058/2057|Xenisma]]<br /> | Sululutrizoma<br /> | 17u1uu3zM<br /> | 2058/2057<br /> | {{Monzo| 1 1 0 3 -2 0 -1 }}<br /> | 0.84143<br /> | [[Margo Schulter]] (2000)<br /> |-<br /> | [[11016/11011|Cyclops comma]]<br /> | Sothululuruma<br /> | 17o3u1uurM<br /> | 11016/11011<br /> | {{Monzo| 3 4 0 -1 -2 -1 1 }}<br /> | 0.78596<br /> | [[Eliora]] (2022)<br /> |-<br /> | [[24576/24565|Mavka comma]], archagallisma<br /> | Trisu-aguma<br /> | 3(17u)gM<br /> | 24576/24565<br /> | {{Monzo| 13 1 -1 0 0 0 -3 }}<br /> | 0.77506<br /> | [[Eliora]] (2022) for ''mavka comma''<br /> |-<br /> | [[2431/2430|Heptacircle comma]]<br /> | Sothologuma<br /> | 17o3o1ogM<br /> | 2431/2430<br /> | {{Monzo| -1 -5 -1 0 1 1 1 }}<br /> | 0.71230<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[2500/2499|Sperasma]]<br /> | Subiruyoyoma<br /> | 17u2ryyM<br /> | 2500/2499<br /> | {{Monzo| 2 -1 4 -2 0 0 -1 }}<br /> | 0.69263<br /> | [[Dawson Berry]] (2023)<br /> |-<br /> | [[2601/2600|Sextantonisma]]<br /> | Sosothuguguma<br /> | 17oo3uggM<br /> | 2601/2600<br /> | {{Monzo| -3 2 -2 0 0 -1 2 }}<br /> | 0.66573<br /> | [[Flora Canou]] (2023)<br /> |-<br /> | [[Semisixthmisma]]<br /> | Trisu-athutriloma<br /> | 3(17u)3u3(1o)M<br /> | 63888/63869<br /> | {{Monzo| 4 1 0 0 3 -1 -3 }}<br /> | 0.51494<br /> | [[User:Xenllium|Xenllium]] (2024)<br /> |-<br /> | [[4914/4913|Baladisma]]<br /> | Trisu-athozoma<br /> | 3(17u)3ozM<br /> | 4914/4913<br /> | {{Monzo| 1 3 0 1 0 1 -3 }}<br /> | 0.35234<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[5832/5831|Chlorisma]]<br /> | Sutriruma<br /> | 17u3rM<br /> | 5832/5831<br /> | {{Monzo| 3 6 0 -3 0 0 -1 }}<br /> | 0.29688<br /> | [[User:Jerdle|Jerdle]] (2021)<br /> |-<br /> | [[Galileisma]]<br /> | Lalesu-aguma<br /> | L11(17u)gM<br /> | 171382426877952 / 171359481538165<br /> | {{Monzo| 14 21 -1 0 0 0 -11 }}<br /> | 0.23180<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Centisma]]<br /> |<br /> |<br /> |<br /> | 2.3.17 {{Monzo| -1001 -400 400 }}<br /> | 0.16345<br /> | [[CompactStar]] (2023)<br /> |-<br /> | [[Flashma]]<br /> | Sotholuzotriguma<br /> | 17o3o1uz3gM<br /> | 12376/12375<br /> | {{Monzo| 3 -2 -3 1 -1 1 1 }}<br /> | 0.13989<br /> | [[User:Kaiveran|Kaiveran]] (2016)<br /> |-<br /> | [[Sparkisma]]<br /> | Sululuruyoyoma<br /> | 17u1uuryyM<br /> | 14400/14399<br /> | {{Monzo| 6 2 2 -1 -2 0 -1 }}<br /> | 0.12023<br /> | [[User:Kaiveran|Kaiveran]] (2016)<br /> |-<br /> | [[Insanobromisma]]<br /> | Sepquinsuyoyoma<br /> | 35(17uyy)M<br /> | <br /> | {{Monzo| 36 -35 70 0 0 0 -35 }}<br /> | 0.095608<br /> | [[Eliora]] (2023)<br /> |-<br /> | [[1257795/1257728|Large triquarterisma]]<br /> | Latrisulo-azoyoma<br /> | L3(17u1o)zyM<br /> | 1257795/1257728<br /> | {{Monzo| -8 3 1 1 3 0 -3 }}<br /> | 0.092222<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[471648/471625|Small triquarterisma]]<br /> | Triso-alutriruguma<br /> | 3(17o)1u3(rg)M<br /> | 471648/471625<br /> | {{Monzo| 5 1 -3 -3 -1 0 3 }}<br /> | 0.084426<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[28561/28560|Pisanoisma]]<br /> | Suquadtho-aruguma<br /> | 17u4(3o)rgM<br /> | 28561/28560<br /> | {{Monzo| -4 -1 -1 -1 0 4 -1 }}<br /> | 0.060616<br /> | [[Budjarn Lambeth]] (2024)<br /> |-<br /> | [[E-shaped comma]]<br /> | Susuthoquadzoma<br /> | 17uu3o4zM<br /> | 31213/31212<br /> | {{Monzo| -2 -3 0 4 0 1 -2 }}<br /> | 0.055466<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Lateral comma]]<br /> | Sasuthotholoyoma<br /> | s17u3oo1oyM<br /> | 37180/37179<br /> | {{Monzo| 2 -7 1 0 1 2 -1 }}<br /> | 0.046564<br /> | [[User:Akselai|Akselai]] (2024)<br /> |-<br /> | [[Clevelandisma]]<br /> | Sotribizoguma<br /> | 17o6(zg)M<br /> | 2000033/2000000<br /> | {{Monzo| -7 0 -6 6 0 0 1 }}<br /> | 0.028565<br /> | [[Lériendil]] (2024)<br /> |-<br /> | [[Scintillisma]]<br /> | Lasuthuluquadzo-aguma<br /> | L17u3u1u4zagM<br /> | 194481/194480<br /> | {{Monzo| -4 4 -1 4 -1 -1 -1 }}<br /> | 0.0089018<br /> | [[Margo Schulter]] (2012)<br /> |-<br /> | [[Aksial comma]]<br /> | Sotritho-aquinru-aguma<br /> | 17o3(3o)5ragM<br /> | 336141/336140<br /> | {{Monzo| -2 2 -1 -5 0 3 1 }}<br /> | 0.0051503<br /> | [[User:Akselai|Akselai]] (2024)<br /> |}<br /> <br /> === 19-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[513/512|Undevicesimal schisma]], undevicesimal formal comma, Boethius' comma<br /> | Lanoma<br /> | L19oM<br /> | 513/512<br /> | 2.3.19 {{Monzo| -9 3 1 }}<br /> | 3.3780<br /> | Plainsound Music Edition (2020)&lt;ref&gt;[https://marsbat.space/pdfs/HEJI2legend+series.pdf The Helmholtz-Ellis JI Pitch Notation (HEJI)]&lt;/ref&gt; for ''undevicesimal schisma''<br /> |-<br /> | [[6144/6137|Langwisma]]<br /> | Nunusuma<br /> | 19uu17uM<br /> | 6144/6137<br /> | {{Monzo| 11 1 0 0 0 0 -1 -2 }}<br /> | 1.9736<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[969/968|Kingfisher comma]]<br /> | Nosoluluma<br /> | 19o17o1uuM<br /> | 969/968<br /> | {{Monzo| -3 1 0 0 -2 0 1 1 }}<br /> | 1.7875<br /> | [[Budjarn Lambeth]] (2025)<br /> |-<br /> | [[Mercurial comma]]<br /> | Quinnosu-abiruyoma<br /> | 5(19o17u)rryyM<br /> | 557122275 / 556583944<br /> | {{Monzo| -3 2 2 -2 0 0 -5 5 }}<br /> | 1.6736<br /> | [[User:Yourmusic Productions|Yourmusic Productions]] (2020)<br /> |-<br /> | [[1216/1215|Password, Eratosthenes' comma]]<br /> | Sanoguma<br /> | s19ogM<br /> | 1216/1215<br /> | {{Monzo| 6 -5 -1 0 0 0 0 1 }}<br /> | 1.4243<br /> | <br /> |-<br /> | [[1331/1330|Solvejgsma]]<br /> | Nutrilo-aruguma<br /> | 19u3(1o)rgM<br /> | 1331/1330<br /> | {{Monzo| -1 0 -1 -1 3 0 0 -1 }}<br /> | 1.3012<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[1445/1444|Aureusma]]<br /> | Nunusosoyoma<br /> | 19uu17ooyM<br /> | 1445/1444<br /> | {{Monzo| -2 0 1 0 0 0 2 -2 }}<br /> | 1.1985<br /> | [[Flora Canou]] (2021)<br /> |-<br /> | [[1521/1520|Pinkanberry]]<br /> | Nuthothoguma<br /> | 19u3oogM<br /> | 1521/1520<br /> | {{Monzo| -4 2 -1 0 0 2 0 -1 }}<br /> | 1.1386<br /> | [[User:Kaiveran|Kaiveran]] (2021)<br /> |-<br /> | [[1540/1539|Kevolisma]]<br /> | Nulozoyoma<br /> | 19u1ozyM<br /> | 1540/1539<br /> | {{Monzo| 2 -4 1 1 1 0 0 -1 }}<br /> | 1.1245<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[3213/3211|Cobaltomenisma]]<br /> | Nusothuthuzoma<br /> | 19u17o3uuzM<br /> | 3213/3211<br /> | {{Monzo| 0 3 0 1 0 -2 1 -1 }}<br /> | 1.0780<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1729/1728|Ramanujanisma]]<br /> | Nothozoma<br /> | 19o3ozM<br /> | 1729/1728<br /> | {{Monzo| -6 -3 0 1 0 1 0 1 }}<br /> | 1.0016<br /> | [[Frédéric Gagné]] (2021)<br /> |-<br /> | [[3971/3969|Heartlandisma]]<br /> | Nonoloruruma<br /> | 19oo1orrM<br /> | 3971/3969<br /> | {{Monzo| 0 -4 0 -2 1 0 0 2 }}<br /> | 0.87216<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[830297/829939|Minthtone schismina]]<br /> | Trinuso-abitholuma<br /> | 3(19u17o)2(3o1u)M<br /> | 830297/829939<br /> | {{Monzo| 0 0 0 0 -2 2 3 -3 }}<br /> | 0.74662<br /> | [[User:Recentlymaterialized|Recentlymaterialized]] (2024)<br /> |-<br /> | [[2376/2375|Trichthonisma]]<br /> | Nulotriguma<br /> | 19u1o3gM<br /> | 2376/2375<br /> | {{Monzo| 3 3 -3 0 1 0 0 -1 }}<br /> | 0.72879<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Crawma]]<br /> | Nuquadso-atrithuma<br /> | 19u4(17o)3(3u)M<br /> | 83521/83486<br /> | {{Monzo| -1 0 0 0 0 -3 4 -1 }}<br /> | 0.72564<br /> | [[groundfault]] (2023)<br /> |-<br /> | [[2432/2431|Blumeyer comma]]<br /> | Nosuthuluma<br /> | 19o17u3u1uM<br /> | 2432/2431<br /> | {{Monzo| 7 0 0 0 -1 -1 -1 1 }}<br /> | 0.71200<br /> | [[Douglas Blumeyer]] (2015)<br /> |-<br /> | [[93347/93312|Trilute comma]]<br /> | Notrisoma<br /> | 19o3(17o)M<br /> | 93347/93312<br /> | {{Monzo| -7 -6 0 0 0 0 3 1 }}<br /> | 0.64924<br /> | [[Xenllium]] (2025)<br /> |-<br /> | [[2926/2925|Neovulture comma, neovulturisma]]<br /> | Nothulozoguguma<br /> | 19o3u1ozggM<br /> | 2926/2925<br /> | {{Monzo| 1 -2 -2 1 1 -1 0 1 }}<br /> | 0.59177<br /> | [[Xenllium]] (2023)<br /> |-<br /> | [[3136/3135|Neomirkwai comma, neomirkwaisma]]<br /> | Nuluzozoguma<br /> | 19u1uzzgM<br /> | 3136/3135<br /> | {{Monzo| 6 -1 -1 2 -1 0 0 -1 }}<br /> | 0.55214<br /> | [[Xenllium]] (2023)<br /> |-<br /> | [[116640/116603|Large tridevisemma]]<br /> | Trinu-asuyoma<br /> | 3(19u)17uyM<br /> | 116640/116603<br /> | {{Monzo| 5 6 1 0 0 0 -1 -3 }}<br /> | 0.54926<br /> | [[Xenllium]] (2025)<br /> |-<br /> | [[3250/3249|Martebisma]]<br /> | Nunuthotriyoma<br /> | 19uu3o3yM<br /> | 3250/3249<br /> | {{Monzo| 1 -2 3 0 0 1 0 -2 }}<br /> | 0.53277<br /> | [[Xenllium]] (2023)<br /> |-<br /> | [[48013/48000|Small tridevisemma]]<br /> | Trino-azotriguma<br /> | 3(19o)z3gM<br /> | 48013/48000<br /> | {{Monzo| -7 -1 -3 1 0 0 0 3 }}<br /> | 0.46881<br /> | [[Xenllium]] (2025)<br /> |-<br /> | [[4200/4199|Neosatanisma]]<br /> | Nusuthuzoyoyoma<br /> | 19u17u3uzyyM<br /> | 4200/4199<br /> | {{Monzo| 3 1 2 1 0 -1 -1 -1 }}<br /> | 0.41225<br /> | [[Xenllium]] (2023)<br /> |-<br /> | [[176000/175959|Triseptichrome comma]]<br /> | Nulotriruyoma<br /> | 19u1o3(ry)M<br /> | 176000/175959<br /> | {{Monzo| 7 -3 3 -3 1 0 0 -1 }}<br /> | 0.40335<br /> | [[Xenllium]] (2025)<br /> |-<br /> | [[5776/5775|Neovish comma, neovishma]]<br /> | Nonoluruguguma<br /> | 19oo1urggM<br /> | 5776/5775<br /> | {{Monzo| 4 -1 -2 -1 -1 0 0 2 }}<br /> | 0.29975<br /> | [[Xenllium]] (2023)<br /> |-<br /> | [[5929/5928|Manzanisma]]<br /> | Nuthubilozoma<br /> | 19u3u2(1oz)M<br /> | 5929/5928<br /> | {{Monzo| -3 -1 0 2 2 -1 0 -1 }}<br /> | 0.29202<br /> | [[Xenllium]] (2025)<br /> |-<br /> | [[5985/5984|Neogrendel comma, neogrendelisma]]<br /> | Nosuluzoyoma<br /> | 19o17u1uzyM<br /> | 5985/5984<br /> | {{Monzo| -5 2 1 1 -1 0 -1 1 }}<br /> | 0.28929<br /> | [[Xenllium]] (2023)<br /> |-<br /> | BMO schismina<br /> | Sabinothuma<br /> | s2(19o3u)M<br /> | 369664/369603<br /> | {{Monzo| 10 -7 0 0 0 -2 0 2 }}<br /> | 0.28570<br /> | <br /> |-<br /> | [[6175/6174|Neonewtisma]]<br /> | Nothotriru-ayoyoma<br /> | 19o3o3rayyM<br /> | 6175/6174<br /> | {{Monzo| -1 -2 2 -3 0 1 0 1 }}<br /> | 0.28038<br /> | [[Xenllium]] (2023)<br /> |-<br /> | [[6860/6859|Devicubisma]]<br /> | Trinuzo-ayoma<br /> | 3(19uz)yM<br /> | 6860/6859<br /> | {{Monzo| 2 0 1 3 0 0 0 -3 }}<br /> | 0.25238<br /> | [[Xenllium]] (2025)<br /> |-<br /> | [[Undevicesimal counterschisma]]<br /> | Seplanuma<br /> | 7L19uM<br /> | &lt;abbr title=&quot; 717897987691852588770249 / 717799705396186072481792&quot;&gt;(48 digits)&lt;/abbr&gt;<br /> | 2.3.19 {{Monzo| -75 50 -1 }}<br /> | 0.23703<br /> | [[Xenllium]] (2025)<br /> |-<br /> | Frouggie comma<br /> | Nusuquinthu-aquadloma<br /> | 19u17u5(3u)4(1o)M<br /> | 119939072 / 119927639<br /> | {{Monzo| 13 0 0 0 4 -5 -1 -1 }}<br /> | 0.16503<br /> | [[Douglas Blumeyer]] (2020)<br /> |-<br /> | [[12636/12635|Padriellisma]]<br /> | Nunuthoruguma<br /> | 19uu3orgM<br /> | 12636/12635<br /> | {{Monzo| 2 5 -1 -1 0 1 0 -2 }}<br /> | 0.13701<br /> | [[Xenllium]] (2025)<br /> |-<br /> | [[Lakisma]]<br /> | Saquadnoso-aguma<br /> | s4(19o17o)gM<br /> | 10884540241 / 10883911680<br /> | {{Monzo| -12 -12 -1 0 0 0 4 4 }}<br /> | 0.09998<br /> | [[User:Flirora|+merlan #flirora]] (2021)<br /> |-<br /> | [[Aubertisma]]<br /> | Nosothutrilu-arutriyoma<br /> | 19o17o3u3(1u)r3yM<br /> | 121125/121121<br /> | {{monzo| 0 1 3 -1 -3 -1 1 1 }}<br /> | 0.057173<br /> | [[Francium]] (2025)<br /> |-<br /> | Pollar comma<br /> | Nunusuquintho-aluluma<br /> | 19uu17u5(3o)1uuM<br /> | 742586/742577<br /> | {{Monzo| 1 0 0 0 -2 5 -1 -2 }}<br /> | 0.020982<br /> | [[Douglas Blumeyer]] (2020)<br /> |-<br /> | [[Decimillisma]], 19-limit decimill<br /> | Sanosorurutriguma<br /> | s19o17orr3gM<br /> | 165376/165375<br /> | {{Monzo| 9 -3 -3 -2 0 0 1 1 }}<br /> | 0.010469<br /> | [[Flora Canou]] (2021), for ''decimillisma''<br /> |-<br /> | [[65/19 atom]]<br /> | Sasa-nuthoyoma<br /> | ss19u3oyM<br /> | 272629760 / 272629233<br /> | {{Monzo| 22 -15 1 0 0 1 0 -1 }}<br /> | 0.0033465<br /> | [[User:Recentlymaterialized|Recentlymaterialized]] (2024)<br /> |-<br /> | [[Devicisma]]<br /> | Nunusothutrilo-azoguma<br /> | 19uu17o3u3(1o)zgM<br /> | 633556/633555<br /> | {{Monzo| 2 -3 -1 1 3 -1 1 -2 }}<br /> | 0.0027326<br /> | [[Xenllium]] (2023)<br /> |-<br /> | [[11859211/11859210|Tredekisma]]<br /> | Quadno-athoquadlu-azoguma<br /> | 19o43o1u4zgM<br /> | 11859211/11859210<br /> | {{Monzo| -1 -4 -1 1 -4 1 0 4 }}<br /> | 0.000146<br /> | [[Eufalesio]] (2026)<br /> |}<br /> <br /> === 23-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[507/506|Laodicisma]]<br /> | Twethuthotholuma<br /> | 23u3oo1uM<br /> | 507/506<br /> | 2.3.11.13.23 {{Monzo| -1 1 -1 2 -1 }}<br /> | 3.4180<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[529/528|Preziosisma]]<br /> | Bitwetho-aluma<br /> | 23oo1uM<br /> | 529/528<br /> | 2.3.11.23 {{Monzo| -4 -1 -1 2 }}<br /> | 3.2758<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[576/575|Worcester comma]]<br /> | Twethuguguma<br /> | 23uggM<br /> | 576/575<br /> | 2.3.5.23 {{Monzo| 6 2 -2 -1 }}<br /> | 3.0082<br /> | [[User:Kaiveran|Kaiveran]] (2023)<br /> |-<br /> | [[9765625/9750528]]<br /> | Labitwethuquinyoma<br /> | L23uu10yM<br /> | 9765625/9750528<br /> | 2.3.5.23 {{Monzo| -11 -2 10 -2 }}<br /> | 2.6784<br /> | <br /> |-<br /> | [[736/735|Harvardisma]]<br /> | Twethoruruguma<br /> | 23orrgM<br /> | 736/735<br /> | 2.3.5.7.23 {{Monzo| 5 -1 -1 -2 1 }}<br /> | 2.3538<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[760/759|Squadronisma]]<br /> | Twethunoluyoma<br /> | 23u19o1uyM<br /> | 760/759<br /> | {{Monzo| 3 -1 1 0 -1 0 0 1 -1 }}<br /> | 2.2794<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[875/874|Nymphisma]]<br /> | Twethunuzotriyoma<br /> | 23u19uz3yM<br /> | 875/874<br /> | 2.5.7.19.23 {{Monzo| -1 3 1 -1 -1 }}<br /> | 1.9797<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[897/896|Lysistratisma]]<br /> | Twethothoruma<br /> | 23o3orM<br /> | 897/896<br /> | 2.3.7.13.23 {{Monzo| -7 1 -1 1 1 }}<br /> | 1.9311<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[3014656/3011499|23/17-schisma]]<br /> | Sasa-twethosuma<br /> | ss23o17uM<br /> | 3014656/3011499<br /> | 2.3.17.23 {{monzo| 17 -11 -1 1 }}<br /> | 1.8139<br /> | <br /> |-<br /> | [[2187/2185|Vashegyitisma]]<br /> | Latwethunuguma<br /> | L23u19ugM<br /> | 2187/2185<br /> | 3.5.19.23 {{monzo| 7 -1 -1 -1 }}<br /> | 1.5839<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1105/1104|Fragarisma]]<br /> | Twethusothoyoma<br /> | 23u17o3oyM<br /> | 1105/1104<br /> | {{Monzo| -4 -1 1 0 0 1 1 0 -1 }}<br /> | 1.5674<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[7942/7935|Brigade comma]]<br /> | Bitwethuno-aloguma<br /> | 23uu19oo1ogM<br /> | 7942/7935<br /> | {{Monzo| 1 -1 -1 0 1 0 0 2 -2 }}<br /> | 1.5266<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1197/1196|Rodessisma]]<br /> | Twethunothuzoma<br /> | 23u19o3uzM<br /> | 1197/1196<br /> | {{Monzo| -2 2 0 1 0 -1 0 1 -1 }}<br /> | 1.4469<br /> | [[Lériendil]] (2025)<br /> |-<br /> | [[1288/1287|Triaphonisma]], santisma<br /> | Twethothuluzoma<br /> | 23o3u1uzM<br /> | 1288/1287<br /> | {{Monzo| 3 -2 0 1 -1 -1 0 0 1 }}<br /> | 1.3446<br /> | [[User:Xenllium|Xenllium]] (2023) for ''santisma''<br /> |-<br /> | [[1496/1495|Turkisma]]<br /> | Twethusothuloguma<br /> | 23u17o3u1ogM<br /> | 1496/1495<br /> | {{Monzo| 3 0 -1 0 1 -1 1 0 -1 }}<br /> | 1.1576<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[7429/7425|Gordaitisma]]<br /> | Twethonosoluguguma<br /> | 23o19o17o1uggM<br /> | 7429/7425<br /> | {{monzo| 0 -3 -2 0 -1 0 1 1 1 }}<br /> | 0.93240<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1863/1862|Antinousisma]]<br /> | Twethonururuma<br /> | 23o19urrM<br /> | 1863/1862<br /> | 2.3.7.19.23 {{Monzo| -1 4 -2 -1 1 }}<br /> | 0.92952<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Kaifsma]]<br /> | Twethunosutholuzozoguma<br /> | 23u19o17u3o1uzzgM<br /> | 193648/193545<br /> | {{Monzo| 4 -2 -1 2 -1 1 -1 1 -1 }}<br /> | 0.92108<br /> | [[User:Kaiveran|Kaiveran]] (2022)<br /> |-<br /> | [[2024/2023|Artifisma]], insincere comma<br /> | Twethosusuloruma<br /> | 23o17uu1orM<br /> | 2024/2023<br /> | 2.7.11.17.23 {{Monzo| 3 -1 1 -2 1 }}<br /> | 0.85556<br /> | [[User:Xenllium|Xenllium]] (2023) for ''insincere comma''<br /> |-<br /> | [[2025/2024|Cupcake comma]], cupcakesma<br /> | Latwethuluyoyoma<br /> | L23u1uyyM<br /> | 2025/2024<br /> | 2.3.5.11.23 {{Monzo| -3 4 2 -1 -1 }}<br /> | 0.85514<br /> | See the page.<br /> |-<br /> | [[2185/2184|Guangdongisma]]<br /> | Twethonothuruyoma<br /> | 23o19o3uryM<br /> | 2185/2184<br /> | {{Monzo| -3 -1 1 -1 0 -1 0 1 1 }}<br /> | 0.79251<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[2300/2299|Travellisma]]<br /> | Twethonubiluyoma<br /> | 23o19u1uuyyM<br /> | 2300/2299<br /> | 2.5.11.19.23 {{Monzo| 2 2 -2 -1 1 }}<br /> | 0.75287<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[2646/2645|Biyativice comma]]<br /> | Bitwethuzo-aguma<br /> | 23uuzzgM<br /> | 2646/2645<br /> | 2.3.5.7.23 {{Monzo| 1 3 -1 2 -2 }}<br /> | 0.65441<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[2737/2736|Kotkisma]]<br /> | Twethonusozoma<br /> | 23o19u17ozM<br /> | 2737/2736<br /> | {{Monzo| -4 -2 0 1 0 0 1 -1 1 }}<br /> | 0.63265<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Kwadransma]]<br /> | Quadtwethuma<br /> | 4(23u)M<br /> | 279936/279841<br /> | {{Monzo| 7 7 0 0 0 0 0 0 -4 }}<br /> | 0.58762<br /> | [[Lériendil]] (2024)<br /> |-<br /> | [[3060/3059|Vicious comma]], viciousma<br /> | Twethunusoruyoma<br /> | 23u19u17oryM<br /> | 3060/3059<br /> | {{Monzo| 2 2 1 -1 0 0 1 -1 -1 }}<br /> | 0.56586<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[3381/3380|Mikkolisma]], seminaiadvice comma<br /> | Twethothuthuzozoguma<br /> | 23o3uuzzgM<br /> | 3381/3380<br /> | {{Monzo| -2 1 -1 2 0 -2 0 0 1 }}<br /> | 0.51212<br /> | See the page.<br /> |-<br /> | [[6877/6875|Grossvice comma]]<br /> | Bitwetho-atholuquadguma<br /> | 23oo3o1u4gM<br /> | 6877/6875<br /> | {{Monzo| 0 0 -4 0 -1 1 0 0 2 }}<br /> | 0.50356<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[3520/3519|Vicedim comma]]<br /> | Twethusuloyoma<br /> | 23u17u1oyM<br /> | 3520/3519<br /> | {{Monzo| 6 -2 1 0 1 0 -1 0 -1 }}<br /> | 0.49190<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[3888/3887|Shoalma]], vicetride comma<br /> | Twethuthuthuma<br /> | 23u3uuM<br /> | 3888/3887<br /> | 2.3.13.23 {{Monzo| 4 5 -2 -1 }}<br /> | 0.44533<br /> | See the page.<br /> |-<br /> | [[8075/8073|Hagendorfisma]]<br /> | Twethunosothuyoyoma<br /> | 23u19o17o3uyyM<br /> | 8075/8073<br /> | {{monzo| 0 -3 2 0 0 -1 1 1 -1 }}<br /> | 0.42884<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4693/4692|Viceaug comma]]<br /> | Twethunonosuthoma<br /> | 23u19oo17u3oM<br /> | 4693/4692<br /> | {{Monzo| -2 -1 0 0 0 1 -1 2 -1 }}<br /> | 0.36894<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[4761/4760|Demiquartervice comma]]<br /> | Bitwetho-asuruguma<br /> | 23oo17urgM<br /> | 4761/4760<br /> | {{Monzo| -3 2 -1 -1 0 0 -1 0 2 }}<br /> | 0.36367<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[5083/5082|Broadviewsma]]<br /> | Twethosotholuluruma<br /> | 23o17o3o1uurM<br /> | 5083/5082<br /> | {{Monzo| -1 -1 0 -1 -2 1 1 0 1 }}<br /> | 0.34063<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[8625/8624|Beerglass comma]]<br /> | Twetholururutriyoma<br /> | 23o1urr3yM<br /> | 8625/8624<br /> | {{Monzo| -4 1 3 -2 -1 0 0 0 1 }}<br /> | 0.20073<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[Galeaclolusisma]]<br /> | Twethususutholuquadyoma<br /> | 23u17uu3o1u4yM<br /> | 73125/73117<br /> | {{Monzo| 0 2 4 0 -1 1 -2 0 -1 }}<br /> | 0.18941<br /> | [[Francium]] (2025)<br /> |-<br /> | [[10626/10625|Demiglace comma]]<br /> | Twethosulozoquadguma<br /> | 23o17u1oz4gM<br /> | 10626/10625<br /> | {{Monzo| 1 1 -4 1 1 0 -1 0 1 }}<br /> | 0.16293<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[Vicetertisma]]<br /> | Tritwethu-athothoma<br /> | 3(23u)3ooM<br /> | 12168/12167<br /> | 2.3.13.23 {{Monzo| 3 2 2 -3 }}<br /> | 0.14228<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Joshuavoisma]]<br /> | Twethusutholozoyoyoma<br /> | 23u17u3o1ozyyM<br /> | 25025/25024<br /> | {{monzo| -6 0 2 1 1 1 -1 0 -1 }}<br /> | 0.06918<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Diarithmedia]]<br /> | Bitwethozo-aguma<br /> | 23oozzgM<br /> | 25921/25920<br /> | 2.3.5.7.23 {{monzo| -6 -4 -1 2 2 }}<br /> | 0.066790<br /> | [[Flora Canou]] (2023), modified by [[Lériendil]] (2024)<br /> |-<br /> | [[Jeffbenisma]]<br /> | Labitwethu-anutholuzoyoma<br /> | L23uu19u3o1uzyM<br /> | 110565/110561<br /> | {{monzo| 0 5 1 1 -1 1 0 -1 -2 }}<br /> | 0.062633<br /> | [[Francium]] (2025)<br /> |}<br /> <br /> === 29-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[551/550|Minor chthonovinema]]<br /> | Twenonoluguguma<br /> | 29o19o1uggM<br /> | 551/550<br /> | 2.5.11.19.29 {{monzo| -1 -2 -1 1 1 }}<br /> | 3.1448<br /> | [[User:Xenllium|Xenllium]] (2024)<br /> |-<br /> | [[552/551|Sigelindisma]]<br /> | Twenutwethonuma<br /> | 29u23o19uM<br /> | 552/551<br /> | 2.3.19.23.29 {{monzo| 3 1 -1 1 -1 }}<br /> | 3.1391<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[609/608|Vineyard comma]]<br /> | Twenonuzoma<br /> | 29o19uzM<br /> | 609/608<br /> | 2.3.7.19.29 {{monzo| -5 1 1 -1 1 }}<br /> | 2.8451<br /> | [[User:Xenllium|Xenllium]] (2024)<br /> |-<br /> | [[638/637|Moirisma]]<br /> | Twenothuloruruma<br /> | 29o3u1orrM<br /> | 638/637<br /> | 2.7.11.13.29 {{monzo| 1 -2 1 -1 1 }}<br /> | 2.7157<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[726/725|Joellisma]]<br /> | Twenubiloguma<br /> | 29u1ooggM<br /> | 726/725<br /> | 2.3.5.11.29 {{monzo| 1 1 -2 2 -1 }}<br /> | 2.3863<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[783/782|Norisma]]<br /> | Twenotwethusuma<br /> | 29o23u17uM<br /> | 783/782<br /> | 2.3.17.23.29 {{monzo| -1 3 -1 -1 1 }}<br /> | 2.2124<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[784/783|Biminorisma]], spoogalactic comma<br /> | Twenuzozoma<br /> | 29uzzM<br /> | 784/783<br /> | 2.3.7.29 {{monzo| 4 -3 2 -1 }}<br /> | 2.2096<br /> | [[Scott Dakota]] for ''biminorisma''<br /> |-<br /> | [[841/840|Arabellisma]]<br /> | Bitweno-aruguma<br /> | 29oorgM<br /> | 841/840<br /> | 2.3.5.7.29 {{monzo| -3 -1 -1 -1 2 }}<br /> | 2.0598<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[1015/1014|Christisma]]<br /> | Twenothuthuzoyoma<br /> | 29o3uuzyM<br /> | 1015/1014<br /> | {{monzo| -1 -1 1 1 0 -2 0 0 0 1 }}<br /> | 1.7065<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1045/1044|Michelisma]]<br /> | Twenunoloyoma<br /> | 29u19o1oyM<br /> | 1045/1044<br /> | {{monzo| -2 -2 1 0 1 0 0 1 0 -1 }}<br /> | 1.6575<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1276/1275|Ucclisma]]<br /> | Twenosuloguguma<br /> | 29o17u1oggM<br /> | 1276/1275<br /> | {{monzo| 2 -1 -2 0 1 0 -1 0 0 1 }}<br /> | 1.3573<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1450/1449|Raimondisma]]<br /> | Twenotwethuruyoyoma<br /> | 29o23uryyM<br /> | 1450/1449<br /> | {{monzo| 1 -2 2 -1 0 0 0 0 -1 1 }}<br /> | 1.1944<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1596/1595|Itzigsohnisma]]<br /> | Twenunoluzoguma<br /> | 29u19o1uzgM<br /> | 1596/1595<br /> | {{monzo| 2 1 -1 1 -1 0 0 1 0 -1 }}<br /> | 1.0851<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1625/1624|Norcma]]<br /> | Twenuthorutriyoma<br /> | 29u3or3yM<br /> | 1625/1624<br /> | 2.5.7.13.29 {{monzo| -3 3 -1 1 -1 }}<br /> | 1.0657<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[1683/1682|Castafiorisma]]<br /> | Bitwenu-asoloma<br /> | 29uu17o1oM<br /> | 1683/1682<br /> | 2.3.11.17.29 {{monzo| -1 2 1 1 -2 }}<br /> | 1.0290<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2001/2000|Major discoverisma]]<br /> | Twenotwethotriguma<br /> | 29o23o3gM<br /> | 2001/2000<br /> | 2.3.5.23.29 {{monzo| -4 1 -3 1 1 }}<br /> | 0.86540<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2002/2001|Minor discoverisma]]<br /> | Twenutwethutholozoma<br /> | 29u23u3o1ozM<br /> | 2002/2001<br /> | {{monzo| 1 -1 0 1 1 1 0 0 -1 -1 }}<br /> | 0.86497<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2176/2175|Donarisma]]<br /> | Twenusoguguma<br /> | 29u17oggM<br /> | 2176/2175<br /> | 2.3.5.17.29 {{monzo| 7 -1 -2 1 -1 }}<br /> | 0.79579<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2205/2204|Glinkisma]]<br /> | Twenunuzozoyoma<br /> | 29u19uzzyM<br /> | 2205/2204<br /> | {{monzo| -2 2 1 2 0 0 0 -1 0 -1 }}<br /> | 0.78532<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2262/2261|Mitidikisma]]<br /> | Twenonusuthoruma<br /> | 29o19u17u3orM<br /> | 2262/2261<br /> | {{monzo| 1 1 0 -1 0 1 -1 -1 0 1 }}<br /> | 0.76552<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2465/2464|Laservine comma]]<br /> | Twenosoluruyoma<br /> | 29o17o1uryM<br /> | 2465/2464<br /> | {{monzo| -5 0 1 -1 -1 0 1 0 0 1 }}<br /> | 0.70247<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2640/2639|Hällströmisma]]<br /> | Twenuthuloruyoma<br /> | 29u3u1oryM<br /> | 2640/2639<br /> | {{monzo| 4 1 1 -1 1 -1 0 0 0 -1 }}<br /> | 0.65589<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2755/2754|Avicema]]<br /> | Twenonosuyoma<br /> | 29o19o17uyM<br /> | 2755/2754<br /> | {{monzo| -1 -4 1 0 0 0 -1 1 0 1 }}<br /> | 0.62851<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[2784/2783|Domeykisma]]<br /> | Twenotwethululuma<br /> | 29o23u1uuM<br /> | 2784/2783<br /> | 2.3.11.23.29 {{monzo| 5 1 -2 -1 1 }}<br /> | 0.62196<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[9251/9248|Helevenisma]]<br /> | Bitwenosu-aloma<br /> | 29oo17uu1oM<br /> | 9251/9248<br /> | 2.11.17.29 {{monzo| -5 1 -2 2 }}<br /> | 0.56151<br /> | [[Zhea Erose]] (2023)<br /> |-<br /> | [[3249/3248|Musashinisma]]<br /> | Twenunonoruma<br /> | 29u19oorM<br /> | 3249/3248<br /> | 2.3.7.19.29 {{monzo| -4 2 -1 2 -1 }}<br /> | 0.53293<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[3451/3450|Mentorisma]]<br /> | Twenotwethusozoguguma<br /> | 29o23u17ozggM<br /> | 3451/3450<br /> | {{monzo| -1 -1 -2 1 0 0 1 0 -1 1 }}<br /> | 0.50173<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[Bronxisma]]<br /> | Twenununusolozoma<br /> | 29u19uu17o1ozM<br /> | 10472/10469<br /> | {{monzo| 3 0 0 1 1 0 1 -2 0 -1 }}<br /> | 0.49603<br /> | [[Francium]] (2024)<br /> |-<br /> | [[3510/3509|Veederisma]]<br /> | Twenutholuluyoma<br /> | 29u3o1uuyM<br /> | 3510/3509<br /> | {{monzo| 1 3 1 0 -2 1 0 0 0 -1 }}<br /> | 0.49330<br /> | [[Francium]] (2024)<br /> |-<br /> | [[4641/4640|Vinecute comma]]<br /> | Twenusothozoguma<br /> | 29u17o3ozgM<br /> | 4641/4640<br /> | {{monzo| -5 1 -1 1 0 1 1 0 0 -1 }}<br /> | 0.37307<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[4785/4784|Petrovsma]]<br /> | Twenotwethuthuloyoma<br /> | 29o23u3u1oyM<br /> | 4785/4784<br /> | {{monzo| -4 1 1 0 1 -1 0 0 -1 1 }}<br /> | 0.36184<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[4901/4900|Large grapevine]]<br /> | Twenothothobiruguma<br /> | 29o3oorrggM<br /> | 4901/4900<br /> | 2.5.7.13.29 {{monzo| -2 -2 -2 2 1 }}<br /> | 0.35328<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[Mynucuvine comma]]<br /> | Labitwenu-athuyoma<br /> | L29uu3uyM<br /> | 10935/10933<br /> | 3.5.13.29 {{monzo| 7 1 -1 -2 }}<br /> | 0.31667<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[5888/5887|Vinocular comma]]<br /> | Bitwenu-atwethoruma<br /> | 29uu23orM<br /> | 5888/5887<br /> | 2.7.23.29 {{monzo| 8 -1 1 -2 }}<br /> | 0.29405<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[5916/5915|Woudisma]]<br /> | Twenosothuthuruguma<br /> | 29o17o3uurgM<br /> | 5916/5915<br /> | {{monzo| 2 1 -1 -1 0 -2 1 0 0 1 }}<br /> | 0.29266<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[7425/7424|Small grapevine]]<br /> | Latwenuloyoyoma<br /> | L29u1oyyM<br /> | 7425/7424<br /> | 2.3.5.11.29 {{monzo| -8 3 2 1 -1 }}<br /> | 0.23318<br /> | [[User:Xenllium|Xenllium]] (2023)<br /> |-<br /> | [[8671/8670|Vinous comma]], vinousma<br /> | Twenotwethosusuthoguma<br /> | 29o23o17uu3ogM<br /> | 8671/8670<br /> | {{monzo| -1 -1 -1 0 0 1 -2 0 1 1 }}<br /> | 0.19967<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[9802/9801|Kakisma]]<br /> | Twenobitholuma<br /> | 29o3oo1uuM<br /> | 9802/9801<br /> | {{Monzo| 1 -4 0 0 -2 2 0 0 0 1 }}<br /> | 0.17663<br /> | [[Lériendil]] (2025)<br /> |-<br /> | [[10557/10556|Rowlandisma]]<br /> | Twenutwethosothuruma<br /> | 29u23o17o3urM<br /> | 10557/10556<br /> | {{monzo| -2 3 0 -1 0 -1 1 0 1 -1 }}<br /> | 0.16400<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[Uma]], umic comma<br /> | Twenotwethoquadru-aguma<br /> | 29o23o4rgM<br /> | 12006/12005<br /> | {{monzo| 1 2 -1 -4 0 0 0 0 1 1 }}<br /> | 0.14420<br /> | <br /> |-<br /> | [[Vuillafansisma]]<br /> | Twenunosoluyoma<br /> | 29u19o17o1uyM<br /> | 25840/25839<br /> | {{monzo| 4 -4 1 0 -1 0 1 1 0 -1 }}<br /> | 0.067000<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Odyssey comma]]<br /> | Bitwenotwetho-athulurutriguma<br /> | 29oo23oo3u1ur3gM<br /> | 4004001/4004000<br /> | {{monzo| -5 2 -3 -1 -1 -1 0 0 2 2 }}<br /> | 0.00043238<br /> | [[Tristan Bay]] (2024)<br /> |}<br /> <br /> === 31-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[496/495|Navatonisma]]<br /> | Thiwoluguma<br /> | 31o1ugM<br /> | 496/495<br /> | 2.3.5.11.31 {{monzo| 4 -2 -1 -1 1 }}<br /> | 3.4939<br /> | [[User:FilterNashi|FilterNashi]] (2025)<br /> |-<br /> | [[528/527|Rezisma]]<br /> | Thiwusuloma<br /> | 31u17u1oM<br /> | 528/527<br /> | 2.3.11.17.31 {{monzo| 4 1 1 -1 -1 }}<br /> | 3.2820<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[589/588|Croatisma]]<br /> | Thiwonoruruma<br /> | 31o19orrM<br /> | 589/588<br /> | 2.3.7.19.31 {{monzo| -2 -1 -2 1 1 }}<br /> | 2.9418<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[621/620|Owowhatsthisma]]<br /> | Thiwutwethoguma<br /> | 31u23ogM<br /> | 621/620<br /> | 2.3.5.23.31 {{monzo| -2 3 -1 1 -1 }}<br /> | 2.7901<br /> | [[HEHEHE I AM A SUPAHSTAR SAGA]] (2021)<br /> |-<br /> | [[651/650|Antiklisma]]<br /> | Thiwothuzoguguma<br /> | 31o3uzggM<br /> | 651/650<br /> | 2.3.5.7.13.31 {{monzo| -1 1 -2 1 -1 1 }}<br /> | 2.6614<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[714/713|Ululisma]]<br /> | Thiwutwethusozoma<br /> | 31u23u17ozM<br /> | 714/713<br /> | 2.3.7.17.23.31 {{monzo| 1 1 1 1 -1 -1 }}<br /> | 2.4264<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[961/960|Tricesimoprimal quartertones comma]]<br /> | Bithiwo-aguma<br /> | 31oogM<br /> | 961/960<br /> | 2.3.5.31 {{monzo| -6 -1 -1 2 }}<br /> | 1.8024<br /> | [[Godtone]] (2024)<br /> |-<br /> | [[1024/1023|Kibisma]]<br /> | Thiwuluma<br /> | 31u1uM<br /> | 1024/1023<br /> | 2.3.11.31 {{Monzo| 10 -1 -1 -1 }}<br /> | 1.6915<br /> | See the page.<br /> |-<br /> | [[2233/2232|Kuznetsovisma]]<br /> | Thiwotwenolozoma<br /> | 31u29o1ozM<br /> | 2233/2232<br /> | 2.3.7.11.29.31 {{monzo| -3 -2 1 1 1 -1 }}<br /> | 0.77547<br /> | [[Francium]] (2024)<br /> |-<br /> | [[3969/3968|Yunzee comma]]<br /> | Lathiwuzozoma<br /> | L31uzzM<br /> | 3969/3968<br /> | 2.3.7.31 {{monzo| -7 4 2 -1 }}<br /> | 0.43624<br /> | [[User:Kaiveran|Kaiveran]] (2021)<br /> |-<br /> | [[4186/4185|Tamashimisma]]<br /> | Thiwutwethothozoguma<br /> | 31u23o3ozgM<br /> | 4186/4185<br /> | 2.3.5.7.13.23.31 {{monzo| 1 -3 -1 1 1 1 -1 }}<br /> | 0.41363<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4992/4991|Kalmanisma]]<br /> | Thiwutwethuthoruma<br /> | 31u23u3orM<br /> | 4992/4991<br /> | 2.3.7.13.23.31 {{monzo| 7 1 -1 1 -1 -1 }}<br /> | 0.34684<br /> | [[Francium]] (2024)<br /> |-<br /> | [[5797/5796|Bivojisma]]<br /> | Thiwotwethusoloruma<br /> | 31o23u17o1orM<br /> | 5797/5796<br /> | 2.3.7.11.17.23.31 {{monzo| -2 -2 -1 1 1 -1 1 }}<br /> | 0.29867<br /> | [[Francium]] (2025)<br /> |-<br /> | [[6076/6075|Large ricegrain]]<br /> | Sathiwobizoguma<br /> | s31ozzggM<br /> | 6076/6075<br /> | 2.3.5.7.31 {{monzo| 2 -5 -2 2 1 }}<br /> | 0.28495<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[6480/6479|Scarlattisma]]<br /> | Thiwunuluyoma<br /> | 31u19u1uyM<br /> | 6480/6479<br /> | 2.3.5.11.19.31 {{monzo| 4 4 1 -1 -1 -1 }}<br /> | 0.26719<br /> | [[Francium]] (2024)<br /> |-<br /> | [[6728/6727|Sushi comma]]<br /> | Bithiwutweno-aruma<br /> | 31uu29oorM<br /> | 6728/6727<br /> | 2.7.29.31 {{monzo| 3 -1 2 -2 }}<br /> | 0.25734<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[16337/16335|Brown rice comma]]<br /> | Bithiwo-asoluluguma<br /> | 31oo17o1uugM<br /> | 16337/16335<br /> | 3.5.11.17.31 {{monzo| -3 -1 -2 1 2 }}<br /> | 0.21195<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[8464/8463|Polishookisma]]<br /> | Thiwubitwetho-athuruma<br /> | 31u23oo3urM<br /> | 8464/8463<br /> | 2.3.7.13.23.31 {{monzo| 4 -1 -1 -1 2 -1 }}<br /> | 0.20455<br /> | [[Francium]] (2024)<br /> |-<br /> | [[8960/8959|Small ricegrain]]<br /> | Thiwususuzoyoma<br /> | 31u17uuzyM<br /> | 8960/8959<br /> | 2.5.7.17.31 {{monzo| 8 1 1 -2 -1 }}<br /> | 0.19323<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[Acronymisma]]<br /> | Thiwotrithu-azoma<br /> | 31o3(3u)zM<br /> | 17577/17576<br /> | 2.3.7.13.31 {{monzo| -3 4 1 -3 1 }}<br /> | 0.098497<br /> | [[User:Lériendil|Lériendil]] (2025)<br /> |-<br /> | [[Totziensisma]]<br /> | Thiwotwetholurutriguma<br /> | 31o23o1ur3gM<br /> | 19251/19250<br /> | 2.3.5.7.11.23.31 {{monzo| -1 3 -3 -1 -1 1 1 }}<br /> | 0.089932<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Honeybrookisma]]<br /> | Thiwobitwenu-atwethuthoma<br /> | 31o29uu23u3oM<br /> | 19344/19343<br /> | 2.3.13.23.29.31 {{monzo| 4 1 1 -1 -2 1 }}<br /> | 0.089500<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Tricecubisma]]<br /> | Trithiwu-anozozoma<br /> | 3(31u)19ozzM<br /> | 29792/29791<br /> | 2.7.19.31 {{monzo| 5 2 1 -3 }}<br /> | 0.058112<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |}<br /> <br /> === 37-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[666/665|Beastisma]]<br /> | Thisonuruguma<br /> | 37o19urgM<br /> | 666/665<br /> | 2.3.5.7.19.37 {{monzo| 1 2 -1 -1 -1 1 }}<br /> | 2.6014<br /> | [[Francium]] (2025)<br /> |-<br /> | [[667/666|Denisisma]]<br /> | Thisutwenotwethoma<br /> | 37u29o23oM<br /> | 667/666<br /> | 2.3.23.29.37 {{monzo| -1 -2 1 1 -1 }}<br /> | 2.5975<br /> | [[Francium]] (2025)<br /> |-<br /> | [[703/702|Noemisma]]<br /> | Thisonothuma<br /> | 37o19o3uM<br /> | 703/702<br /> | 2.3.13.19.37 {{monzo| -1 -3 -1 1 1 }}<br /> | 2.4644<br /> | [[Francium]] (2025)<br /> |-<br /> | [[704/703|Minimyna]]<br /> | Thisunuloma<br /> | 37u19u1oM<br /> | 704/703<br /> | 2.11.19.37 {{monzo| 6 1 -1 -1 }}<br /> | 2.4609<br /> | [[User:Kaiveran|Kaiveran]] (2023)<br /> |-<br /> | [[741/740|Botolphisma]]<br /> | Thisunothoguma<br /> | 37u19o3ogM<br /> | 741/740<br /> | 2.3.5.13.19.37 {{monzo| -2 1 -1 1 1 -1 }}<br /> | 2.3379<br /> | [[Francium]] (2025)<br /> |-<br /> | [[851/850|Zeissisma]]<br /> | Thisotwethosuguguma<br /> | 37o23o17uggM<br /> | 851/850<br /> | 2.5.17.23.37 {{monzo| -1 -2 -1 1 1 }}<br /> | 2.0355<br /> | [[Francium]] (2025)<br /> |-<br /> | [[925/924|Alphonsinisma]]<br /> | Thisoluruyoyoma<br /> | 37o1uryyM<br /> | 925/924<br /> | 2.3.5.7.11.37 {{monzo| -2 -1 2 -1 -1 1 }}<br /> | 1.8726<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1036/1035|Ganymedisma]]<br /> | Thisotwethuzoguma<br /> | 37o23uzgM<br /> | 1036/1035<br /> | 2.3.5.7.23.37 {{monzo| 2 -2 -1 1 -1 1 }}<br /> | 1.6719<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1184/1183|Gaeisma]]<br /> | Thisothuthuruma<br /> | 37o3uurM<br /> | 1184/1183<br /> | 2.7.13.37 {{monzo| 5 -1 -2 1}}<br /> | 1.4628<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1332/1331|Marconisma]]<br /> | Thisotriluma<br /> | 37o3(1u)M<br /> | 1332/1331<br /> | 2.3.11.37 {{monzo| 2 2 -3 1 }}<br /> | 1.3002<br /> | [[Francium]] (2024)<br /> |-<br /> | [[1480/1479|Aunusisma]]<br /> | Thisotwenusuyoma<br /> | 37o29u17uyM<br /> | 1480/1479<br /> | 2.3.5.17.29.37 {{monzo| 3 -1 1 -1 -1 1 }}<br /> | 1.1702<br /> | [[Francium]] (2024)<br /> |-<br /> | [[1665/1664|Gabisma]]<br /> | Thisothuyoma<br /> | 37o3uyM<br /> | 1665/1664<br /> | 2.3.5.13.37 {{monzo| -7 2 1 -1 1 }}<br /> | 1.0401<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1666/1665|Gentisma]]<br /> | Thisusozozoguma<br /> | 37u17ozzgM<br /> | 1666/1665<br /> | 2.3.5.7.17.37 {{monzo| 1 -2 -1 2 1 -1 }}<br /> | 1.0395<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1702/1701|Kalaharisma]]<br /> | Sathisotwethoruma<br /> | S37o23orM<br /> | 1702/1701<br /> | 2.3.7.23.37 {{monzo| 1 -5 -1 1 1 }}<br /> | 1.0175<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1925/1924|Misericorde]]<br /> | Thisuthulozoyoyoma<br /> | 37u3u1ozyyM<br /> | 1925/1924<br /> | 2.5.7.11.13.37 {{monzo| -2 2 1 1 -1 -1 }}<br /> | 0.89958<br /> | [[User:Kaiveran|Kaiveran]] (2023)<br /> |-<br /> | [[2109/2108|Dhotelisma]]<br /> | Thisothiwunosuma<br /> | 37o31u19o17uM<br /> | 2109/2108<br /> | 2.3.17.19.31.37 {{monzo| -2 1 -1 1 -1 1 }}<br /> | 0.82107<br /> | [[Francium]] (2025)<br /> |-<br /> | [[2146/2145|Stentorisma]]<br /> | Thisotwenothuluguma<br /> | 37o29o3u1ugM<br /> | 2146/2145<br /> | 2.3.5.11.13.29.37 {{monzo| 1 -1 -1 -1 -1 1 1 }}<br /> | 0.80691<br /> | [[Francium]] (2024)<br /> |-<br /> | [[2553/2552|Viljevisma]]<br /> | Thisotwenutwetholuma<br /> | 37o29u23o1uM<br /> | 2553/2552<br /> | 2.3.11.23.29.37 {{monzo| -3 1 -1 1 -1 1 }}<br /> | 0.67825<br /> | [[Francium]] (2024)<br /> |-<br /> | [[2850/2849|Mozhaiskisma]]<br /> | Thisunoluruyoyoma<br /> | 37u19o1uryyM<br /> | 2850/2849<br /> | 2.3.5.7.11.19.37 {{monzo| 1 1 2 -1 -1 1 -1 }}<br /> | 0.60756<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3146/3145|Datonisma]]<br /> | Thisusutholologuma<br /> | 37u17u3o1oogM<br /> | 3146/3145<br /> | 2.5.11.13.17.37 {{monzo| 1 -1 2 1 -1 -1 }}<br /> | 0.55038<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3220/3219|Murayamisma]]<br /> | Thisutwenutwethozoyoma<br /> | 37u29u23ozyM<br /> | 3220/3219<br /> | 2.3.5.7.23.29.37 {{monzo| 2 -1 1 1 1 -1 -1 }}<br /> | 0.53773<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3256/3255|Daguerrisma]]<br /> | Thisothiwuloruguma<br /> | 37o31u1orgM<br /> | 3256/3255<br /> | 2.3.5.7.11.31.37 {{monzo| 3 -1 -1 -1 1 -1 1 }}<br /> | 0.53179<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3367/3366|Alexisma]]<br /> | Thisosutholuzoma<br /> | 37o17u3o1uzM<br /> | 3367/3366<br /> | 2.3.7.11.13.17.37 {{monzo| -1 -2 1 -1 1 -1 1 }}<br /> | 0.51425<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3553/3552|Meranisma]]<br /> | Thisunosoloma<br /> | 37u19o17o1oM<br /> | 3553/3552<br /> | 2.3.11.17.19.37 {{monzo| -5 -1 1 1 1 -1 }}<br /> | 0.48733<br /> | [[Francium]] (2024)<br /> |-<br /> | [[3626/3625|Ohsakisma]]<br /> | Thisotwenuzozotriguma<br /> | 37o29uzz3gM<br /> | 3626/3625<br /> | 2.5.7.29.37 {{monzo| 1 -3 2 -1 1 }}<br /> | 0.47752<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3627/3626|Sayersisma]]<br /> | Thisuthiwothoruruma<br /> | 37u31o3orrM<br /> | 3627/3626<br /> | 2.3.7.13.31.37 {{monzo| -1 2 -2 1 1 -1 }}<br /> | 0.47738<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3774/3773|Megumisma]]<br /> | Thisosolutriruma<br /> | 37o17o1u3rM<br /> | 3774/3773<br /> | 2.3.7.11.17.37 {{monzo| 1 1 -3 -1 1 1 }}<br /> | 0.45879<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4625/4624|Shchedrinisma]]<br /> | Thisosusutriyoma<br /> | 37o17uu3yM<br /> | 4625/4624<br /> | 2.5.17.37 {{monzo| -4 3 -2 1 }}<br /> | 0.37436<br /> | [[Francium]] (2024)<br /> |-<br /> | [[5292/5291|Bullionisma]]<br /> | Thisuthuluzozoma<br /> | 37u3u1uzzM<br /> | 5292/5291<br /> | 2.3.7.11.13.37 {{monzo| 2 3 2 -1 -1 -1 }}<br /> | 0.32717<br /> | [[Eliora]] (2023)<br /> |-<br /> | [[5440/5439|Teraosma]]<br /> | Thisusoruruyoma<br /> | 37u17orryM<br /> | 5440/5439<br /> | 2.3.5.7.17.37 {{monzo| 6 -1 1 -2 1 -1 }}<br /> | 0.31827<br /> | [[Francium]] (2025)<br /> |-<br /> | [[7105/7104|Yousyozanisma]]<br /> | Thisutwenozozoyoma<br /> | 37u29ozzyM<br /> | 7105/7104<br /> | 2.3.5.7.29.37 {{monzo| -6 -1 1 2 1 -1 }}<br /> | 0.24368<br /> | [[Francium]] (2025)<br /> |-<br /> | [[7696/7695|Liebisma]]<br /> | Sathisonuthoguma<br /> | S37o19u3ogM<br /> | 7696/7695<br /> | 2.3.5.13.19.37 {{monzo| 4 -4 -1 1 -1 1 }}<br /> | 0.22497<br /> | [[Francium]] (2025)<br /> |-<br /> | [[8991/8990|Solidarity comma]]<br /> | Thisothiwutwenuguma<br /> | 37o31u29ugM<br /> | 8991/8990<br /> | 2.3.5.29.31.37 {{monzo| -1 5 -1 -1 -1 1 }}<br /> | 0.19256<br /> | [[Francium]] (2025)<br /> |-<br /> | [[9177/9176|Donsaarisma]]<br /> | Thisuthiwutwethonozoma<br /> | 37u31u23o19oM<br /> | 9177/9176<br /> | 2.3.7.19.23.31.37 {{monzo| -3 1 1 1 1 -1 -1 }}<br /> | 0.18866<br /> | [[Francium]] (2025)<br /> |-<br /> | [[9251/9250|Harchisma]]<br /> | Thisubitweno-alotriguma<br /> | 37u29oo1o3gM<br /> | 9251/9250<br /> | 2.5.11.29.37 {{monzo| -1 -3 1 2 -1 }}<br /> | 0.18715<br /> | [[Francium]] (2025)<br /> |-<br /> | [[9361/9360|Friesachisma]]<br /> | Thisotwethothuloguma<br /> | 37o23o3u1ogM<br /> | 9361/9360<br /> | 2.3.5.11.13.23.37 {{monzo| -4 -2 -1 1 -1 1 1}}<br /> | 0.18495<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Zangarisma]]<br /> | Thisososoluma<br /> | 37o17oo1uM<br /> | 10693/10692<br /> | 2.3.11.17.37 {{monzo| -2 -5 -1 2 1 }}<br /> | 0.16191<br /> | [[Francium]] (2024)<br /> |-<br /> | [[23275/23273|Sunrise comma]]<br /> | Bithisu-anosubizoyoma<br /> | 37uu19o17uzzyyM<br /> | 23275/23273<br /> | 5.7.17.19.37 {{monzo| 2 2 -1 1 -2 }}<br /> | 0.14877<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[Sinachopoulosisma]]<br /> | Thisotwethonunuluzoma<br /> | 37o23o19uu1uzM<br /> | 11914/11913<br /> | 2.3.7.11.19.23.37 {{monzo| 1 -1 1 -1 -2 1 1 }}<br /> | 0.14532<br /> | [[Francium]] (2024)<br /> |-<br /> | [[12321/12320|Zurakowskisma]]<br /> | Bithiso-aluruguma<br /> | 37oo1urgM<br /> | 12321/12320<br /> | 2.3.5.7.11.37 {{monzo| -5 2 -1 -1 -1 2 }}<br /> | 0.14052<br /> | [[Francium]] (2025)<br /> |-<br /> | [[13690/13689|Lesleymartin comma]]<br /> | Bithisothu-ayoma<br /> | 37oo3uuyM<br /> | 13690/13689<br /> | 2.3.5.13.37 {{monzo| 1 -4 1 -2 2 }}<br /> | 0.12646<br /> | [[User:Xenllium|Xenllium]] (2025)<br /> |-<br /> | [[Berylisma]]<br /> | Quadthisoluma<br /> | 4(37o1u)M<br /> | 1874161/1874048<br /> | 2.11.37 {{monzo| -7 -4 4 }}<br /> | 0.10439<br /> | [[User:Jerdle|Jerdle]] (2023)<br /> |-<br /> | [[Genzelisma]]<br /> | Thisotwenonusoguma<br /> | 37o29o19u17ogM<br /> | 18241/18240<br /> | 2.3.5.17.19.29.37 {{monzo| -6 -1 -1 1 -1 1 1 }}<br /> | 0.094912<br /> | [[Francium]] (2024)<br /> |-<br /> | [[33264/33263|Maryrogersisma]]<br /> | Thisuthiwutwenulozoma<br /> | 37u31u29u1ozM<br /> | 33264/33263<br /> | 2.3.7.11.29.31.37 {{monzo| 4 3 1 1 -1 -1 -1 }}<br /> | 0.052046<br /> | [[Francium]] (2025)<br /> |-<br /> | [[Jouvisma]]<br /> | Thisotwethotholuluzoguma<br /> | 37o23o3o1uuzgM<br /> | 77441/77440<br /> | 2.5.7.11.13.23.37 {{monzo| -7 -1 1 -2 1 1 1 }}<br /> | 0.022356<br /> | [[Francium]] (2024)<br /> |}<br /> <br /> === 41-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[575/574|Renatisma]]<br /> | Fowutwethoruyoyoma<br /> | 41u23oryyM<br /> | 575/574<br /> | 2.5.7.23.41 {{monzo| -1 2 -1 1 -1 }}<br /> | 3.0135<br /> | [[Francium]] (2025)<br /> |-<br /> | [[616/615|Ellisma]]<br /> | Fowulozoguma<br /> | 41u1ozgM<br /> | 616/615<br /> | 2.3.5.7.11.41 {{monzo| 3 -1 -1 1 1 -1 }}<br /> | 2.8127<br /> | [[Francium]] (2024)<br /> |-<br /> | [[780/779|Wiesentisma]]<br /> | Fowunuthoyoma<br /> | 41u19u3oyM<br /> | 780/779<br /> | 2.3.5.13.19.41 {{monzo| 2 1 1 1 -1 -1 }}<br /> | 2.2210<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1025/1024|Kilobytisma]]<br /> | Fowoyoyoma<br /> | 41oyyM<br /> | 1025/1024<br /> | 2.5.41 {{Monzo| -10 2 1 }}<br /> | 1.6898<br /> | [[CompactStar]] (2024)<br /> |-<br /> | [[1026/1025|Ingridisma]]<br /> | Fowunoguguma<br /> | 41u19oggM<br /> | 1026/1025<br /> | 2.3.5.19.41 {{monzo| 1 3 -2 1 -1 }}<br /> | 1.6882<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1190/1189|Pelagisma]]<br /> | Fowutwenusozoyoma<br /> | 41u29u17ozyM<br /> | 1190/1189<br /> | 2.5.7.17.29.41 {{monzo| 1 1 1 1 -1 -1 }}<br /> | 1.4554<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1518/1517|Rovaniemisma]]<br /> | Fowuthisutwetholoma<br /> | 41u37u23o1oM<br /> | 1518/1517<br /> | 2.3.11.23.37.41 {{monzo|1 1 1 1 -1 -1 }}<br /> | 1.1408<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1682/1681|Shaftesburisma]]<br /> | Bifowutwenoma<br /> | 41uu29ooM<br /> | 1682/1681<br /> | 2.29.41 {{monzo| 1 2 -2 }}<br /> | 1.0296<br /> | [[Budjarn Lambeth]] (2023)<br /> |-<br /> | [[2255/2254|Qinghaisma]]<br /> | Fowotwethuloruruyoma<br /> | 41o23u1orryM<br /> | 2255/2254<br /> | 2.5.7.11.23.41 {{monzo| -1 1 -2 1 -1 1 }}<br /> | 0.76790<br /> | [[Francium]] (2025)<br /> |-<br /> | [[2871/2870|Schoberisma]]<br /> | Fowutwenoloruguma<br /> | 41u29o1orgM<br /> | 2871/2870<br /> | 2.3.5.7.11.29.41 {{monzo| -1 2 -1 -1 1 1 -1 }}<br /> | 0.60311<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3773/3772|Smithsonianisma]]<br /> | Fowutwethulotrizoma<br /> | 41u23u1o3zM<br /> | 3773/3772<br /> | 2.7.11.23.41 {{monzo| -2 3 1 -1 -1 }}<br /> | 0.45891<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4060/4059|Deipylosisma]]<br /> | Fowutwenoluzoyoma<br /> | 41u29o1uzyM<br /> | 4060/4059<br /> | 2.3.5.7.11.29.41 {{monzo| 2 -2 1 1 -1 1 -1 }}<br /> | 0.42646<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4675/4674|Ohbokisma]]<br /> | Fowunusoloyoyoma<br /> | 41u19u17o1oyyM<br /> | 4675/4674<br /> | 2.3.5.11.17.19.41 {{monzo| -1 -1 2 1 1 -1 -1 }}<br /> | 0.37036<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4921/4920|Volontisma]]<br /> | Fowuthisonozoguma<br /> | 41u37o19ozgM<br /> | 4921/4920<br /> | 2.3.5.7.19.37.41 {{monzo| -3 -1 -1 1 1 1 -1 }}<br /> | 0.35184<br /> | [[Francium]] (2025)<br /> |-<br /> | [[5577/5576|Priestlisma]]<br /> | Fowusuthotholoma<br /> | 41u17u3oo1oM<br /> | 5577/5576<br /> | 2.3.11.13.17.41 {{monzo| -3 1 1 2 -1 -1 }}<br /> | 0.31045<br /> | [[Francium]] (2025)<br /> |-<br /> | [[6069/6068|Cevolanisma]]<br /> | Fowuthisusosozoma<br /> | 41u37u17oozM<br /> | 6069/6068<br /> | 2.3.7.17.37.41 {{monzo| -2 1 1 2 -1 -1 }}<br /> | 0.28528<br /> | [[Francium]] (2025)<br /> |-<br /> | [[6930/6929|Bedanisma]]<br /> | Fowuthuthulozoyoma<br /> | 41u3uu1ozyM<br /> | 6930/6929<br /> | 2.3.5.7.11.13.41 {{monzo| 1 2 1 1 1 -2 -1 }}<br /> | 0.24984<br /> | [[Francium]] (2025)<br /> |-<br /> | [[7176/7175|Kunijisma]]<br /> | Fowutwethothoruguguma<br /> | 41u23o3orggM<br /> | 7176/7175<br /> | 2.3.5.7.13.23.41 {{monzo| 3 1 -2 -1 1 1 -1 }}<br /> | 0.24127<br /> | [[Francium]] (2025)<br /> |-<br /> | [[8569/8568|Mamelisma]]<br /> | Fowonosuloruma<br /> | 41o19o17u1orM<br /> | 8569/8568<br /> | 2.3.7.11.17.19.41 {{monzo| -3 -2 -1 1 -1 1 1 }}<br /> | 0.20205<br /> | [[Francium]] (2025)<br /> |-<br /> | [[9472/9471|Brugesisma]]<br /> | Fowuthisoluruma<br /> | 41u37o1urM<br /> | 9472/9471<br /> | 2.3.7.11.37.41 {{monzo| 8 -1 -1 -1 1 -1 }}<br /> | 0.18278<br /> | [[Francium]] (2025)<br /> |-<br /> | [[Etampesisma]]<br /> | Fowutwethunotholuzoma<br /> | 41u23u19o3o1uzM<br /> | 10374/10373<br /> | 2.3.7.11.13.19.23.41 {{monzo| 1 1 1 -1 1 1 -1 -1 }}<br /> | 0.16689<br /> | [[Francium]] (2024)<br /> |-<br /> | [[11440/11439|Massironisma]]<br /> | Fowuthiwutholoyoma<br /> | 41u31u3o1oyM<br /> | 11440/11439<br /> | 2.3.5.11.13.31.41 {{monzo| 4 -2 1 1 1 -1 -1 }}<br /> | 0.15134<br /> | [[Francium]] (2025)<br /> |-<br /> | [[15376/15375|Martakisma]]<br /> | Fowubithiwo-atriguma<br /> | 41u31oo3gM<br /> | 15376/15375<br /> | 2.3.5.31.41 {{monzo| 4 -1 -3 2 -1 }}<br /> | 0.11260<br /> | [[Francium]] (2025)<br /> |-<br /> | [[Canupisma]]<br /> | Fowutwenuthotrizo-aguma<br /> | 41u29u3o3zagM<br /> | 17836/17835<br /> | 2.3.5.7.13.29.41 {{monzo| 2 -1 -1 3 1 -1 -1 }}<br /> | 0.097067<br /> | [[Francium]] (2024)<br /> |-<br /> | [[76384/76383|Vernonisma]]<br /> | Fowuthiwotwethulozoma<br /> | 41u31o23u1ozM<br /> | 76384/76383<br /> | 2.3.7.11.23.31.41 {{monzo| 5 -4 1 1 -1 1 -1 }}<br /> | 0.022665<br /> | [[Francium]] (2025)<br /> |-<br /> | [[Mebisma]]<br /> | Safowuthiwuluguguma<br /> | s41u31u1uggM<br /> | 1048576/1048575<br /> | 2.3.5.11.31.41 {{Monzo| 20 -1 -2 -1 -1 -1 }}<br /> | 0.0016510<br /> | See the page.<br /> |}<br /> <br /> === 43-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[646/645|Kastalisma]]<br /> | Fothunosoguma<br /> | 43u19o17ogM<br /> | 646/645<br /> | 2.3.5.17.19.43 {{monzo| 1 -1 -1 1 1 -1 }}<br /> | 2.6820<br /> | [[Francium]] (2025)<br /> |-<br /> | [[990/989|Yerkesisma]]<br /> | Fothutwethuloyoma<br /> | 43u23u1oyM<br /> | 990/989<br /> | 2.3.5.11.23.43 {{monzo| 1 2 1 1 -1 -1 }}<br /> | 1.7496<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1333/1332|Cevelonisma]]<br /> | Fothothisuthiwoma<br /> | 43o37u31oM<br /> | 1333/1332<br /> | 2.3.31.37.43 {{monzo| -2 -2 1 -1 1 }}<br /> | 1.2992<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1377/1376|Roberbauxisma]]<br /> | Lafothusoma<br /> | L43u17oM<br /> | 1377/1376<br /> | 2.3.17.43 {{monzo| -5 4 1 -1}}<br /> | 1.2577<br /> | [[Francium]] (2025)<br /> |-<br /> | [[1463/1462|Nordenmarkisma]]<br /> | Fothunosulozoma<br /> | 43u19o17uozM<br /> | 1463/1462<br /> | 2.7.11.17.19.43 {{monzo| -1 1 1 -1 1 -1 }}<br /> | 1.1838<br /> | [[Francium]] (2025)<br /> |-<br /> | [[Magnetisma]]<br /> | Tritrila-quinquadtrifothutwenoma<br /> | 9L60(43u29o)M<br /> | <br /> | 2.3.29.43 {{monzo| -61 60 60 -60 }}<br /> | 0.86936<br /> | [[User:Eliora|Eliora]] (2022)<br /> |-<br /> | [[2925/2924|Beattisma]]<br /> | Fothusuthoyoyoma<br /> | 43u17u3oyyM<br /> | 2925/2924<br /> | 2.3.5.13.17.43 {{monzo| -2 2 2 1 -1 -1 }}<br /> | 0.59198<br /> | [[Francium]] (2025)<br /> |-<br /> | [[3312/3311|Pedersenisma]]<br /> | Fothutwetholuruma<br /> | 43u23o1urM<br /> | 3312/3311<br /> | 2.3.7.11.23.43 {{monzo| 4 2 -1 -1 1 -1 }}<br /> | 0.52279<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4000/3999|Hipparchusisma]]<br /> | Fothuthiwutriyoma<br /> | 43u31u3yM<br /> | 4000/3999<br /> | 2.3.5.31.43 {{monzo| 5 -1 3 -1 -1 }}<br /> | 0.43286<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4301/4300|Boydenisma]]<br /> | Fothutwethosologuguma<br /> | 43u23o17o1oggM<br /> | 4301/4300<br /> | 2.5.11.17.23.43 {{monzo| -2 -2 1 1 1 -1 }}<br /> | 0.40257<br /> | [[Francium]] (2025)<br /> |-<br /> | [[4774/4773|Hobetsisma]]<br /> | Fothuthisuthiwolozoma<br /> | 43u37u31o1ozM<br /> | 4774/4773<br /> | 2.3.7.11.31.37.43 {{monzo| 1 -1 1 1 1 -1 -1 }}<br /> | 0.36268<br /> | [[Francium]] (2025)<br /> |-<br /> | [[5720/5719|Halweaverisma]]<br /> | Fothunutholoruyoma<br /> | 43u19u3o1oryM<br /> | 5720/5719<br /> | 2.5.7.11.13.19.43 {{monzo| 3 1 -1 1 1 -1 -1 }}<br /> | 0.30269<br /> | [[Francium]] (2025)<br /> |-<br /> | [[7225/7224|Huntressisma]]<br /> | Fothusosoruyoyoma<br /> | 43u17ooryyM<br /> | 7225/7224<br /> | 2.3.5.7.17.43 {{monzo| -3 -1 2 -1 2 -1 }}<br /> | 0.23963<br /> | [[Francium]] (2025)<br /> |-<br /> | [[7956/7955|Yajinisma]]<br /> | Fothuthisusothoguma<br /> | 43u37u17o3ogM<br /> | 7956/7955<br /> | 2.3.5.13.17.37.43 {{monzo| 2 2 -1 1 1 -1 -1 }}<br /> | 0.21761<br /> | [[Francium]] (2025)<br /> |-<br /> | [[9504/9503|Lionelisma]]<br /> | Fothusuthuloma<br /> | 43u17u3u1oM<br /> | 9504/9503<br /> | 2.3.11.13.17.43 {{monzo| 5 3 1 -1 -1 -1 }}<br /> | 0.18217<br /> | [[Francium]] (2025)<br /> |-<br /> | [[9633/9632|Coturisma]]<br /> | Fothunothothoruma<br /> | 43u19o3oorM<br /> | 9633/9632<br /> | 2.3.7.13.19.43 {{monzo| -5 1 -1 2 1 -1 }}<br /> | 0.17973<br /> | [[Francium]] (2025)<br /> |-<br /> | [[Girardisma]]<br /> | Fothunoloyoyoma<br /> | 43u19o1oyyM<br /> | 10450/10449<br /> | 2.3.5.11.19.43 {{monzo| 1 -5 2 1 1 -1 }}<br /> | 0.16567<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Kaguyisma]]<br /> | Fothutwethusoluyoma<br /> | 43u23u17o1uyM<br /> | 10880/10879<br /> | 2.5.11.17.23.43 {{monzo| 7 1 -1 1 -1 -1 }}<br /> | 0.15913<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Manheimisma]]<br /> | Fothutwenosuloloyoma<br /> | 43u29o17u1ooyM<br /> | 17545/17544<br /> | 2.3.5.11.17.29.43 {{monzo| -3 -1 1 2 -1 1 -1 }}<br /> | 0.098677<br /> | [[Francium]] (2024)<br /> |-<br /> | [[Dimigenes comma]]<br /> | Fothosepyoma<br /> | 43o7yM<br /> | 3359375/3359232<br /> | 2.3.5.43 {{monzo| -9 -8 7 1 }}<br /> | 0.073696<br /> | [[User:Akselai|Akselai]] (2024)<br /> |-<br /> | [[27048/27047|Jangongisma]]<br /> | Fothuthisutwethosuzozoma<br /> | 43u37u23o17uzzM<br /> | 27048/27047<br /> | 2.3.7.17.23.37.43 {{monzo| 3 1 2 -1 1 -1 -1 }}<br /> | 0.064007<br /> | [[Francium]] (2025)<br /> |-<br /> | [[29241/29240|Locquirecisma]]<br /> | Fothunonosuguma<br /> | 43u19oo17ugM<br /> | 29241/29240<br /> | 2.3.5.17.19.43 {{monzo| -3 4 -1 -1 2 -1 }}<br /> | 0.059207<br /> | [[Francium]] (2025)<br /> |}<br /> <br /> === Higher-limit commas ===<br /> {| class=&quot;wikitable&quot;<br /> |-<br /> ! Name(s)<br /> ! colspan=&quot;2&quot; | [[Color name]]<br /> ! [[Ratio]]<br /> ! [[Monzo]]<br /> ! [[Cent]]s<br /> ! Named by<br /> |-<br /> | [[7936/7921|Lily comma]]<br /> | <br /> | 89uu31oM<br /> | 7936/7921<br /> | 2.31.89 {{monzo| 8 1 -2 }}<br /> | 3.2753<br /> | [[Budjarn Lambeth]] (2023)<br /> |-<br /> | [[Molar comma]]<br /> | <br /> | 3(89o)1u3gM<br /> | 704969/704000<br /> | 2.5.11.89 {{monzo| -9 -3 -1 3 }}<br /> | 2.3813<br /> | [[Budjarn Lambeth]] (2023)<br /> |-<br /> | [[750/749|Ancient Chinese tempering comma]]{{Clarify}}<br /> | <br /> | 107ur3yM<br /> | 750/749<br /> | 2.3.5.7.107 {{monzo| 1 1 3 -1 -1 }}<br /> | 2.3099<br /> | <br /> |-<br /> | [[1176/1175|Lucidorisma]]<br /> | Fosubizoguma<br /> | 47uzzggM<br /> | 1176/1175<br /> | 2.3.5.7.47 {{monzo| 3 1 -2 2 -1 }}<br /> | 1.4728<br /> | [[Francium]] (2025)<br /> |-<br /> | [[2520/2519|Platonisma]]<br /> | <br /> | 229u1uzyM<br /> | 2520/2519<br /> | 2.3.5.7.11.229 {{monzo| 3 2 1 1 -1 -1 }}<br /> | 0.68713<br /> | [[User:Eliora|Eliora]] (2022)<br /> |-<br /> | [[5041/5040|Third brown pair comma]], 19th highly compositema<br /> |<br /> | 71oorgM<br /> | 5041/5040<br /> | 2.3.5.7.71 {{monzo| -4 -2 -1 -1 2 }}<br /> | 0.34347<br /> | [[Eliora]] (2022)<br /> |-<br /> | [[7777/7776|Pulsar comma]]<br /> | <br /> | 101o1ozM<br /> | 7777/7776<br /> | 2.3.7.11.101 {{monzo| -5 -5 1 1 1 }}<br /> | 0.22262<br /> | [[Eliora]] (2022)<br /> |-<br /> | Palimilli<br /> | <br /> | 1003001o23o1uM<br /> | 23069023 / 23068672<br /> | 2.11.23.1003001 {{monzo| -21 -1 1 1 }}<br /> | 0.026341<br /> | [[User:Kaiveran|Kaiveran]] (2021)<br /> |-<br /> | [[Sulbasutrisma]]<br /> | <br /> | 577oo17uuM<br /> | 332929/332928<br /> | 2.3.17.577 {{monzo| -7 -2 -2 2 }}<br /> | 0.0052000<br /> | [[User:2^67-1|Cole]] (2024)<br /> |-<br /> | [[Zudilisma]]<br /> | <br /> | 4L397u23urM<br /> | 68630377364883 / 68630356164608<br /> | 2.3.7.23.397 {{monzo| -30 29 -1 -1 -1 }}<br /> | 0.00053479<br /> | [[Budjarn Lambeth]] (2023)<br /> |-<br /> | [[Borcherdsma]]<br /> | <br /> | 71u3(59u)47o31o 29o19o3u1uur5yM<br /> | 160561400000 / 160561399999<br /> | 2.5.7.11.13.19.29.31.47.59.71 {{monzo| 6 5 -1 -2 -1 1 1 1 1 -3 -1 }}<br /> | 1.0783 × 10&lt;sup&gt;-8&lt;/sup&gt;<br /> | [[User:Akselai|Akselai]] (2024)<br /> |}<br /> <br /> == Notes ==<br /> &lt;references /&gt;<br /> <br /> == See also ==<br /> * [[Comma and diesis]]<br /> <br /> [[Category:Unnoticeable commas| ]] &lt;!-- main article --&gt;<br /> [[Category:Lists of commas]]<br /> {{Todo|complete table|add color name}}</div> FloraC https://en.xen.wiki/index.php?title=Enneadeca&diff=232406 Enneadeca 2026-06-18T08:11:57Z <p>FloraC: I haven&#039;t seen anyone use the term &quot;19-tone-comma&quot;. It&#039;s not very clear anyway</p> <hr /> <div>{{Infobox Interval<br /> | Monzo = -14 -19 19<br /> | Name = enneadeca<br /> | Color name = y&lt;sup&gt;19&lt;/sup&gt;-4, Neyo comma<br /> | Comma = yes<br /> }}<br /> The '''enneadeca''' ({{monzo|legend=1| -14 -19 19 }}) is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] of 2.816 [[cent]]s. It is the amount by which nineteen [[6/5|classical minor thirds]] fall short of five [[2/1|octaves]], that is, 2&lt;sup&gt;5&lt;/sup&gt;/(6/5)&lt;sup&gt;19&lt;/sup&gt;. <br /> <br /> == Temperament ==<br /> [[Tempering out]] the enneadeca leads to the 5-limit [[enneadecal]] temperament, [[support]]ed by equal divisions divisible by 19 such as [[19edo]], [[38edo]], [[57edo]], [[76edo]], [[114edo]], [[152edo]], [[171edo]], [[190edo]] and [[228edo]]. <br /> <br /> == Etymology ==<br /> This comma was named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''enneadecal''&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic &amp; co'']&lt;/ref&gt;, for the temperament has 19 periods per octave. The comma was at one point dubbed ''enneadecima''&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']&lt;/ref&gt;, though it was ''enneadeca'' that stuck. <br /> <br /> == See also ==<br /> * [[Septimal enneadeca]]<br /> <br /> == References ==<br /> <br /> [[Category:Enneadecal]]<br /> [[Category:Commas named for their periods per equave]]</div> FloraC https://en.xen.wiki/index.php?title=Minortone_family&diff=232405 Minortone family 2026-06-18T08:01:05Z <p>FloraC: Units &amp; misc. cleanup</p> <hr /> <div>{{Technical data page}}<br /> The '''minortone family''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[minortone comma]] ({{monzo|legend=1| -16 35 -17 }}). <br /> <br /> == Minortone ==<br /> The head of this family is the 5-limit minortone temperament, with generator a minor tone.<br /> <br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: {{monzo| -16 35 -17 }}<br /> <br /> {{Mapping|legend=1| 1 -1 -3 | 0 17 35 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10/9 = 182.466{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}<br /> <br /> [[Badness]] (Smith): 0.029765<br /> <br /> == Mitonic ==<br /> As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, {{monzo| -16 35 -17 }}. 10/9 can be taken as the generator, with 17 of them giving a ~6, 18 of them a ~20/3, and 35 of them giving a ~40. The generator should be tuned about 1/16 of a cent flat, with 6&lt;sup&gt;1/17&lt;/sup&gt; being 0.06423 cents flat and 40&lt;sup&gt;1/35&lt;/sup&gt; being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.<br /> <br /> However, as noted before, 32/21 is only a ragisma shy of (10/9)&lt;sup&gt;4&lt;/sup&gt;, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. 21 generators gives a ~64/7. [[Mos scale]]s of size 20, 33, 46 or 79 notes can be used for mitonic.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 2100875/2097152<br /> <br /> {{Mapping|legend=1| 1 -1 -3 6 | 0 17 35 -21 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~10/9 = 182.458{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}<br /> <br /> [[Badness]] (Smith): 0.025184<br /> <br /> === Mineral ===<br /> Extending mitonic to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: ''mineral'' (46 &amp;amp; 171) and ''ore'' (46 &amp;amp; 125). The mineral temperament tempers out 441/440 and 16384/16335 in the 11-limit. In the 17-limit, both mineral and ore temper out 833/832, 1225/1224, 1701/1700, and 4096/4095 (2.3.5.7.13.17 commas). The word &quot;mineral&quot; is related to &quot;mine&quot; (an excavation from which ore or solid minerals are taken) and &quot;miner&quot; (a person who works in a mine, also as a pun on &quot;minor&quot;).<br /> <br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 4375/4374, 16384/16335<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 | 0 17 35 -21 -43 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.482{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125e, 171, 217, 605ee, 822dee }}<br /> <br /> Badness (Smith): 0.059060<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 364/363, 441/440, 3584/3575, 4375/4374<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 11 | 0 17 35 -21 -43 -48 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.481{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125e, 171, 217, 605ee, 822dee }}<br /> <br /> Badness (Smith): 0.033140<br /> <br /> ==== 17-limit ====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 364/363, 441/440, 595/594, 1156/1155, 3584/3575<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 11 5 | 0 17 35 -21 -43 -48 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.481{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125e, 171, 217, 605ee, 822dee }}<br /> <br /> Badness (Smith): 0.019792<br /> <br /> === Ore ===<br /> The ore temperament tempers out 385/384 and 1331/1323 in the 11-limit, and maps [[11/8]] to three generators.<br /> <br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 385/384, 1331/1323, 4375/4374<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 | 0 17 35 -21 3 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.449{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171e }}<br /> <br /> Badness (Smith): 0.053662<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 352/351, 385/384, 1331/1323, 3267/3250<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 11 | 0 17 35 -21 3 -48 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.470{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125, 171e, 388ee }}<br /> <br /> Badness (Smith): 0.046170<br /> <br /> ===== 17-limit =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 352/351, 385/384, 561/560, 715/714, 1452/1445<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 11 5 | 0 17 35 -21 3 -48 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.471{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125, 171e, 388ee }}<br /> <br /> Badness (Smith): 0.028423<br /> <br /> ==== Goldmine ====<br /> The goldmine temperament (46 &amp; 79) is another 13-limit extension of ore, equating [[13/12]] with [[14/13]] and [[16/13]] with two [[10/9]]s.<br /> <br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 169/168, 325/324, 385/384, 1331/1323<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 4 | 0 17 35 -21 3 -2 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.437{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 79, 125f, 171ef, 296eff }}<br /> <br /> Badness (Smith): 0.039302<br /> <br /> ===== 17-limit =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 169/168, 273/272, 325/324, 385/384, 1331/1323<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 4 5 | 0 17 35 -21 3 -2 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.444{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 125f, 171ef }}<br /> <br /> Badness (Smith): 0.027440<br /> <br /> === Seminar ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 2100875/2097152<br /> <br /> Mapping: {{mapping| 2 -2 -6 12 13 | 0 17 35 -21 -20 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~10/9 = 182.457{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 46, 204c, 250, 296, 342 }}<br /> <br /> Badness (Smith): 0.026808<br /> <br /> == Domain ==<br /> {{See also| Landscape microtemperaments #Domain }}<br /> <br /> Domain adds the [[landscape comma]], 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Subgroup temperaments #Terrain|terrain]].<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 250047/250000, 645700815/645657712<br /> <br /> {{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~10/9 = 182.467{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}<br /> <br /> [[Badness]] (Smith): 0.013979<br /> <br /> === Hemidomain ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 250047/250000, 14348907/14348180<br /> <br /> Mapping: {{mapping| 6 11 17 20 24 | 0 -17 -35 -36 -37 }}<br /> : mapping generators: ~55/49 = 200.000{{c}}, ~100/99 = 17.533{{c}}<br /> <br /> Optimal tuning (CTE): ~100/99 = 17.533<br /> <br /> {{Optimal ET sequence|legend=0| 342, 480, 822, 1164, 1506, 1848, … }}<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Minortone family| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=Mineral&diff=232404 Mineral 2026-06-18T07:55:10Z <p>FloraC: Update &amp; recategorize (mitonic extension)</p> <hr /> <div>#REDIRECT [[Minortone family #Mineral]]<br /> <br /> [[Category:Mitonic]]</div> FloraC https://en.xen.wiki/index.php?title=Seminar&diff=232403 Seminar 2026-06-18T07:54:43Z <p>FloraC: Update &amp; recategorize (mitonic extension)</p> <hr /> <div>#REDIRECT [[Minortone family #Seminar]]<br /> <br /> [[Category:Mitonic]]</div> FloraC https://en.xen.wiki/index.php?title=Domain_(temperament)&diff=232402 Domain (temperament) 2026-06-18T07:53:44Z <p>FloraC: Update &amp; recategorize</p> <hr /> <div>#redirect [[Minortone family #Domain]]<br /> <br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Minortone family]]<br /> [[Category:Landscape microtemperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Mitonic&diff=232401 Mitonic 2026-06-18T07:52:11Z <p>FloraC: Update &amp; + categories</p> <hr /> <div>#redirect [[Minortone family #Mitonic]]<br /> <br /> [[Category:Mitonic| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Minortone family]]<br /> [[Category:Ragismic microtemperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Minortone&diff=232400 Minortone 2026-06-18T07:50:44Z <p>FloraC: + category</p> <hr /> <div>#REDIRECT [[Minortone family #Minortone]]<br /> <br /> [[Category:Minortone| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Minortone family]]</div> FloraC https://en.xen.wiki/index.php?title=Category:Minortone_family&diff=232399 Category:Minortone family 2026-06-18T07:50:01Z <p>FloraC: + category</p> <hr /> <div>{{Cat main}}<br /> <br /> [[Category:Minortone]]<br /> [[Category:Temperament families]]</div> FloraC https://en.xen.wiki/index.php?title=Category:Minortone_family&diff=232398 Category:Minortone family 2026-06-18T07:49:35Z <p>FloraC: FloraC moved page Category:Minortonic family to Category:Minortone family without leaving a redirect: The temp&#039;s name is *minortone*</p> <hr /> <div>{{Cat main}}<br /> [[Category:Temperament families]]</div> FloraC https://en.xen.wiki/index.php?title=Minortone&diff=232397 Minortone 2026-06-18T07:49:13Z <p>FloraC: Update &amp; + categories</p> <hr /> <div>#REDIRECT [[Minortone family #Minortone]]<br /> <br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Minortone family]]</div> FloraC https://en.xen.wiki/index.php?title=Minortone_node&diff=232396 Minortone node 2026-06-18T07:48:15Z <p>FloraC: Changed redirect target from Minortonic family#Minortone to Minortone family#Minortone</p> <hr /> <div>#redirect [[Minortone family #Minortone]]</div> FloraC https://en.xen.wiki/index.php?title=Minortonic_family&diff=232395 Minortonic family 2026-06-18T07:47:46Z <p>FloraC: FloraC moved page Minortonic family to Minortone family: The temp&#039;s name is *minortone*</p> <hr /> <div>#REDIRECT [[Minortone family]]</div> FloraC https://en.xen.wiki/index.php?title=Minortone_family&diff=232394 Minortone family 2026-06-18T07:47:46Z <p>FloraC: FloraC moved page Minortonic family to Minortone family: The temp&#039;s name is *minortone*</p> <hr /> <div>{{Technical data page}}<br /> The '''minortonic family''' tempers out the minortone comma (also known as &quot;minortonma&quot;), {{monzo| -16 35 -17 }}. The head of this family is 5-limit minortone temperament, with generator a minor tone.<br /> <br /> == Minortone ==<br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: {{monzo| -16 35 -17 }}<br /> <br /> {{Mapping|legend=1| 1 -1 -3 | 0 17 35 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.466<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171, 388, 559, 730, 1289, 2019, 2749, 4768, 16323, 21091 }}<br /> <br /> [[Badness]]: 0.029765<br /> <br /> == Mitonic ==<br /> As a 5-limit temperament, mitonic becomes minortonic, a super-accurate microtemperament tempering out the minortone comma, {{monzo| -16 35 -17 }}. 10/9 can be taken as the generator, with 17 of them giving a ~6, 18 of them a ~20/3, and 35 of them giving a ~40. The generator should be tuned about 1/16 of a cent flat, with 6&lt;sup&gt;1/17&lt;/sup&gt; being 0.06423 cents flat and 40&lt;sup&gt;1/35&lt;/sup&gt; being 0.06234 cents flat. 171, 559 and 730 are possible equal temperament tunings.<br /> <br /> However, as noted before, 32/21 is only a ragisma shy of (10/9)&lt;sup&gt;4&lt;/sup&gt;, and so a 7-limit interpretation, if not quite so super-accurate, is more or less inevitable. While 559 or 730 are still fine as tunings, the error of the 7-limit is lower by a whisker in [[171edo]]. 21 generators gives a ~64/7. [[Mos scale]]s of size 20, 33, 46 or 79 notes can be used for mitonic.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 2100875/2097152<br /> <br /> {{Mapping|legend=1| 1 -1 -3 6 | 0 17 35 -21 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 182.458<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171, 1927d, 2098d, …, 3637bcdd }}<br /> <br /> [[Badness]]: 0.025184<br /> <br /> === Mineral ===<br /> Extending mitonic to the 11-limit is not so simple. There are two mappings that are comparable in complexity and error: ''mineral'' (46 &amp;amp; 171) and ''ore'' (46 &amp;amp; 125). The mineral temperament tempers out 441/440 and 16384/16335 in the 11-limit. In the 17-limit, both mineral and ore temper out 833/832, 1225/1224, 1701/1700, and 4096/4095 (2.3.5.7.13.17 commas). The word &quot;mineral&quot; is related to &quot;mine&quot; (an excavation from which ore or solid minerals are taken) and &quot;miner&quot; (a person who works in a mine, also as a pun on &quot;minor&quot;).<br /> <br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 4375/4374, 16384/16335<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 | 0 17 35 -21 -43 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.482<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}<br /> <br /> Badness: 0.059060<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 364/363, 441/440, 3584/3575, 4375/4374<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 11 | 0 17 35 -21 -43 -48 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}<br /> <br /> Badness: 0.033140<br /> <br /> ==== 17-limit ====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 364/363, 441/440, 595/594, 1156/1155, 3584/3575<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 10 11 5 | 0 17 35 -21 -43 -48 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.481<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125e, 171, 217, 605ee, 822dee }}<br /> <br /> Badness: 0.019792<br /> <br /> === Ore ===<br /> The ore temperament tempers out 385/384 and 1331/1323 in the 11-limit, and maps [[11/8]] to three generators.<br /> <br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 385/384, 1331/1323, 4375/4374<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 | 0 17 35 -21 3 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.449<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171e }}<br /> <br /> Badness: 0.053662<br /> <br /> ==== 13-limit ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 352/351, 385/384, 1331/1323, 3267/3250<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 11 | 0 17 35 -21 3 -48 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.470<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171e, 388ee }}<br /> <br /> Badness: 0.046170<br /> <br /> ===== 17-limit =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 352/351, 385/384, 561/560, 715/714, 1452/1445<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 11 5 | 0 17 35 -21 3 -48 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.471<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125, 171e, 388ee }}<br /> <br /> Badness: 0.028423<br /> <br /> ==== Goldmine ====<br /> The goldmine temperament (46 &amp;amp; 79) is another 13-limit extension of ore, equating [[13/12]] with [[14/13]] and [[16/13]] with two [[10/9]]s.<br /> <br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 169/168, 325/324, 385/384, 1331/1323<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 4 | 0 17 35 -21 3 -2 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.437<br /> <br /> {{Optimal ET sequence|legend=1| 46, 79, 125f, 171ef, 296eff }}<br /> <br /> Badness: 0.039302<br /> <br /> ===== 17-limit =====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 169/168, 273/272, 325/324, 385/384, 1331/1323<br /> <br /> Mapping: {{mapping| 1 -1 -3 6 3 4 5 | 0 17 35 -21 3 -2 -6 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.444<br /> <br /> {{Optimal ET sequence|legend=1| 46, 125f, 171ef }}<br /> <br /> Badness: 0.027440<br /> <br /> === Seminar ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 2100875/2097152<br /> <br /> Mapping: {{mapping| 2 -2 -6 12 13 | 0 17 35 -21 -20 }}<br /> <br /> Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 182.457<br /> <br /> {{Optimal ET sequence|legend=1| 46, 204c, 250, 296, 342 }}<br /> <br /> Badness: 0.026808<br /> <br /> == Domain ==<br /> {{See also| Landscape microtemperaments #Domain }}<br /> <br /> Domain adds the [[landscape comma]], 250047/250000, to the minortone comma, giving a temperament which is perhaps most notable for its inclusion of the remarkable subgroup temperament [[Subgroup temperaments #Terrain|terrain]].<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 250047/250000, 645700815/645657712<br /> <br /> {{Mapping|legend=1| 3 -3 -9 -8 | 0 17 35 36 }}<br /> <br /> [[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 182.467<br /> <br /> {{Optimal ET sequence|legend=1| 171, 1164, 1335, 1506, 1677, 1848, 2019, 11943, 13962, 15981, 18000, 20019, 22038 }}<br /> <br /> [[Badness]]: 0.013979<br /> <br /> === Hemidomain ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 250047/250000, 14348907/14348180<br /> <br /> Mapping: {{mapping| 6 11 17 20 24 | 0 -17 -35 -36 -37 }}<br /> <br /> : mapping generators: ~55/49 = 1\6, ~100/99 = 17.533<br /> <br /> Optimal tuning (CTE): ~100/99 = 17.533<br /> <br /> {{Optimal ET sequence|legend=1| 342, 480, 822, 1164, 1506, 1848, … }}<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Minortonic family| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=Catalog_of_rank-4_temperaments&diff=232393 Catalog of rank-4 temperaments 2026-06-18T07:44:50Z <p>FloraC: Re-add</p> <hr /> <div>{{Technical data page}}<br /> A '''rank-4 temperament''' has a [[period]] and three additional independent [[generator]]s, for a total of four [[rank and codimension|dimensions]]. Typical examples include [[7-limit]] [[JI]], full 11-limit temperament with a one-dimensional [[comma basis]], and full 13-limit temperament with a two-dimensional comma basis. <br /> <br /> == Cake (45/44) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[45/44]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -2 | 0 1 0 0 2 | 0 0 1 0 1 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1202.4372{{c}}, ~3/2 = 693.2306{{c}}, ~5/4 = 374.6677{{c}}, ~7/4 = 963.8387{{c}}<br /> : [[error map]]: {{val| +2.437 -6.287 -6.772 -0.113 +14.685 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 693.1966{{c}}, ~5/4 = 376.0821{{c}}, ~7/4 = 965.0600{{c}}<br /> : error map: {{val| 0.000 -8.758 -10.232 -3.766 +11.157 }}<br /> <br /> {{Optimal ET sequence|legend=1| 7d, 9, 10, 12, 19, 26, 45 }}<br /> <br /> [[Badness]] (Sintel): 0.400<br /> <br /> == Mothwellsmic (99/98) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[99/98]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 1 | 0 1 0 0 -2 | 0 0 1 0 0 | 0 0 0 1 2 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.3175{{c}}, ~3/2 = 700.0109{{c}}, ~5/4 = 385.6677{{c}}, ~7/4 = 973.2571{{c}}<br /> : [[error map]]: {{val| +0.318 -1.627 -0.011 +5.066 -3.873 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.0599{{c}}, ~5/4 = 385.9307{{c}}, ~7/4 = 973.4880{{c}}<br /> : error map: {{val| 0.000 -1.895 -0.383 +4.662 -4.462 }}<br /> <br /> {{Optimal ET sequence|legend=1| 5, 8d, 9, 12, 17c, 19e, 22, 31, 53, 84e, 96, 127 }}<br /> <br /> [[Badness]] (Sintel): 0.545<br /> <br /> == Ptolemismic (100/99) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[100/99]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 -2 | 0 0 1 0 2 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.2633{{c}}, ~3/2 = 704.5205{{c}}, ~5/4 = 383.8317{{c}}, ~7/4 = 970.2843{{c}}<br /> : [[error map]]: {{val| -0.737 +1.829 -3.955 -0.015 +4.358 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 704.4751{{c}}, ~5/4 = 383.0756{{c}}, ~7/4 = 969.8904{{c}}<br /> : error map: {{val| 0.000 +2.520 -3.238 +1.065 +5.883 }}<br /> <br /> {{Optimal ET sequence|legend=1| 7d, 8d, 10e, 12, 15, 19, 22, 27e, 34d, 41, 90e, 131e }} &lt;nowiki&gt;*&lt;/nowiki&gt;<br /> <br /> &lt;nowiki&gt;*&lt;/nowiki&gt; [[optimal patent val]]: [[104edo|104]]<br /> <br /> [[Badness]] (Sintel): 0.411<br /> <br /> == Biyatismic (121/120) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[121/120]]<br /> <br /> {{Mapping|legend=1| 1 0 1 0 2 | 0 1 1 0 1 | 0 0 -2 0 -1 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~3, ~11/10, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.6628{{c}}, ~3/2 = 701.8452{{c}}, ~11/10 = 157.8337{{c}}, ~7/4 = 967.4929{{c}}<br /> : [[error map]]: {{val| +0.663 +0.553 +1.190 -0.007 -5.318 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9848{{c}}, ~11/10 = 157.6099{{c}}, ~7/4 = 967.8187{{c}}<br /> : error map: {{val| 0.000 +0.030 +0.451 -1.007 -6.943 }}<br /> <br /> {{Optimal ET sequence|legend=1| 14c, 15, 22, 31, 46, 53, 60e, 68, 77, 91e, 99, 130e, 159ee, 190ee }}<br /> <br /> [[Badness]] (Sintel): 0.629<br /> <br /> == Valinorsmic (176/175) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[176/175]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -4 | 0 1 0 0 0 | 0 0 1 0 2 | 0 0 0 1 1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.3113{{c}}, ~3/2 = 702.6414{{c}}, ~5/4 = 389.5404{{c}}, ~7/4 = 971.5534{{c}}<br /> : [[error map]]: {{val| -0.689 -0.022 +1.849 +1.350 -2.061 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5869{{c}}, ~5/4 = 389.3935{{c}}, ~7/4 = 971.5196{{c}}<br /> : error map: {{val| 0.000 +0.632 +3.080 +2.694 -1.011 }}<br /> <br /> {{Optimal ET sequence|legend=1| 22, 27e, 31, 46, 53, 58, 80, 111, 237cd, 268cd }}<br /> <br /> [[Badness]] (Sintel): 0.339<br /> <br /> === Tridecimal valinorsmic ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 176/175, 351/350<br /> <br /> Mapping: {{Mapping| 1 0 0 0 -4 1 | 0 1 0 0 0 -3 | 0 0 1 0 2 2 | 0 0 0 1 1 1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.3397{{c}}, ~3/2 = 702.5360{{c}}, ~5/4 = 389.5451{{c}}, ~7/4 = 971.5415{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.6943{{c}}, ~5/4 = 389.3823{{c}}, ~7/4 = 971.5305{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 22, 27e, 31, 46, 53, 58, 80, 104c, 111, 268cd }}<br /> <br /> Badness (Sintel): 0.603<br /> <br /> == Rastmic (243/242) ==<br /> Rastmic halves [[3/2]] into two [[11/9]]'s, [[32/27]] into two [[12/11]]'s, and [[25/24]] into two [[45/44]][[~]][[55/54]]'s.<br /> <br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[243/242]]<br /> <br /> {{Mapping|legend=1| 1 1 0 0 2 | 0 2 0 0 5 | 0 0 1 0 0 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~11/9, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0635{{c}}, ~11/9 = 350.5439{{c}}, ~5/4 = 386.1857{{c}}, ~7/4 = 968.6977{{c}}<br /> : [[error map]]: {{val| +0.064 -0.804 -0.001 -0.001 +1.529 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~11/9 = 350.5486{{c}}, ~5/4 = 386.2387{{c}}, ~7/4 = 968.7352{{c}}<br /> : error map: {{val| 0.000 -0.858 -0.075 -0.091 +1.425 }}<br /> <br /> {{Optimal ET sequence|legend=1| 7d, 10, 14c, 17c, 24, 27e, 31, 41, 58, 72, 130, 202 }}<br /> <br /> [[Badness]] (Sintel): 0.928<br /> <br /> == Frostmic (245/242) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[245/242]]<br /> <br /> {{Mapping|legend=1| 1 0 1 0 0 | 0 1 0 0 0 | 0 0 2 0 1 | 0 0 0 1 1 }}<br /> : Mapping generators: ~2, ~3, ~11/7, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.2442{{c}}, ~3/2 = 701.7038{{c}}, ~11/7 = 792.3594{{c}}, ~7/4 = 964.4060{{c}}<br /> : [[error map]]: {{val| +0.244 -0.007 -1.351 -3.931 +5.936 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7533{{c}}, ~11/7 = 792.3351{{c}}, ~7/4 = 964.5274{{c}}<br /> : error map: {{val| 0.000 -0.202 -1.644 -4.298 +5.545 }}<br /> <br /> {{Optimal ET sequence|legend=1| 9, 12, 15, 23de, 24, 26, 27e, 38d, 41, 91, 106d }}<br /> <br /> [[Badness]] (Sintel): 1.64<br /> <br /> == Akua (352/351, 847/845) ==<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 352/351, 847/845<br /> <br /> {{Mapping|legend=1| 1 0 0 10 0 5 | 0 1 0 -6 0 -3 | 0 0 1 1 0 0 | 0 0 0 0 1 1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~11<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.6918{{c}}, ~3/2 = 702.7270{{c}}, ~5/4 = 386.9729{{c}}, ~11/8 = 551.3122{{c}}<br /> : [[error map]]: {{val| -0.308 +0.464 +0.043 -0.064 -0.930 +1.062 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.8960{{c}}, ~5/4 = 386.7835{{c}}, ~11/8 = 551.0679{{c}}<br /> : error map: {{val| 0.000 +0.941 +0.470 +0.581 -0.025 +1.852 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12f, 17c, 24d, 29, 41, 46, 53, 58, 87, 111, 140, 152f, 198, 350f, 437f, 490f }}<br /> <br /> [[Badness]] (Sintel): 0.669<br /> <br /> == Keenanismic (385/384) ==<br /> {{Main| Keenanismic family }}<br /> <br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[385/384]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 1 | 0 0 1 0 -1 | 0 0 0 1 -1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.4104{{c}}, ~3/2 = 701.6916{{c}}, ~5/4 = 385.1761{{c}}, ~7/4 = 967.5421{{c}}<br /> : [[error map]]: {{val| +0.410 +0.147 -0.317 -0.463 -0.703 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6933{{c}}, ~5/4 = 385.1491{{c}}, ~7/4 = 967.3004{{c}}<br /> : error map: {{val| 0.000 -0.262 -1.165 -1.525 -2.074 }}<br /> <br /> [[Minimax tuning]]: <br /> * [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~3 = {{monzo| 0 1 0 0 0 }}, ~5 = {{monzo| 7/3 1/3 2/3 -1/3 -1/3 }}, ~7 = {{monzo| 7/3 1/3 -1/3 2/3 -1/3 }}<br /> : [[eigenmonzo basis|Unchanged-interval (eigenmonzo) basis]]: 2.3.7/5.11/5<br /> <br /> {{Optimal ET sequence|legend=1| 9, 10, 12e, 15, 19, 22, 31, 41, 53, 68, 72, 118, 159, 190, 212, 284, 330e, 402de }}<br /> <br /> [[Badness]] (Sintel): 0.277<br /> <br /> === Martwin ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 325/324, 385/384<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 2 | 0 1 0 0 1 4 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 0 }}<br /> <br /> Lattice basis: <br /> : 4/3 length = 1.0820, 6/5 length = 1.3935, 10/9 length = 1.6247<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.3494{{c}}, ~3/2 = 702.2131{{c}}, ~5/4 = 384.8666{{c}}, ~7/4 = 967.8487{{c}}<br /> : [[error map]]: {{val| +0.349 +0.608 -0.748 -0.278 -0.422 -0.710 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.1659{{c}}, ~5/4 = 384.8721{{c}}, ~7/4 = 967.6109{{c}}<br /> : error map: {{val| 0.000 +0.211 -1.442 -1.215 -1.635 -1.608 }}<br /> <br /> [[Minimax tuning]]: <br /> * [[13-odd-limit|13-]] and [[15-odd-limit]]: ~2 = {{val| 1 0 0 0 0 0 }}, ~3 = {{val| 0 1 0 0 0 0 }}, ~5 = {{val| 2/3 4/3 1/3 0 0 -1/3 }}, ~7 = {{val| 19/6 -1/6 -1/6 1/2 -1/2 1/6 }}<br /> : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.3.11/7.13/5<br /> <br /> {{Optimal ET sequence|legend=1| 12e, 15, 19, 22f, 26, 31f, 41, 46, 53, 72, 87, 125f, 140, 159, 212, 299, 371df, 465cef, 677cdeeff, 764cdeeff }}<br /> <br /> [[Badness]] (Sintel): 0.579<br /> <br /> === Ancient ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 385/384, 625/624<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 -4 | 0 1 0 0 1 -1 | 0 0 1 0 -1 4 | 0 0 0 1 -1 0 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.4130{{c}}, ~3/2 = 701.6863{{c}}, ~5/4 = 385.2319{{c}}, ~7/4 = 967.5188{{c}}<br /> : [[error map]]: {{val| +0.413 +0.144 -0.256 -0.481 -0.730 -0.047 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6838{{c}}, ~5/4 = 385.2497{{c}}, ~7/4 = 967.2556{{c}}<br /> : error map: {{val| 0.000 -0.271 -1.064 -1.570 -2.139 -1.213 }}<br /> <br /> {{Optimal ET sequence|legend=1| 15, 19, 22, 31, 50, 53, 72, 87, 103, 140, 159, 190, 243e, 315ef, 330e, 402def }}<br /> <br /> [[Badness]] (Sintel): 0.675<br /> <br /> === Commas 351/350, 385/384 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 351/350, 385/384<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 1 | 0 1 0 0 1 -3 | 0 0 1 0 -1 2 | 0 0 0 1 -1 1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.6793{{c}}, ~3/2 = 700.7455{{c}}, ~5/4 = 385.5609{{c}}, ~7/4 = 967.5816{{c}}<br /> : [[error map]]: {{val| +0.679 -0.530 +0.606 +0.114 -0.998 -1.343 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.5141{{c}}, ~5/4 = 385.6072{{c}}, ~7/4 = 967.1521{{c}}<br /> : error map: {{val| 0.000 -1.441 -0.706 -1.674 -3.563 -3.703 }}<br /> <br /> {{Optimal ET sequence|legend=1| 19, 22, 26, 31, 46, 53, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 495bdeefff, 545bddeefff, 598bcdeeefff }}<br /> <br /> [[Badness]] (Sintel): 0.781<br /> <br /> === Zaxa ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 352/351, 385/384<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 -2 | 0 0 1 0 -1 -1 | 0 0 0 1 -1 -1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.1117{{c}}, ~3/2 = 702.6588{{c}}, ~5/4 = 385.6821{{c}}, ~7/4 = 968.0061{{c}}<br /> : [[error map]]: {{val| +0.112 +0.815 -0.408 -0.596 -1.901 +1.137 }}<br /> * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 702.6029{{c}}, ~5/4 = 385.6441{{c}}, ~7/4 = 967.9030{{c}}<br /> : error map: {{val| 0.000 +0.648 -0.670 -0.923 -2.262 +0.720 }}<br /> <br /> {{Optimal ET sequence|legend=1| 22, 31, 41, 46, 53, 77, 87, 118, 140, 258e, 461e }}<br /> <br /> [[Badness]] (Sintel): 0.880<br /> <br /> === Commas 364/363, 385/384 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 364/363, 385/384<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 1 3 | 0 0 1 0 -1 -2 | 0 0 0 1 -1 -3 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.4593{{c}}, ~3/2 = 701.9714{{c}}, ~5/4 = 384.8903{{c}}, ~7/4 = 966.4090{{c}}<br /> : [[error map]]: {{val| +0.459 +0.476 -0.505 -1.498 +1.191 -1.325 }}<br /> * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.9809{{c}}, ~5/4 = 384.8523{{c}}, ~7/4 = 966.1074{{c}}<br /> : error map: {{val| 0.000 +0.026 -1.461 -2.719 -0.297 -2.612 }}<br /> <br /> {{Optimal ET sequence|legend=1| 9, 15, 22, 26, 31f, 37, 41, 46, 63, 72, 87, 159 }}<br /> <br /> [[Badness]] (Sintel): 0.871<br /> <br /> === Commas 385/384, 847/845 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 385/384, 847/845<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 7 | 0 1 0 0 1 1 | 0 0 1 1 -2 -2 | 0 0 0 2 -2 -1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~13/11<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.3530{{c}}, ~3/2 = 701.7283{{c}}, ~5/4 = 385.4633{{c}}, ~13/11 = 291.0352{{c}}<br /> : [[error map]]: {{val| +0.353 +0.126 -0.144 -0.586 -1.175 +0.651 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7205{{c}}, ~5/4 = 385.3656{{c}}, ~13/11 = 290.9769{{c}}<br /> : error map: {{val| 0.000 -0.235 -0.948 -1.507 -2.282 -0.515 }}<br /> <br /> {{Optimal ET sequence|legend=1| 34, 37, 41, 46, 53, 87, 103, 140, 190, 243e, 330e, 520de, 573dee }}<br /> <br /> [[Badness]] (Sintel): 1.09<br /> <br /> == Werckismic (441/440) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[441/440]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -3 | 0 1 0 0 2 | 0 0 1 0 -1 | 0 0 0 1 2 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.1734{{c}}, ~3/2 = 701.4907{{c}}, ~5/4 = 386.2784{{c}}, ~7/4 = 967.5667{{c}}<br /> : [[error map]]: {{val| +0.173 -0.291 +0.311 -0.912 +0.692 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4963{{c}}, ~5/4 = 386.4317{{c}}, ~7/4 = 967.5883{{c}}<br /> : error map: {{val| 0.000 -0.459 +0.118 -1.238 +0.420 }}<br /> <br /> [[Minimax tuning]]: <br /> * [[11-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 }}, ~3 = {{monzo| 1/2 2/3 1/6 -1/3 1/6 }}, ~5 = {{monzo| 0 0 1 0 0 }}, ~7 = {{monzo| 1 -2/3 1/3 1/3 1/3 }}<br /> : [[eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5.9/7.11<br /> <br /> {{Optimal ET sequence|legend=1| 10, 12, 15, 19e, 26, 27e, 31, 41, 58, 72, 118, 130, 190, 248, 289, 320, 609d }}<br /> <br /> [[Badness]] (Sintel): 0.189<br /> <br /> === Commas 364/363, 441/440 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 364/363, 441/440<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -3 -8 | 0 1 0 0 2 5 | 0 0 1 0 -1 -2 | 0 0 0 1 2 3 }}<br /> <br /> [[Mapping to lattice]]: [{{val| 0 1 1 -1 -1 0 }}, {{val| 0 0 1 0 -1 -2 }}, {{val| 0 0 1 1 1 1 }}]<br /> <br /> Lattice basis: <br /> : 3/2 length = 1.2263, 14/11 length = 1.4629, 21/16 length = 1.4657<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0145{{c}}, ~3/2 = 701.8745{{c}}, ~5/4 = 386.4853{{c}}, ~7/4 = 967.8244{{c}}<br /> : [[error map]]: {{val| +0.014 -0.066 +0.201 -0.972 +1.609 -0.667 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.8716{{c}}, ~5/4 = 386.4975{{c}}, ~7/4 = 967.8241{{c}}<br /> : error map: {{val| 0.000 -0.083 +0.184 -1.002 +1.576 -0.692 }}<br /> <br /> [[Minimax tuning]]: <br /> * [[13-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 0 }}, ~3 = {{monzo| 5/3 0 1/3 -1/3 -1/3 1/3 }}, ~5 = {{monzo| 1/6 0 5/6 2/3 -5/6 1/3 }}, ~7 = {{monzo| 0 0 0 1 0 0 }}<br /> : [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7.11/5.13<br /> * [[15-odd-limit]]: ~2 = {{monzo| 1 0 0 0 0 0 }}, ~3 = {{monzo| 5/4 1/4 1/4 -1/4 -1/4 1/4 }}, ~5 = {{monzo| 5/4 -3/4 5/4 -1/4 -1/4 1/4 }}, ~7 = {{monzo| 17/8 -11/8 5/8 -1/8 3/8 1/8 }}<br /> : [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3.11/9.13/7<br /> <br /> {{Optimal ET sequence|legend=1| 12f, 14cf, 15, 17c, 26, 29, 31f, 41, 46, 58, 72, 87, 130, 217, 289 }}<br /> <br /> [[Badness]] (Sintel): 0.452<br /> <br /> === Commas 351/350, 441/440 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 351/350, 441/440<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -3 1 | 0 1 0 0 2 -3 | 0 0 1 0 -1 2 | 0 0 0 1 2 1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.2006{{c}}, ~3/2 = 701.0354{{c}}, ~5/4 = 386.8579{{c}}, ~7/4 = 968.2226{{c}}<br /> : [[error map]]: {{val| +0.201 -0.719 +0.945 -0.202 +0.541 -0.893 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.0371{{c}}, ~5/4 = 387.0417{{c}}, ~7/4 = 968.2546{{c}}<br /> : error map: {{val| 0.000 -0.918 +0.728 -0.571 +0.224 -1.301 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12f, 14cf, 19e, 26, 27e, 31, 45ef, 46, 58, 72, 103, 130, 233, 279, 409, 512bf, 642bf }}<br /> <br /> [[Badness]] (Sintel): 0.524<br /> <br /> === Commas 196/195, 352/351 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 196/195, 352/351<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -3 2 | 0 1 0 0 2 -1 | 0 0 1 0 -1 -1 | 0 0 0 1 2 2 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.6830{{c}}, ~3/2 = 702.6689{{c}}, ~5/4 = 387.7765{{c}}, ~7/4 = 967.0260{{c}}<br /> : [[error map]]: {{val| -0.317 +0.397 +0.829 -2.434 -0.022 +2.128 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7536{{c}}, ~5/4 = 387.5834{{c}}, ~7/4 = 966.9373{{c}}<br /> : error map: {{val| 0.000 +0.799 +1.270 -1.889 +0.480 +3.010 }}<br /> <br /> {{Optimal ET sequence|legend=1| 10, 12f, 17c, 19e, 27e, 29, 31, 41, 46, 58, 87, 118, 145, 232 }}<br /> <br /> [[Badness]] (Sintel): 0.548<br /> <br /> === Tannic ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 441/440, 1287/1280<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -3 11 | 0 1 0 0 2 -4 | 0 0 1 0 -1 2 | 0 0 0 1 2 -2 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.7398{{c}}, ~3/2 = 700.6733{{c}}, ~5/4 = 385.4125{{c}}, ~7/4 = 966.9648{{c}}<br /> : [[error map]]: {{val| +0.740 -0.542 +0.578 -0.381 -0.714 -1.147 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 700.3274{{c}}, ~5/4 = 385.8974{{c}}, ~7/4 = 966.8107{{c}}<br /> : error map: {{val| 0.000 -1.628 -0.416 -2.015 -2.939 -3.664 }}<br /> <br /> [[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 700.555{{c}}, ~5/4 = 387.816{{c}}, ~7/4 = 967.984{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 17c, 26, 29, 31, 43, 46, 60e, 72, 103, 149, 221ef, 324bdef, 473bdeeff, 545bddeefff }}<br /> <br /> [[Badness]] (Sintel): 1.23<br /> <br /> ==== 17-limit ====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 273/272, 441/440, 561/560<br /> <br /> Mapping: {{mapping| 1 0 0 0 -3 11 7 | 0 1 0 0 2 -4 -3 | 0 0 1 0 -1 2 2 | 0 0 0 1 2 -2 -1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1200.7320{{c}}, ~3/2 = 700.7374{{c}}, ~5/4 = 385.2303{{c}}, ~7/4 = 966.8369{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.3909{{c}}, ~5/4 = 385.7215{{c}}, ~7/4 = 966.6922{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 17cg, 26, 29g, 31, 43, 46, 60e, 72, 103, 149, 221ef }}<br /> <br /> Badness (Sintel): 0.701<br /> <br /> === Commas 441/440, 847/845 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 441/440, 847/845<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -3 -3 | 0 1 0 0 2 2 | 0 0 1 1 1 1 | 0 0 0 2 4 5 }}<br /> : Mapping generators: ~2, ~3, ~5, ~13/11<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.1778{{c}}, ~3/2 = 701.4785{{c}}, ~5/4 = 385.4755{{c}}, ~13/11 = 290.3844{{c}}<br /> : [[error map]]: {{val| +0.178 -0.299 +0.517 -1.226 -0.170 +1.005 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4843{{c}}, ~5/4 = 386.6332{{c}}, ~13/11 = 290.3162{{c}}<br /> : error map: {{val| 0.000 -0.471 +0.319 -1.560 -0.451 +0.655 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12f, 16, 17c, 25e, 29, 41, 46, 58, 87, 103, 145, 149, 161, 190, 248, 438d }}<br /> <br /> [[Badness]] (Sintel): 1.11<br /> <br /> == Swetismic (540/539) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[540/539]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 0 3 | 0 0 1 0 1 | 0 0 0 1 -2 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9149{{c}}, ~3/2 = 701.7196{{c}}, ~5/4 = 386.2545{{c}}, ~7/4 = 969.6659{{c}}<br /> : [[error map]]: {{val| -0.085 -0.321 -0.229 +0.670 +0.508 }}<br /> * [[CWE]]: ~2 = 1200.000{{c}}, ~3/2 = 701.6950{{c}}, ~5/4 = 386.1795{{c}}, ~7/4 = 969.6366{{c}}<br /> : error map: {{val| 0.000 -0.260 -0.134 +0.811 +0.673 }}<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 9, 10, 12e, 14c, 17c, 19, 22, 27e, 31, 41, 53, 58, 72, 130, 152, 224, 354, 506e, 578, 730de, 761d, 985d, 1115de, 1267dde }}<br /> <br /> [[Badness]] (Sintel): 0.191<br /> <br /> === Commas 540/539, 729/728 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 540/539, 729/728<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 0 3 6 | 0 0 1 0 1 0 | 0 0 0 1 -2 -1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9170{{c}}, ~3/2 = 701.7128{{c}}, ~5/4 = 386.2521{{c}}, ~7/4 = 969.6598{{c}}<br /> : [[error map]]: {{val| -0.083 -0.325 -0.228 +0.668 +0.504 +0.006 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.7231{{c}}, ~5/4 = 386.1819{{c}}, ~7/4 = 969.6608{{c}}<br /> : error map: {{val| 0.000 -0.232 -0.132 +0.835 +0.712 +0.150 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12e, 14cf, 17c, 19, 22f, 31f, 39df, 41, 53, 58, 72, 111, 130, 183, 224, 354, 578, 985d, 1267ddef }}<br /> <br /> [[Badness]] (Sintel): 0.454<br /> <br /> === Commas 540/539, 625/624 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 540/539, 625/624<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 -4 | 0 1 0 0 3 -1 | 0 0 1 0 1 4 | 0 0 0 1 -2 0 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0035{{c}}, ~3/2 = 701.6973{{c}}, ~5/4 = 385.6264{{c}}, ~7/4 = 969.4616{{c}}<br /> : [[error map]]: {{val| +0.004 -0.254 -0.680 +0.643 +0.488 +0.291 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.6983{{c}}, ~5/4 = 385.6278{{c}}, ~7/4 = 969.4622{{c}}<br /> : error map: {{val| 0.000 -0.257 -0.686 +0.636 +0.480 +0.285 }}<br /> <br /> {{Optimal ET sequence|legend=1| 19, 22, 31, 49f, 50, 53, 72, 103, 121, 152f, 193, 224 }}<br /> <br /> [[Badness]] (Sintel): 0.943<br /> <br /> === Commas 540/539, 676/675 ===<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: 540/539, 676/675<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 -1 | 0 2 0 0 6 3 | 0 0 1 0 1 1 | 0 0 0 1 -2 0 }}<br /> : Mapping generators: ~2, ~26/15, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.7990{{c}}, ~26/15 = 950.9130{{c}}, ~5/4 = 386.8478{{c}}, ~7/4 = 970.1529{{c}}<br /> : [[error map]]: {{val| -0.201 -0.129 +0.132 +0.925 +0.702 -1.142 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~26/15 = 950.9953{{c}}, ~5/4 = 386.7094{{c}}, ~7/4 = 970.1192{{c}}<br /> : error map: {{val| 0.000 +0.036 +0.396 +1.293 +1.125 -0.832 }}<br /> <br /> {{Optimal ET sequence|legend=1| 9, 10, 14cf, 19, 33cdff, 39df, 48c, 49, 53, 58, 72, 111, 121, 130, 183, 251e, 304d, 376, 434de }}<br /> <br /> [[Badness]] (Sintel): 0.802<br /> <br /> === Commas 540/539, 847/845 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 540/539, 847/845<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 2 | 0 1 0 0 3 3 | 0 0 1 1 -1 -1 | 0 0 0 2 -4 -3 }}<br /> : Mapping generators: ~2, ~3, ~5, ~13/11<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.8339{{c}}, ~3/2 = 701.4961{{c}}, ~5/4 = 386.5624{{c}}, ~13/11 = 291.6840{{c}}<br /> : [[error map]]: {{val| -0.166 -0.625 -0.084 +0.772 -0.627 +1.848 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4439{{c}}, ~5/4 = 386.4201{{c}}, ~13/11 = 291.7287{{c}}<br /> : error map: {{val| 0.000 -0.511 +0.106 +1.052 -0.321 +2.198 }}<br /> <br /> {{Optimal ET sequence|legend=1| 8d, 9, 12e, 17c, 32f, 33cd, 36ce, 41, 53, 58, 94, 103, 111, 152f, 255, 407f }}<br /> <br /> [[Badness]] (Sintel): 1.04<br /> <br /> == Pentacircle (896/891) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: 896/891<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 | 0 1 0 0 -4 | 0 0 1 0 0 | 0 0 0 1 1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.3774{{c}}, ~3/2 = 703.4693{{c}}, ~5/4 = 387.5573{{c}}, ~7/4 = 969.3690{{c}}<br /> : [[error map]]: {{val| -0.623 +0.892 -0.002 -0.702 +1.061 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.7426{{c}}, ~5/4 = 387.2445{{c}}, ~7/4 = 969.0476{{c}}<br /> : error map: {{val| 0.000 +1.788 +0.931 +0.222 +2.759 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12, 17c, 19e, 22, 34d, 39d, 41, 58, 80, 87, 99e, 121, 145, 167, 208, 266e, 699bbcdeee }}<br /> <br /> [[Badness]] (Sintel): 1.20<br /> <br /> === Tridecimal pentacircle (gentle) ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 352/351, 364/363<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 12 | 0 1 0 0 -4 -7 | 0 0 1 0 0 0 | 0 0 0 1 1 1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.3706{{c}}, ~3/2 = 703.4872{{c}}, ~5/4 = 387.5708{{c}}, ~7/4 = 969.3987{{c}}<br /> : [[error map]]: {{val| -0.629 +0.903 -0.002 -0.686 +0.985 +0.055 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 703.8328{{c}}, ~5/4 = 387.2881{{c}}, ~7/4 = 969.1612{{c}}<br /> : error map: {{val| 0.000 +1.878 +0.974 +0.335 +2.512 +1.804 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12f, 17c, 22, 29, 34d, 41, 46, 58, 80, 87, 121, 167, 179ef, 208, 266ef, 433bceef, 641bbceeeff, 699bbcdeeeff }}<br /> <br /> [[Badness]] (Sintel): 0.885<br /> <br /> == Topsy (847/845, 1001/1000) ==<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 847/845, 1001/1000<br /> <br /> {{Mapping|legend=1| 1 0 0 -2 3 2 | 0 1 0 0 0 0 | 0 0 1 1 1 1 | 0 0 0 4 -3 -1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~20/13<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0343{{c}}, ~3/2 = 701.9205{{c}}, ~5/4 = 386.6098{{c}}, ~20/13 = 745.4658{{c}}<br /> : [[error map]]: {{val| +0.034 -0.000 +0.365 -0.353 -0.934 +0.753 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9261{{c}}, ~5/4 = 386.6458{{c}}, ~20/13 = 745.4431{{c}}<br /> : error map: {{val| 0.000 -0.029 +0.332 -0.408 -1.001 +0.675 }}<br /> <br /> [[Optimal tuning]] ([[CTE]]): ~2 = 1200.000{{c}}, ~3/2 = 701.955{{c}}, ~5/4 = 386.699{{c}}, ~13/10 = 454.558{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 21, 24d, 29, 37, 45ef, 50, 53, 58, 87, 103, 111, 140, 190, 198, 301, 388, 689e }}<br /> <br /> [[Badness]] (Sintel): 1.04<br /> <br /> == Lehmerismic (3025/3024) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[3025/3024]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 | 0 1 0 1 2 | 0 0 1 0 -1 | 0 0 0 2 1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~55/36<br /> <br /> [[Optimal tuning]]: <br /> * [[WE]]: ~2 = 1200.0197{{c}}, ~3/2 = 701.9725{{c}}, ~5/4 = 386.2210{{c}}, ~55/36 = 733.4363{{c}}<br /> : [[error map]]: {{val| +0.020 +0.037 -0.053 +0.039 -0.118 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9782{{c}}, ~5/4 = 386.2319{{c}}, ~55/36 = 733.4299{{c}}<br /> : error map: {{val| 0.000 +0.023 -0.082 +0.012 -0.164 }}<br /> <br /> {{Optimal ET sequence|legend=1| 15, 23de, 24d, 26, 31, 41, 65d, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 4002e, 5720e, 7168cee }}<br /> <br /> [[Badness]] (Sintel): 0.0802<br /> <br /> === Commas 2080/2079, 3025/3024 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 2080/2079, 3025/3024<br /> <br /> {{Mapping|legend=1| 1 0 0 0 2 -3 | 0 1 0 1 2 6 | 0 0 1 0 -1 -2 | 0 0 0 2 1 3 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9717{{c}}, ~3/2 = 702.0958{{c}}, ~5/4 = 386.2618{{c}}, ~55/36 = 733.4380{{c}}<br /> : [[error map]]: {{val| -0.028 +0.113 -0.108 +0.118 -0.007 -0.134 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0990{{c}}, ~5/4 = 386.2477{{c}}, ~55/36 = 733.4490{{c}}<br /> : error map: {{val| 0.000 +0.144 -0.066 +0.171 +0.081 -0.082 }}<br /> <br /> {{Optimal ET sequence|legend=1| 15, 24d, 26, 31f, 39df, 41, 46, 65d, 72, 87, 111, 152f, 183, 198, 224, 270, 494, 764, 1075, 1569, 1839, 2333, 3408d }}<br /> <br /> [[Badness]] (Sintel): 0.272<br /> <br /> == Trimitone (8019/8000) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[8019/8000]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 6 | 0 1 0 0 -6 | 0 0 1 0 3 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.1317{{c}}, ~3/2 = 701.4920{{c}}, ~5/4 = 386.4054{{c}}, ~7/4 = 968.5622{{c}}<br /> : [[error map]]: {{val| +0.132 -0.331 +0.355 -0.000 -0.263 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4730{{c}}, ~5/4 = 386.5375{{c}}, ~7/4 = 968.6211{{c}}<br /> : error map: {{val| 0.000 -0.482 +0.224 -0.205 -0.543 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12, 19, 26, 39d, 46, 53, 58, 72, 118, 130, 183, 190, 248, 255, 301, 373, 804, 876, 1177be }}<br /> <br /> [[Badness]] (Sintel): 1.50<br /> <br /> === Commas 729/728, 1001/1000 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 729/728, 1001/1000<br /> <br /> {{Mapping|legend=1| 1 0 0 0 6 -3 | 0 1 0 0 -6 6 | 0 0 1 0 3 0 | 0 0 0 1 0 -1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.1318{{c}}, ~3/2 = 701.4926{{c}}, ~5/4 = 386.4063{{c}}, ~7/4 = 968.5613{{c}}<br /> : [[error map]]: {{val| +0.132 -0.331 +0.356 -0.001 -0.264 -0.002 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.4770{{c}}, ~5/4 = 386.5437{{c}}, ~7/4 = 968.6150{{c}}<br /> : error map: {{val| 0.000 -0.478 +0.230 -0.211 -0.549 -0.280 }}<br /> <br /> {{Optimal ET sequence|legend=1| 53, 58, 72, 111, 130, 183, 190, 243e, 248, 301, 373, 804, 1177be }}<br /> <br /> [[Badness]] (Sintel): 0.875<br /> <br /> === Commas 351/350, 2080/2079 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 351/350, 2080/2079<br /> <br /> {{Mapping|legend=1| 1 0 0 0 6 1 | 0 1 0 0 -6 -3 | 0 0 1 0 3 2 | 0 0 0 1 0 1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9538{{c}}, ~3/2 = 701.5852{{c}}, ~5/4 = 387.1356{{c}}, ~7/4 = 969.7495{{c}}<br /> : [[error map]]: {{val| -0.046 -0.416 +0.730 +0.831 +0.301 -1.447 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.5936{{c}}, ~5/4 = 387.0975{{c}}, ~7/4 = 969.7451{{c}}<br /> : error map: {{val| 0.000 -0.361 +0.784 +0.919 +0.413 -1.369 }}<br /> <br /> {{Optimal ET sequence|legend=1| 19, 26, 39df, 46, 53, 58, 72, 111, 130, 183, 313 }}<br /> <br /> [[Badness]] (Sintel): 0.677<br /> <br /> == Kalismic (9801/9800) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[9801/9800]]<br /> <br /> {{Mapping|legend=1| 2 0 0 0 3 | 0 1 0 0 -2 | 0 0 1 0 1 | 0 0 0 1 1 }}<br /> : Mapping generators: ~99/70, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]: <br /> * [[WE]]: ~99/70 = 600.0018{{c}}, ~3/2 = 701.9397{{c}}, ~5/4 = 386.3193{{c}}, ~7/4 = 968.8374{{c}}<br /> : [[error map]]: {{val| +0.004 -0.012 +0.013 +0.019 -0.028 }}<br /> * [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 701.9399{{c}}, ~5/4 = 386.3226{{c}}, ~7/4 = 968.8399{{c}}<br /> : error map: {{val| 0.000 -0.015 +0.009 +0.014 -0.035 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12, 22, 34d, 46, 58, 72, 118, 130, 152, 224, 270, 342, 612, 836, 1084, 1106, 1236, 1506, 1578, 1848, 2684, 4038, 4190, 4532, 11254, 15786e, 21896e }}<br /> <br /> [[Badness]] (Sintel): 0.0415<br /> <br /> === Commas 1716/1715, 2080/2079 ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 1716/1715, 2080/2079<br /> <br /> {{Mapping|legend=1| 2 0 0 0 3 -7 | 0 1 0 0 -2 1 | 0 0 1 0 1 0 | 0 0 0 1 1 2 }}<br /> <br /> Lattice basis: <br /> : 3/2 length = 1.1956, 7/4 length = 1.4506, 14/13 length = 1.8299<br /> <br /> [[Optimal tuning]]: <br /> * [[WE]]: ~99/70 = 599.9732{{c}}, ~3/2 = 702.0465{{c}}, ~5/4 = 386.4214{{c}}, ~7/4 = 969.1757{{c}}<br /> : [[error map]]: {{val| -0.054 +0.038 +0.001 +0.243 -0.001 -0.210 }}<br /> * [[CWE]]: ~99/70 = 600.0000{{c}}, ~3/2 = 702.0554{{c}}, ~5/4 = 386.3788{{c}}, ~7/4 = 969.1756{{c}}<br /> : error map: {{val| 0.000 +0.100 +0.065 +0.350 +0.126 -0.121 }}<br /> <br /> [[Minimax tuning]]: <br /> * [[13-odd-limit|13-]] and [[15-odd-limit]]: ~99/70 = {{monzo| 1/2 0 0 0 0 0 }}, ~3 = {{monzo| 7/10 4/5 0 -2/5 0 1/5 }}, ~5 = {{monzo| 7/10 -1/5 1 -2/5 0 1/5 }}, ~7 = {{monzo| 7/5 -2/5 0 1/5 0 2/5 }}<br /> : [[eigenmonzo basis|eigenmonzo (unchanged-intervals) basis]]: 2.5/3.9/7.13<br /> <br /> {{Optimal ET sequence|legend=1| 12f, 14cf, 22f, 26, 36ce, 46, 58, 72, 130, 198, 224, 270, 494, 764, 1258, 1810d, 2304d, 2574d }}<br /> <br /> [[Badness]] (Sintel): 0.256<br /> <br /> == Unisquary (12005/11979) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[12005/11979]]<br /> <br /> {{Mapping|legend=1| 1 0 0 -6 -8 | 0 1 0 2 2 | 0 0 1 2 3 | 0 0 0 3 4 }}<br /> : Mapping generators: ~2, ~3, ~5, ~44/35<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0306{{c}}, ~5/4 = 386.2325{{c}}, ~44/35 = 397.2749{{c}}<br /> : [[error map]]: {{val| -0.000 +0.076 -0.081 +0.243 -0.475 +0.541 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0306{{c}}, ~5/4 = 386.2325{{c}}, ~44/35 = 397.2750{{c}}<br /> : error map: {{val| 0.000 +0.076 -0.081 -0.475 +0.541 }}<br /> <br /> {{Optimal ET sequence|legend=1| 12, 21, 23de, 26, 37, 46, 58, 72, 118, 130, 190, 239, 311, 441, 559, 752e, 870 }}<br /> <br /> [[Badness]] (Sintel): 2.43<br /> <br /> === Hensquary ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 364/363, 1716/1715<br /> <br /> {{Mapping|legend=1| 1 0 0 -6 -8 -12 | 0 1 0 2 2 3 | 0 0 1 2 3 4 | 0 0 0 3 4 5 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.7826{{c}}, ~3/2 = 702.2831{{c}}, ~5/4 = 386.9208{{c}}, ~44/35 = 396.8581{{c}}<br /> : [[error map]]: {{val| -0.217 +0.111 +0.172 +0.156 +1.443 -1.487 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2535{{c}}, ~5/4 = 386.7762{{c}}, ~44/35 = 397.0993{{c}}<br /> : error map: {{val| 0.000 +0.298 +0.463 +0.531 +1.915 -1.166 }}<br /> <br /> {{Optimal ET sequence|legend=1| 26, 37, 46, 58, 72, 121, 130, 193, 239, 251e, 323e, 369 }}<br /> <br /> [[Badness]] (Sintel): 0.988<br /> <br /> === Ekasquary ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 1575/1573, 4459/4455<br /> <br /> {{Mapping|legend=1| 1 0 0 -6 -8 10 | 0 1 0 2 2 0 | 0 0 1 2 3 -2 | 0 0 0 3 4 -5 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9999{{c}}, ~3/2 = 701.9524{{c}}, ~5/4 = 386.1388{{c}}, ~44/35 = 397.4088{{c}}<br /> : [[error map]]: {{val| -0.000 -0.003 -0.175 -0.417 +0.639 +0.150 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9524{{c}}, ~5/4 = 386.1388{{c}}, ~44/35 = 397.4089{{c}}<br /> : error map: {{val| 0.000 -0.003 -0.175 -0.417 +0.639 +0.150 }}<br /> <br /> {{Optimal ET sequence|legend=1| 46f, 49f, 58, 72, 118, 121, 130, 190, 193, 248, 311, 441, 752e, 1072 }}<br /> <br /> [[Badness]] (Sintel): 1.12<br /> <br /> == Semicanousmic (14641/14580) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[14641/14580]]<br /> <br /> {{Mapping|legend=1| 1 0 -2 0 0 | 0 1 2 0 2 | 0 0 4 0 1 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~3, ~11/9, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0495{{c}}, ~3/2 = 702.2793{{c}}, ~11/9 = 345.4721{{c}}, ~7/4 = 968.7265{{c}}<br /> : [[error map]]: {{val| +0.049 +0.374 +0.133 -0.000 -1.188 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2918{{c}}, ~11/9 = 345.4516{{c}}, ~7/4 = 968.7556{{c}}<br /> : error map: {{val| 0.000 +0.337 +0.077 -0.070 -1.283 }}<br /> <br /> {{Optimal ET sequence|legend=1| 14c, 17c, 24, 31, 63, 80, 87, 111, 118, 198, 212, 292, 323, 410, 851e }}<br /> <br /> [[Badness]] (Sintel): 6.40<br /> <br /> == Semiporwellismic (16384/16335) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: 16384/16335<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 | 0 1 1 0 -2 | 0 0 2 0 -1 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~3, ~128/99, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.7329{{c}}, ~3/2 = 702.3657{{c}}, ~128/99 = 442.1589{{c}}, ~7/4 = 969.3599{{c}}<br /> : [[error map]]: {{val| -0.267 +0.144 +0.103 -0.000 +0.456 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.5107{{c}}, ~128/99 = 442.2243{{c}}, ~7/4 = 969.4120{{c}}<br /> : error map: {{val| 0.000 +0.556 +0.646 +0.586 +1.436 }}<br /> <br /> {{Optimal ET sequence|legend=1| 19, 22, 41, 65d, 68, 84, 87, 111, 130, 152, 239, 282, 328, 369, 521e, 1370bcdeee, 1411bcdeee, 1609bccdeee }}<br /> <br /> [[Badness]] (Sintel): 4.00<br /> <br /> === Tridecimal semiporwellismic ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 2080/2079, 3584/3575<br /> <br /> {{Mapping|legend=1| 1 0 0 0 7 2 | 0 1 1 0 -2 0 | 0 0 2 0 -1 -3 | 0 0 0 1 0 1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.7102{{c}}, ~3/2 = 702.2488{{c}}, ~84/65 = 442.3476{{c}}, ~7/4 = 969.1583{{c}}<br /> : [[error map]]: {{val| -0.290 +0.004 +0.341 -0.247 +0.388 +0.429 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.3927{{c}}, ~84/65 = 442.4436{{c}}, ~7/4 = 969.1894{{c}}<br /> : error map: {{val| 0.000 +0.438 +0.966 +0.364 +1.453 +1.331 }}<br /> <br /> {{Optimal ET sequence|legend=1| 19, 22f, 27, 38e, 41, 46, 65d, 68, 84, 87, 111, 130, 198, 282, 328, 369f, 697cef, 1546bccdeeeffff, 1676bccdeeeffff }}<br /> <br /> [[Badness]] (Sintel): 1.13<br /> <br /> == Symbiotic (19712/19683) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[19712/19683]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -8 | 0 1 0 0 9 | 0 0 1 0 0 | 0 0 0 1 -1 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9290{{c}}, ~3/2 = 702.2265{{c}}, ~5/4 = 386.4556{{c}}, ~7/4 = 968.8979{{c}}<br /> : [[error map]]: {{val| -0.071 +0.201 -0.000 -0.070 -0.106 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2440{{c}}, ~5/4 = 386.4064{{c}}, ~7/4 = 968.8593{{c}}<br /> : error map: {{val| 0.000 +0.289 +0.093 +0.033 +0.019 }}<br /> <br /> {{Optimal ET sequence|legend=1| 17c, 19e, 24, 34d, 41, 53, 58, 94, 99e, 118, 152, 270, 581, 733, 851, 1003, 1273, 1854, 2124b }}<br /> <br /> [[Badness]] (Sintel): 2.19<br /> <br /> === Tridecimal symbiotic ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 2080/2079, 19712/19683<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -8 -13 | 0 1 0 0 9 12 | 0 0 1 0 0 -1 | 0 0 0 1 -1 0 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9268{{c}}, ~3/2 = 702.2293{{c}}, ~5/4 = 386.4554{{c}}, ~7/4 = 968.9114{{c}}<br /> : [[error map]]: {{val| -0.073 +0.201 -0.005 -0.061 -0.093 -0.012 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.2544{{c}}, ~5/4 = 386.4007{{c}}, ~7/4 = 968.8979{{c}}<br /> : error map: {{val| 0.000 +0.299 +0.087 +0.072 +0.074 +0.125 }}<br /> <br /> {{Optimal ET sequence|legend=1| 17c, 34dff, 36ce, 41, 53, 58, 94, 111, 152f, 212, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bf }}<br /> <br /> [[Badness]] (Sintel): 0.868<br /> <br /> === 2.3.5.7.11.13.19 subgroup ===<br /> Subgroup: 2.3.5.7.11.13.19<br /> <br /> Comma list: 1216/1215, 1540/1539, 2080/2079<br /> <br /> Mapping: {{mapping| 1 0 0 0 -8 -13 -6 | 0 1 0 0 9 12 5 | 0 0 1 0 0 -1 1 | 0 0 0 1 -1 0 0 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.9273{{c}}, ~3/2 = 702.2289{{c}}, ~5/4 = 386.4508{{c}}, ~7/4 = 968.9092{{c}}<br /> * CWE: ~2 = 1200.000{{c}}, ~3/2 = 702.2554{{c}}, ~5/4 = 386.4080{{c}}, ~7/4 = 968.9015{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 17ch, 24f, 34dffh, 36ceh, 41, 53, 58h, 94, 111, 152f, 212h, 217, 270, 581, 851, 1003, 1273, 1854, 2124b, 3127bfh }}<br /> <br /> Badness (Sintel): 0.375<br /> <br /> == Argyric (41503/41472) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[41503/41472]]<br /> <br /> {{Mapping|legend=1| 1 0 0 1 3 | 0 1 0 0 2 | 0 0 1 0 0 | 0 0 0 2 -3 }}<br /> : Mapping generators: ~2, ~3, ~5, ~144/77<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0485{{c}}, ~3/2 = 701.9606{{c}}, ~5/4 = 386.2167{{c}}, ~144/77 = 1084.3250{{c}}<br /> : [[error map]]: {{val| +0.049 +0.054 -0.000 -0.127 -0.129 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9739{{c}}, ~5/4 = 386.2460{{c}}, ~144/77 = 1084.2953{{c}}<br /> : error map: {{val| 0.000 +0.019 -0.068 -0.235 -0.256 }}<br /> <br /> {{Optimal ET sequence|legend=1| 19, 22, 31, 41, 53, 72, 166, 167, 176, 198, 239, 270, 342, 612, 954, 1566, 3101de, 3443de, 4055de, 4397cdee, 4667dee, 5009cddee }}<br /> <br /> [[Badness]] (Sintel): 0.777<br /> <br /> == Chrysic (43923/43904) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[43923/43904]]<br /> <br /> {{Mapping|legend=1| 1 0 0 3 4 | 0 1 0 3 2 | 0 0 1 0 0 | 0 0 0 -4 -3 }}<br /> : Mapping generators: ~2, ~3, ~5, ~33/14<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0167{{c}}, ~3/2 = 701.9323{{c}}, ~5/4 = 386.2803{{c}}, ~33/28 = 284.2370{{c}}<br /> : [[error map]]: {{val| +0.017 -0.006 -0.000 +0.056 -0.114 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9341{{c}}, ~5/4 = 386.2927{{c}}, ~33/28 = 284.2352{{c}}<br /> : error map: {{val| 0.000 -0.021 -0.021 +0.036 -0.155 }}<br /> <br /> {{Optimal ET sequence|legend=1| 17c, 26, 29, 34d, 43, 46, 72, 118, 152, 224, 270, 342, 612, 836, 1106, 1448, 2554, 2715, 2985, 3327e, 3479, 3821, 4091e, 4433e, 5539e }}<br /> <br /> [[Badness]] (Sintel): 0.770<br /> <br /> == Elysic (117649/117612) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[117649/117612]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 -1 | 0 2 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 3 }}<br /> : Mapping generators: ~2, ~343/198, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0027{{c}}, ~343/198 = 950.9861{{c}}, ~5/4 = 386.3082{{c}}, ~7/4 = 968.7558{{c}}<br /> : [[error map]]: {{val| +0.003 +0.017 -0.000 -0.065 +0.033 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~343/198 = 950.9850{{c}}, ~5/4 = 386.3105{{c}}, ~7/4 = 968.7571{{c}}<br /> : error map: {{val| 0.000 +0.015 -0.003 -0.069 +0.028 }}<br /> <br /> {{Optimal ET sequence|legend=1| 49, 58, 72, 130, 193, 198, 212, 270, 342, 612, 954, 1084, 1354, 1547, 1817, 2159, 3243, 3513, 5060, 5402, 5672, 8915d, 11074d }}<br /> <br /> [[Badness]] (Sintel): 0.901<br /> <br /> == Olympic (131072/130977) ==<br /> Olympic is highly accurate yet easy to conceptualize and notate on the staff. It equates [[33/32]] with ([[64/63]])&lt;sup&gt;2&lt;/sup&gt;, and [[36/35]] with [[1053/1024]], reducing the four [[formal comma]]s required for the [[13-limit]] to two. Therefore it can be notated in [[chain-of-fifths notation]] with two additional set of accidentals, one for the septimal comma step, and the other for the [[aberschisma]] step. It can be viewed as the [[detemperament]] of [[cassaschismic]] that decouples the Pythagorean and septimal commas. <br /> <br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[131072/130977]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 17 | 0 1 0 0 -5 | 0 0 1 0 0 | 0 0 0 1 -2 }}<br /> : Mapping generators: ~2, ~3, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9460{{c}}, ~3/2 = 702.0489{{c}}, ~5/4 = 386.4217{{c}}, ~7/4 = 968.9839{{c}}<br /> : [[error map]]: {{val| -0.054 +0.040 -0.000 +0.050 +0.038 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0853{{c}}, ~5/4 = 386.4125{{c}}, ~7/4 = 969.0242{{c}}<br /> : error map: {{val| 0.000 +0.130 +0.099 +0.198 +0.207 }}<br /> <br /> {{Optimal ET sequence|legend=1| 41, 53, 84, 87, 130, 183, 224, 270, 494, 764, 1164, 1205, 1475, 1969, 2239, 3133de, 4608cde, 5102bcde, 10474bbccdddeee }}<br /> <br /> [[Badness]] (Sintel): 2.05<br /> <br /> === Tridecimal olympic ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 2080/2079, 4096/4095<br /> <br /> {{Mapping|legend=1| 1 0 0 0 17 12 | 0 1 0 0 -5 -2 | 0 0 1 0 0 -1 | 0 0 0 1 -2 -1 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9638{{c}}, ~3/2 = 702.0645{{c}}, ~5/4 = 386.3208{{c}}, ~7/4 = 968.9712{{c}}<br /> : [[error map]]: {{val| -0.036 +0.073 -0.065 +0.073 +0.128 -0.166 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.0884{{c}}, ~5/4 = 386.3269{{c}}, ~7/4 = 969.0015{{c}}<br /> : error map: {{val| 0.000 +0.133 +0.013 +0.176 +0.237 -0.033 }}<br /> <br /> {{Optimal ET sequence|legend=1| 41, 46, 53, 84, 87, 130, 183, 217, 224, 270, 494, 764, 935, 1075, 1205, 1699, 2280, 2774e }} *<br /> <br /> &lt;nowiki&gt;*&lt;/nowiki&gt; [[optimal patent val]]: [[3044edo|3044]]<br /> <br /> [[Badness]] (Sintel): 0.292<br /> <br /> === Metaolympic ===<br /> Metaolympic is a [[weak extension]] of olympic, requiring the split of the prime 7 in half; or alternatively, the septimal comma or the garischisma. It is better without prime 17, but prime 17 can be added easily into the temperament by also tempering out 4200/4199, which also takes advantage of the split prime 7, at the cost of higher complexity. <br /> <br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 2080/2079, 4096/4095, 35000/34969<br /> <br /> Mapping: {{mapping| 1 0 0 1 15 11 -13 | 0 1 0 0 -5 -2 5 | 0 0 1 0 0 -1 2 | 0 0 0 2 -4 -2 5 }}<br /> : mapping generators: ~2, ~3, ~5, ~187/100<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.9530{{c}}, ~3/2 = 702.0493{{c}}, ~5/4 = 386.2541{{c}}, ~187/100 = 1084.4393{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0798{{c}}, ~5/4 = 386.2658{{c}}, ~187/100 = 1084.4811{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 43, 53, 84, 94, 137, 176g, 217, 270, 311, 487, 571e, 581, 935, 1516e, 2234eg, 2815eg }}<br /> <br /> Badness (Sintel): 1.59<br /> <br /> ==== 19-limit ====<br /> Subgroup: 2.3.5.7.11.13.17.19<br /> <br /> Comma list: 2080/2079, 3250/3249, 4096/4095, 4200/4199<br /> <br /> Mapping: {{mapping| 1 0 0 1 15 11 -13 6 | 0 1 0 0 -5 -2 5 -2 | 0 0 1 0 0 -1 2 1 | 0 0 0 2 -4 -2 5 -1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.9539{{c}}, ~3/2 = 702.0464{{c}}, ~5/4 = 386.2644{{c}}, ~187/100 = 1084.4405{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.0768{{c}}, ~5/4 = 386.2655{{c}}, ~187/100 = 1084.4813{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 43, 53, 84, 94, 137, 176g, 217, 270, 311, 487, 571e, 581, 935, 1516e, 2234eg, 2451eg }}<br /> <br /> Badness (Sintel): 0.764<br /> <br /> == Alphaxenic (131769/131072) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: 131769/131072<br /> <br /> {{Mapping|legend=1| 2 1 0 0 8 | 0 2 0 0 -1 | 0 0 1 0 0 | 0 0 0 1 0 }}<br /> : mapping generators: ~363/256, ~16/11, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~363/256 = 600.1590{{c}}, ~16/11 = 650.8508{{c}}, ~5/4 = 385.6773{{c}}, ~7/4 = 968.1894{{c}}<br /> : [[error map]]: {{val| +0.318 -0.094 -0.000 -0.000 -0.897 }}<br /> * [[CWE]]: ~363/256 = 600.0000{{c}}, ~16/11 = 650.7321{{c}}, ~5/4 = 385.7900{{c}}, ~7/4 = 968.1927{{c}}<br /> : error map: {{val| 0.000 -0.491 -0.524 -0.633 -2.050 }}<br /> <br /> {{Optimal ET sequence|legend=1| 22, 46, 68, 72, 118, 190, 212, 284, 330e, 402de, 498e, 544e, 616ee, 806dee, 828cee, 946cdeee, 1018cdeee }}<br /> <br /> [[Badness]] (Sintel): 23.0<br /> <br /> == Seascape (160083/160000) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[160083/160000]]<br /> <br /> {{Mapping|legend=1| 1 0 0 0 4 | 0 2 0 0 -3 | 0 0 1 0 2 | 0 0 0 1 -1 }}<br /> : Mapping generators: ~2, ~400/231, ~5, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1200.0285{{c}}, ~400/231 = 950.9641{{c}}, ~5/4 = 386.3335{{c}}, ~7/4 = 968.7129{{c}}<br /> : [[error map]]: {{val| +0.028 -0.027 +0.077 -0.056 -0.085 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~400/231 = 950.9492{{c}}, ~5/4 = 386.3638{{c}}, ~7/4 = 969.7159{{c}}<br /> : error map: {{val| 0.000 -0.057 +0.050 -0.110 -0.154 }}<br /> <br /> {{Optimal ET sequence|legend=1| 14c, 15, 19, 29, 39d, 43, 53, 58, 72, 130, 183, 198, 212, 255, 270, 342, 612, 954, 1084, 1354, 1696, 2833e, 3575, 3917e, 4187e, 4529de, 5883de }}<br /> <br /> [[Badness]] (Sintel): 0.596<br /> <br /> == Fifthchromismic (1610510/1594323) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: [[1610510/1594323]]<br /> <br /> {{Mapping|legend=1| 1 0 -6 0 1 | 0 1 3 0 2 | 0 0 5 0 -1 | 0 0 0 1 0 }}<br /> : Mapping generators: ~2, ~3, ~18/11, ~7<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9757{{c}}, ~3/2 = 702.7610{{c}}, ~18/11 = 855.5656{{c}}, ~7/4 = 968.8735{{c}}<br /> : [[error map]]: {{val| -0.024 +0.782 -0.130 -0.001 -1.434 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.7565{{c}}, ~18/11 = 855.5885{{c}}, ~7/4 = 968.8591{{c}}<br /> : error map: {{val| 0.000 +0.801 -0.102 +0.033 -1.393 }}<br /> <br /> {{Optimal ET sequence|legend=1| 70, 73, 77, 80, 87, 157, 167, 171e, 251, 258e, 338, 432, 519 }}<br /> <br /> [[Badness]] (Sintel): 97.2<br /> <br /> === Fifthchroma ===<br /> {{See also| Fifth-chroma temperaments }}<br /> <br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 352/351, 951665/944784<br /> <br /> {{Mapping|legend=1| 1 0 -6 0 1 6 | 0 1 3 0 2 -1 | 0 0 5 0 -1 -1 | 0 0 0 1 0 0 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.8431{{c}}, ~3/2 = 702.9005{{c}}, ~18/11 = 855.4090{{c}}, ~7/4 = 969.1386{{c}}<br /> : [[error map]]: {{val| -0.157 +0.789 -0.097 -0.001 -1.396 +0.379 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 702.9326{{c}}, ~18/11 = 855.5400{{c}}, ~7/4 = 969.1437{{c}}<br /> : error map: {{val| 0.000 +0.978 +0.184 +0.318 -0.993 +1.000 }}<br /> <br /> {{Optimal ET sequence|legend=1| 70, 73, 77, 80, 87, 157, 167, 171e, 181, 244, 251, 261, 338, 599b }}<br /> <br /> [[Badness]] (Sintel): 7.63<br /> <br /> ==== 17-limit ====<br /> Subgroup: 2.3.5.7.11.13.17<br /> <br /> Comma list: 352/351, 715/714, 155771/155520<br /> <br /> Mapping: {{mapping| 1 0 -6 0 1 6 0 | 0 1 3 0 2 -1 3 | 0 0 5 0 -1 -1 3 | 0 0 0 1 0 0 -1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.8126{{c}}, ~3/2 = 702.8981{{c}}, ~11/9 = 855.3764{{c}}, ~7/4 = 969.3543{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9376{{c}}, ~11/9 = 855.5306{{c}}, ~7/4 = 969.4313{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 70, 73g, 77, 80, 87, 94, 157, 167, 181, 251, 261, 338, 432, 599bg }}<br /> <br /> Badness (Sintel): 3.65<br /> <br /> ==== 19-limit ====<br /> Subgroup: 2.3.5.7.11.13.17.19<br /> <br /> Comma list: 352/351, 715/714, 1463/1458, 2057/2052<br /> <br /> Mapping: {{mapping| 1 0 -6 0 1 6 0 0 | 0 1 3 0 2 -1 3 4 | 0 0 5 0 -1 -1 3 1 | 0 0 0 1 0 0 -1 -1 }}<br /> <br /> Optimal tunings: <br /> * WE: ~2 = 1199.8128{{c}}, ~3/2 = 702.9226{{c}}, ~11/9 = 855.3621{{c}}, ~7/4 = 969.3187{{c}}<br /> * CWE: ~2 = 1200.0000{{c}}, ~3/2 = 702.9618{{c}}, ~11/9 = 855.5163{{c}}, ~7/4 = 969.3961{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 70, 73gh, 77, 80, 87, 94, 157, 167h, 181, 251, 261, 338, 599bg }}<br /> <br /> Badness (Sintel): 2.63<br /> <br /> == Quartismic (117440512/117406179) ==<br /> [[Subgroup]]: 2.3.5.7.11<br /> <br /> [[Comma list]]: 117440512/117406179<br /> <br /> {{Mapping|legend=1| 1 0 0 1 5 | 0 1 0 1 -1 | 0 0 1 0 0 | 0 0 0 5 1 }}<br /> : mapping generators: ~2, ~3, ~5, ~33/32<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9875{{c}}, ~3/2 = 701.9753{{c}}, ~5/4 = 386.3387{{c}}, ~33/32 = 53.3743{{c}}<br /> : [[error map]]: {{val| -0.012 +0.008 -0.000 -0.004 +0.031 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9802{{c}}, ~5/4 = 386.3343{{c}}, ~33/32 = 53.3730{{c}}<br /> : error map: {{val| 0.000 +0.025 +0.021 +0.019 +0.075 }}<br /> <br /> {{Optimal ET sequence|legend=1| 21, 22, 43, 46, 65d, 68, 89, 111, 159, 202, 224, 270, 494, 742, 764, 966, 1236, 1506, 2159, 2653, 3125, 3395, 7060, 7554, 10949e, 14614e, 15850ee, 22168bdee, 23404bcdee, 26799bcdeee, 34353bcdeeee }}<br /> <br /> [[Badness]] (Sintel): 5.00<br /> <br /> === Tridecimal quartismic ===<br /> [[Subgroup]]: 2.3.5.7.11.13<br /> <br /> [[Comma list]]: 6656/6655, 123201/123200<br /> <br /> {{Mapping|legend=1| 1 0 0 1 5 6 | 0 1 0 1 -1 -3 | 0 0 1 0 0 1 | 0 0 0 5 1 3 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[WE]]: ~2 = 1199.9884{{c}}, ~3/2 = 701.9674{{c}}, ~5/4 = 386.3432{{c}}, ~33/32 = 53.3763{{c}}<br /> : [[error map]]: {{val| -0.012 +0.001 +0.006 -0.000 +0.045 -0.016 }}<br /> * [[CWE]]: ~2 = 1200.0000{{c}}, ~3/2 = 701.9728{{c}}, ~5/4 = 386.3385{{c}}, ~33/32 = 53.3748{{c}}<br /> : error map: {{val| 0.000 +0.018 +0.025 +0.021 +0.084 +0.017 }}<br /> <br /> {{Optimal ET sequence|legend=1| 22, 43f, 46, 65d, 89f, 111, 159, 224, 270, 494, 764, 1012, 1236, 1506, 2901, 3125, 3395, 8026e, 8296e, 11421e, 11691e, 12927e, 13421e, 16322ee, 16816dee }}<br /> <br /> [[Badness]] (Sintel): 0.456<br /> <br /> [[Category:Temperaments]]<br /> [[Category:Lists of temperaments]]<br /> [[Category:Temperament collections]]<br /> [[Category:Regular temperament theory]]<br /> [[Category:Rank 4| ]] &lt;!-- main article --&gt;</div> FloraC https://en.xen.wiki/index.php?title=149edo&diff=232392 149edo 2026-06-18T07:15:49Z <p>FloraC: + note about 894edo</p> <hr /> <div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> == Theory ==<br /> 149edo is the smallest division which is [[consistency|uniquely consistent]] through the [[17-odd-limit]]. It has a general flat tendency, with the fifth 1.28{{c}} flat, but the major third is a quarter of a cent sharp. <br /> <br /> In the 5-limit it [[tempering out|tempers out]] the [[sensipent comma]], 78732/78125; in the [[7-limit]], [[1029/1024]], [[3136/3125]] and [[19683/19600]]; in the [[11-limit]] [[385/384]] and [[441/440]]; in the [[13-limit]] [[351/350]], [[676/675]] and [[729/728]]; in the [[17-limit]] [[273/272]] and [[561/560]]; in the [[19-limit]] [[286/285]] and [[343/342]]. It provides the [[optimal patent val]] for 7-, 11-, 13-, and 17-limit [[heinz]] temperament and the rank-3 temperament [[gamelismic family #Ominous|ominous]] in the 13- and 17-limit.<br /> <br /> It is also usable in the [[23-limit]], only missing [[19/11]], [[21/11]], and their [[octave complement]]s in the [[23-odd-limit]]. In the [[27-odd-limit]], additional inconsistencies include [[25/21]], [[25/22]], [[27/20]], [[27/25]], [[27/19]], and their octave complements.<br /> <br /> === Prime harmonics ===<br /> {{Harmonics in equal|149}}<br /> <br /> === Subsets and supersets ===<br /> 149edo is the 35th [[prime edo]]. As such, it does not contain any nontrivial subset edos. <br /> <br /> [[894edo]], which slices its step in six, is a notable system for the higher-limit, also consistent to the 17-odd-limit. <br /> <br /> == Regular temperament properties ==<br /> {| class=&quot;wikitable center-4 center-5 center-6&quot;<br /> |-<br /> ! rowspan=&quot;2&quot; | [[Subgroup]]<br /> ! rowspan=&quot;2&quot; | [[Comma list]]<br /> ! rowspan=&quot;2&quot; | [[Mapping]]<br /> ! rowspan=&quot;2&quot; | Optimal&lt;br&gt;8ve stretch (¢)<br /> ! colspan=&quot;2&quot; | Tuning error<br /> |-<br /> ! [[TE error|Absolute]] (¢)<br /> ! [[TE simple badness|Relative]] (%)<br /> |-<br /> | 2.3<br /> | {{Monzo| -236 149 }}<br /> | {{Mapping| 149 236 }}<br /> | +0.405<br /> | 0.405<br /> | 5.03<br /> |-<br /> | 2.3.5<br /> | 78732/78125, {{monzo| -34 20 1 }}<br /> | {{Mapping| 149 236 346 }}<br /> | +0.232<br /> | 0.411<br /> | 5.11<br /> |-<br /> | 2.3.5.7<br /> | 1029/1024, 3136/3125, 19683/19600<br /> | {{Mapping| 149 236 346 418 }}<br /> | +0.386<br /> | 0.445<br /> | 5.53<br /> |-<br /> | 2.3.5.7.11<br /> | 385/384, 441/440, 3136/3125, 19683/19600<br /> | {{Mapping| 149 236 346 418 515 }}<br /> | +0.521<br /> | 0.481<br /> | 5.97<br /> |-<br /> | 2.3.5.7.11.13<br /> | 351/350, 385/384, 441/440, 676/675, 847/845<br /> | {{Mapping| 149 236 346 418 515 551 }}<br /> | +0.567<br /> | 0.451<br /> | 5.60<br /> |-<br /> | 2.3.5.7.11.13.17<br /> | 273/272, 351/350, 385/384, 441/440, 676/675, 847/845<br /> | {{Mapping| 149 236 346 418 515 551 609 }}<br /> | +0.495<br /> | 0.453<br /> | 5.62<br /> |}<br /> <br /> === Rank-2 temperaments ===<br /> {| class=&quot;wikitable center-all left-5&quot;<br /> |+ style=&quot;font-size: 105%;&quot; | Table of rank-2 temperaments by generator<br /> |-<br /> ! Periods&lt;br&gt;per 8ve<br /> ! Generator*<br /> ! Cents*<br /> ! Associated&lt;br&gt;ratio*<br /> ! Temperaments<br /> |-<br /> | 1<br /> | 3\149<br /> | 24.16<br /> | 686/675<br /> | [[Sengagen]]<br /> |-<br /> | 1<br /> | 16\149<br /> | 128.86<br /> | 14/13<br /> | [[Tertiathirds]]<br /> |-<br /> | 1<br /> | 18\149<br /> | 144.97<br /> | 49/45<br /> | [[Swetneus]]<br /> |-<br /> | 1<br /> | 24\149<br /> | 193.29<br /> | 28/25<br /> | [[Hemithirds]]<br /> |-<br /> | 1<br /> | 29\149<br /> | 233.56<br /> | 8/7<br /> | [[Slendric]]<br /> |-<br /> | 1<br /> | 47\149<br /> | 378.52<br /> | 56/45<br /> | [[Subpental]]<br /> |-<br /> | 1<br /> | 55\149<br /> | 442.95<br /> | 162/125<br /> | [[Sensipent]]<br /> |-<br /> | 1<br /> | 57\149<br /> | 459.06<br /> | 125/96<br /> | [[Majvam]]<br /> |-<br /> | 1<br /> | 60\149<br /> | 483.22<br /> | 45/34<br /> | [[Hemiseven]]<br /> |-<br /> | 1<br /> | 61\149<br /> | 491.28<br /> | 3645/2744<br /> | [[Fifthplus]]<br /> |-<br /> | 1<br /> | 68\149<br /> | 547.65<br /> | 11/8<br /> | [[Heinz]]<br /> |}<br /> &lt;nowiki/&gt;* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct<br /> <br /> [[Category:Heinz]]</div> FloraC https://en.xen.wiki/index.php?title=624edo&diff=232391 624edo 2026-06-18T07:09:47Z <p>FloraC: Corrections</p> <hr /> <div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> == Theory ==<br /> 624edo is [[consistent]] to the [[27-odd-limit]]. As an equal temperament, it [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnuzma]]) and {{monzo| -69 45 -1 }} ([[counterschisma]]) in the [[5-limit]]; [[250047/250000]], [[2460375/2458624]], and 134217728/133984375 in the [[7-limit]]; [[9801/9800]], 46656/46585, [[131072/130977]], and [[151263/151250]] in the [[11-limit]]; [[1716/1715]], [[2080/2079]], [[4096/4095]], 34398/34375, and 39366/39325 in the [[13-limit]]; [[936/935]], [[1701/1700]], [[2025/2023]], and [[2058/2057]] in the [[17-limit]]; [[1521/1520]], [[2376/2375]], [[2432/2431]], and 3328/3325 in the [[19-limit]]; [[2024/2023]], [[2025/2024]], [[2646/2645]], [[3520/3519]], and [[3888/3887]] in the [[23-limit]].<br /> <br /> It provides an excellent [[optimal patent val]] for the rank-6 temperament tempering out 936/935, as well as the rank-5 no-7 [[retraction]] thereof. <br /> <br /> === Prime harmonics ===<br /> {{Harmonics in equal|624|columns=11}}<br /> {{Harmonics in equal|624|columns=11|start=12|collapsed=true|title=Approximation of prime harmonics in 624edo (continued)}}<br /> <br /> === Subsets and supersets ===<br /> Since 624 factors into primes as {{nowrap| 2&lt;sup&gt;4&lt;/sup&gt; × 3 × 13 }}, 624edo has subset edos {{EDOs| 2, 3, 4, 6, 8, 12, 13, 16, 24, 26, 39, 48, 52, 78, 156, and 312 }}.<br /> <br /> == Regular temperament properties ==<br /> {| class=&quot;wikitable center-4 center-5 center-6&quot;<br /> |-<br /> ! rowspan=&quot;2&quot; | [[Subgroup]]<br /> ! rowspan=&quot;2&quot; | [[Comma list]]<br /> ! rowspan=&quot;2&quot; | [[Mapping]]<br /> ! rowspan=&quot;2&quot; | Optimal&lt;br&gt;8ve stretch (¢)<br /> ! colspan=&quot;2&quot; | Tuning error<br /> |-<br /> ! [[TE error|Absolute]] (¢)<br /> ! [[TE simple badness|Relative]] (%)<br /> |-<br /> | 2.3<br /> | {{Monzo| -989 624 }}<br /> | {{Mapping| 624 989 }}<br /> | +0.0101<br /> | 0.0101<br /> | 0.52<br /> |-<br /> | 2.3.5<br /> | {{Monzo| 23 6 -14 }}, {{monzo| -69 45 -1 }}<br /> | {{Mapping| 624 989 1449 }}<br /> | −0.0256<br /> | 0.0510<br /> | 2.65<br /> |-<br /> | 2.3.5.7<br /> | 250047/250000, 2460375/2458624, 134217728/133984375<br /> | {{Mapping| 624 989 1449 1752 }}<br /> | −0.0552<br /> | 0.0678<br /> | 3.52<br /> |-<br /> | 2.3.5.7.11<br /> | 9801/9800, 46656/46585, 131072/130977, 151263/151250<br /> | {{Mapping| 624 989 1449 1752 2159 }}<br /> | −0.0792<br /> | 0.0772<br /> | 4.02<br /> |-<br /> | 2.3.5.7.11.13<br /> | 1716/1715, 2080/2079, 4096/4095, 34398/34375, 39366/39325<br /> | {{Mapping| 624 989 1449 1752 2159 2309 }}<br /> | −0.0595<br /> | 0.0831<br /> | 4.32<br /> |-<br /> | 2.3.5.7.11.13.17<br /> | 936/935, 1701/1700, 1716/1715, 2025/2023, 4096/4095, 11016/11011<br /> | {{Mapping| 624 989 1449 1752 2159 2309 2551 }}<br /> | −0.0795<br /> | 0.0911<br /> | 4.74<br /> |-<br /> | 2.3.5.7.11.13.17.19<br /> | 936/935, 1521/1520, 1701/1700, 1716/1715, 2025/2023, 2376/2375, 11016/11011<br /> | {{Mapping| 624 989 1449 1752 2159 2309 2551 2651 }}<br /> | −0.0861<br /> | 0.0870<br /> | 4.53<br /> |-<br /> | 2.3.5.7.11.13.17.19.23<br /> | 936/935, 1521/1520, 1701/1700, 1716/1715, 2024/2023, 2025/2023, 2376/2375, 2646/2645<br /> | {{Mapping| 624 989 1449 1752 2159 2309 2551 2651 2823 }}<br /> | −0.0906<br /> | 0.0830<br /> | 4.32<br /> |}<br /> <br /> === Rank-2 temperaments ===<br /> {| class=&quot;wikitable center-all left-5&quot;<br /> |+ style=&quot;font-size: 105%;&quot; | Table of rank-2 temperaments by generator<br /> |-<br /> ! Periods&lt;br&gt;per 8ve<br /> ! Generator*<br /> ! Cents*<br /> ! Associated&lt;br&gt;ratio*<br /> ! Temperaments<br /> |-<br /> | 1<br /> | 259\624<br /> | 498.08<br /> | 4/3<br /> | [[Counterschismic]]<br /> |-<br /> | 1<br /> | 311\624<br /> | 598.08<br /> | 847/600<br /> | [[Vydubychi]]<br /> |-<br /> | 2<br /> | 37\624<br /> | 71.15<br /> | 25/24<br /> | [[Vishnu]] (5-limit)<br /> |-<br /> | 3<br /> | 73\624<br /> | 140.38<br /> | 243/224<br /> | [[Septichrome]]<br /> |-<br /> | 6<br /> | 177\624&lt;br&gt;(31\624)<br /> | 340.38&lt;br&gt;(59.62)<br /> | 162/133&lt;br&gt;(88/85)<br /> | [[Semiseptichrome]]<br /> |-<br /> | 12<br /> | 259\624&lt;br&gt;(1\624)<br /> | 498.08&lt;br&gt;(1.92)<br /> | 4/3&lt;br&gt;(32805/32768)<br /> | [[Atomic]]<br /> |-<br /> | 13<br /> | 259\624&lt;br&gt;(19\624)<br /> | 498.08&lt;br&gt;(36.54)<br /> | 4/3&lt;br&gt;(?)<br /> | [[Aluminium]] (5-limit)<br /> |-<br /> | 16<br /> | 259\624&lt;br&gt;(14\624)<br /> | 498.08&lt;br&gt;(48.077)<br /> | 4/3&lt;br&gt;(?)<br /> | [[Sulfur]]<br /> |-<br /> | 24<br /> | 303\624&lt;br&gt;(9\624)<br /> | 582.69&lt;br&gt;(17.31)<br /> | 7/5&lt;br&gt;(100/99)<br /> | [[Chromium]]<br /> |-<br /> | 26<br /> | 259\624&lt;br&gt;(19\624)<br /> | 498.08&lt;br&gt;(36.54)<br /> | 4/3&lt;br&gt;(?)<br /> | [[Iron]]<br /> |}<br /> &lt;nowiki /&gt;* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct<br /> <br /> == Music ==<br /> ; [[Eliora]]<br /> * [https://www.youtube.com/watch?v=vEDajIHqRUw&amp;pp=ygUGNjI0ZWRv ''Etude in Iron''] (2024)<br /> <br /> [[Category:Ainismic]]<br /> [[Category:Listen]]</div> FloraC https://en.xen.wiki/index.php?title=6115295232/6103515625&diff=232390 6115295232/6103515625 2026-06-18T06:58:58Z <p>FloraC: Update</p> <hr /> <div>#redirect [[Vishnu comma]]</div> FloraC https://en.xen.wiki/index.php?title=Category:Vishnu&diff=232389 Category:Vishnu 2026-06-18T06:57:57Z <p>FloraC: </p> <hr /> <div>{{Cat main}}<br /> <br /> [[Category:Categories by temperament]]</div> FloraC https://en.xen.wiki/index.php?title=Ananta&diff=232388 Ananta 2026-06-18T06:57:20Z <p>FloraC: Update &amp; recategorize (vishnu extension)</p> <hr /> <div>#redirect [[Vishnu family #Ananta]]<br /> <br /> [[Category:Vishnu]]</div> FloraC https://en.xen.wiki/index.php?title=Acyuta&diff=232387 Acyuta 2026-06-18T06:56:58Z <p>FloraC: Update &amp; recategorize (vishnu extension)</p> <hr /> <div>#redirect [[Vishnu family #Acyuta]]<br /> <br /> [[Category:Vishnu]]</div> FloraC https://en.xen.wiki/index.php?title=Decavish&diff=232386 Decavish 2026-06-18T06:56:17Z <p>FloraC: Update &amp; recategorize</p> <hr /> <div>#REDIRECT [[Vishnu family #Decavish]]<br /> <br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Vishnu family]]<br /> [[Category:Wizmic microtemperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Narayana&diff=232385 Narayana 2026-06-18T06:55:07Z <p>FloraC: Update &amp; recategorize</p> <hr /> <div>#redirect [[Vishnu family #Narayana]]<br /> <br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Vishnu family]]<br /> [[Category:Horwell temperaments]]<br /> [[Category:Varunismic temperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Quarvish&diff=232384 Quarvish 2026-06-18T06:53:56Z <p>FloraC: </p> <hr /> <div>#redirect [[Vishnu family #Quarvish]]<br /> <br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Vishnu family]]<br /> [[Category:Breedsmic temperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Quarvish&diff=232383 Quarvish 2026-06-18T06:53:47Z <p>FloraC: Update &amp; recategorize</p> <hr /> <div>#redirect [[Vishnu family #Quarvish]]<br /> <br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Vishnuzmic family]]<br /> [[Category:Breedsmic temperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu&diff=232382 Vishnu 2026-06-18T06:52:29Z <p>FloraC: + category</p> <hr /> <div>#redirect [[Vishnu family #Vishnu]]<br /> <br /> [[Category:Vishnu| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Microtemperaments]]<br /> [[Category:Vishnu family]]<br /> [[Category:Ragismic microtemperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnean&diff=232381 Vishnean 2026-06-18T06:51:52Z <p>FloraC: Update &amp; recategorize</p> <hr /> <div>#REDIRECT [[Vishnu family #Vishnean]]<br /> <br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Vishnu family]]<br /> [[Category:Starling temperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu&diff=232380 Vishnu 2026-06-18T06:50:30Z <p>FloraC: Update &amp; recategorize</p> <hr /> <div>#redirect [[Vishnu family #Vishnu]]<br /> <br /> [[Category:Vishnu| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank-2 temperaments]]<br /> [[Category:Vishnu family]]<br /> [[Category:Ragismic microtemperaments]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_family&diff=232379 Vishnu family 2026-06-18T06:49:25Z <p>FloraC: Units, misc. cleanup, - redundant category</p> <hr /> <div>{{Technical data page}}<br /> The '''vishnu family''' [[tempering out|tempers out]] the [[vishnu comma]] ({{monzo|legend=1| 23 6 -14 }}, [[ratio]]: 6 115 295 232 / 6 103 515 625), a [[5-limit]] comma of about 3 [[cent]]s. It is the amount by which seven just chromatic semitones of [[25/24]] fall short of a just perfect fourth of [[4/3]], or in other words (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;.<br /> <br /> == Vishnu ==<br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}<br /> : mapping generators: ~78125/55296, ~25/24<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~25/24 = 71.1556{{c}}<br /> * [[POTE]]: ~78125/55296 = 600.000{{c}}, ~25/24 = 71.143{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}<br /> <br /> [[Badness]] (Smith): 0.031181<br /> <br /> == Septimal vishnu ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 29360128/29296875<br /> <br /> {{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~10125/7168 = 600.0000{{c}}, ~25/24 = 71.1175{{c}}<br /> * [[POTE]]: ~10125/7168 = 600.000{{c}}, ~25/24 = 71.107{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}<br /> <br /> [[Badness]] (Smith): 0.041912<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1142{{c}}<br /> * POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.105{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}<br /> <br /> Badness (Smith): 0.014180<br /> <br /> ==== Ananta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}<br /> <br /> Optimal tuning: <br /> * CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1173{{c}}<br /> * POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.117{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118, 152, 270, 928, 1198, 1468 }}<br /> <br /> Badness (Smith): 0.023678<br /> <br /> ==== Acyuta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.1079{{c}}<br /> * POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.101{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}<br /> <br /> Badness (Smith): 0.015805<br /> <br /> == Vishnean ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 540225/524288<br /> <br /> {{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~735/512 = 600.0000{{c}}, ~25/24 = 71.4956{{c}}<br /> * [[POTE]]: ~735/512 = 600.000{{c}}, ~25/24 = 71.779{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}<br /> <br /> [[Badness]] (Smith): 0.161398<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 385/384, 1350/1331<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~63/44 = 600.0000{{c}}, ~25/24 = 71.6218{{c}}<br /> * POTE: ~63/44 = 600.000{{c}}, ~25/24 = 71.924{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Smith): 0.071990<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 105/104, 126/125, 144/143, 847/845<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~55/39 = 600.0000{{c}}, ~25/24 = 71.6369{{c}}<br /> * POTE: ~55/39 = 600.000{{c}}, ~25/24 = 71.926{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 16, 34, 50 }}<br /> <br /> Badness (Smith): 0.040739<br /> <br /> == Narayana ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 65625/65536, 321489/320000<br /> <br /> {{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~567/400 = 600.0000{{c}}, ~25/24 = 71.2706{{c}}<br /> * [[POTE]]: ~567/400 = 600.000{{c}}, ~25/24 = 71.265{{c}}<br /> <br /> {{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}<br /> <br /> [[Badness]] (Smith): 0.094295<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 8019/8000, 65625/65536<br /> <br /> Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 600.0000{{c}}, ~25/24 = 71.2609{{c}}<br /> * POTE: ~99/70 = 600.000{{c}}, ~25/24 = 71.248{{c}}<br /> <br /> {{Optimal ET sequence|legend=0| 34e, 84, 118, 202, 320 }}<br /> <br /> Badness (Smith): 0.045908<br /> <br /> == Quarvish ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 2401/2400, 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~78125/55296 = 600.0000{{c}}, ~7/5 = 582.2115{{c}} (~110592/109375 = 17.7885{{c}})<br /> * [[POTE]]: ~78125/55296 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~110592/109375 = 17.787{{c}})<br /> <br /> {{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> [[Badness]] (Smith): 0.045029<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 2401/2400, 9801/9800, 172032/171875<br /> <br /> Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 600.0000{{c}}, ~7/5 = 582.2122{{c}} (~99/98 = 17.7878{{c}})<br /> * POTE: ~99/70 = 600.000{{c}}, ~7/5 = 582.213{{c}} (~99/98 = 17.787{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> Badness (Smith): 0.019868<br /> <br /> == Decavish ==<br /> The decavish temperament (50 &amp; 270) tempers out the wizma, {{monzo| -6 -8 2 5 }} = 420175/419904 and the [[linus comma]], {{monzo| 11 -10 -10 10 }} = 578509309952/576650390625.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 420175/419904, 2202927104/2197265625<br /> <br /> {{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}<br /> : mapping generators: ~15/14, ~54/49<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8587{{c}} (~25/24 = 71.1413{{c}}, or ~36/35 = 48.8587{{c}})<br /> * [[POTE]]: ~15/14 = 120.000{{c}}, ~54/49 = 168.871{{c}} (~25/24 = 71.129{{c}}, or ~36/35 = 48.871{{c}})<br /> <br /> {{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}<br /> <br /> [[Badness]] (Smith): 0.114531<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 41503/41472, 172032/171875<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})<br /> * POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.141{{c}}, or ~36/35 = 48.859{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, …, 220, 270, 860, 1130, 1400 }}<br /> <br /> Badness (Smith): 0.036938<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~15/14 = 120.0000{{c}}, ~54/49 = 168.8583{{c}} (~25/24 = 71.1417{{c}}, or ~36/35 = 48.8583{{c}})<br /> * POTE: ~15/14 = 120.000{{c}}, ~54/49 = 168.859{{c}} (~25/24 = 71.151{{c}}, or ~36/35 = 48.859{{c}})<br /> <br /> {{Optimal ET sequence|legend=0| 50, 220, 270, 590, 860, 1130 }}<br /> <br /> Badness (Smith): 0.021906<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Vishnu family| ]] &lt;!-- main article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=338edo&diff=232378 338edo 2026-06-18T06:44:04Z <p>FloraC: Not a notable vishnu tuning</p> <hr /> <div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> The equal temperament [[tempering out|tempers out]] {{monzo| 23 6 -14 }} ([[vishnu comma]]) in the [[5-limit]], and [[2401/2400]], [[5120/5103]] and [[10976/10935]] in the [[7-limit]]. It provides the [[optimal patent val]] for 7-limit [[hemififths]], the {{nowrap| 99 &amp; 239 }} temperament.<br /> <br /> === Odd harmonics ===<br /> {{Harmonics in equal|338}}<br /> <br /> === Subsets and supersets ===<br /> Since 338 factors into {{nowrap| 2 × 13&lt;sup&gt;2&lt;/sup&gt; }}, 338edo has subset edos {{EDOs| 2, 13, 26, and 169 }}. <br /> <br /> [[Category:Hemififths]]</div> FloraC https://en.xen.wiki/index.php?title=1400edo&diff=232377 1400edo 2026-06-18T06:41:35Z <p>FloraC: Misc. cleanup</p> <hr /> <div>{{Infobox ET}}<br /> {{ED intro}}<br /> <br /> == Theory ==<br /> 1400edo is only [[consistent]] in the [[5-odd-limit]], where it provides the [[optimal patent val]] for the 5-limit [[vishnu]] temperament. Aside from that it is poor at simple harmony. In the higher limits, it is good at the 2.3.19.23.29.31 subgroup. It also tempers out the [[barium comma]] and the [[linus comma]] using the patent val.<br /> <br /> Aside from the patent val, there is a number of mappings to be considered. 1400cd val uses the 28edo mapping for 5 and gives a tuning close to the [[POTE]] tuning for the 11-limit [[oquatonic]] temperament. 1400ccdd val is a tuning for the 11-limit [[silicon]] temperament. It is worth noting, patent val can be considered a tuning for the 2.3.11 subgroup silicon - for which it conveniently provides a 70-tone mos reaching [[3/2]] in 1 generator up and [[11/8]] in 3 generators down. 1400bbbc val is a tuning for the [[manganese]] temperament.<br /> <br /> === Prime harmonics ===<br /> {{Harmonics in equal|1400}}<br /> <br /> === Subsets and supersets ===<br /> 1400edo has subset edos {{EDOs| 2, 4, 5, 7, 8, 10, 14, 20, 25, 28, 35, 40, 50, 56, 70, 100, 140, 175, 200, 280, 350, 700 }}. One step of 1400edo is the relative cent for 14edo.<br /> <br /> == Regular temperament properties ==<br /> {| class=&quot;wikitable center-all left-5&quot;<br /> |+ style=&quot;font-size: 105%;&quot; | Table of rank-2 temperaments by generator<br /> |-<br /> ! Periods&lt;br&gt;per 8ve<br /> ! Generator*<br /> ! Cents*<br /> ! Associated&lt;br&gt;ratio*<br /> ! Temperaments<br /> |-<br /> | 1<br /> | 317\1400<br /> | 271.714<br /> | {{Monzo| 66 -23 -9 -3 }}<br /> | [[Counterorson]]<br /> |-<br /> | 2<br /> | 83\1400<br /> | 71.143<br /> | 25/24<br /> | [[Vishnu]] (5-limit)<br /> |-<br /> | 8<br /> | 86\1400<br /> | 73.714<br /> | 24/23<br /> | [[Octium]] (2.3.19.23.29.31)<br /> |-<br /> | 14<br /> | 581\1400&lt;br&gt;(81\1400)<br /> | 498.000&lt;br&gt;(69.429)<br /> | 4/3&lt;br&gt;(?)<br /> | [[Silicon]] (2.3.11)<br /> |-<br /> | 28<br /> | 581\1400&lt;br&gt;(31\1400)<br /> | 498.000&lt;br&gt;(26.571)<br /> | 4/3&lt;br&gt;(126/125)<br /> | [[Oquatonic]] (1400cd)<br /> |-<br /> | 56<br /> | 581\1400&lt;br&gt;(6\1400)<br /> | 498.000&lt;br&gt;(5.143)<br /> | 4/3&lt;br&gt;(126/125)<br /> | [[Barium]]<br /> |}<br /> &lt;nowiki/&gt;* [[Normal forms #Equave-reduced-generator form|Octave-reduced form]], reduced to the first half-octave, and [[normal forms #Minimal-generator form|minimal form]] in parentheses if distinct<br /> <br /> == Scales ==<br /> * Silicon[70]: (19 24 19 19 19)×14<br /> <br /> == Music ==<br /> ; [[Mercury Amalgam]]<br /> * [https://www.youtube.com/watch?v=o9aAB4csKBQ ''Apple In Your Mouth''] – Silicon[70], Oxygen[24], Magnesium[175], Vishnu[34]<br /> <br /> [[Category:Vishnu]]<br /> [[Category:Listen]]</div> FloraC https://en.xen.wiki/index.php?title=Category:Vishnu_family&diff=232376 Category:Vishnu family 2026-06-18T06:37:35Z <p>FloraC: Update</p> <hr /> <div>{{Cat main}}<br /> <br /> [[Category:Vishnu]]<br /> [[Category:Temperament families]]</div> FloraC https://en.xen.wiki/index.php?title=Category:Vishnu_family&diff=232375 Category:Vishnu family 2026-06-18T06:37:09Z <p>FloraC: FloraC moved page Category:Vishnuzmic family to Category:Vishnu family without leaving a redirect: The temp&#039;s name is *vishnu*</p> <hr /> <div>'''Main article: [[Vishnuzmic family]]'''<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Vishnuzmic]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnuzmic_family&diff=232374 Vishnuzmic family 2026-06-18T06:36:48Z <p>FloraC: FloraC moved page Vishnuzmic family to Vishnu family: The temp&#039;s name is *vishnu*</p> <hr /> <div>#REDIRECT [[Vishnu family]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_family&diff=232373 Vishnu family 2026-06-18T06:36:48Z <p>FloraC: FloraC moved page Vishnuzmic family to Vishnu family: The temp&#039;s name is *vishnu*</p> <hr /> <div>{{Technical data page}}<br /> The '''vishnuzmic family''' of [[temperament]]s [[Tempering out|tempers out]] the [[vishnuzma]], {{monzo| 23 6 -14 }} = 6115295232/6103515625, a [[5-limit]] comma of about 3 [[cent]]s. It is the amount by which seven just chromatic semitones of [[25/24]] fall short of a just perfect fourth of [[4/3]], or in other words (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;.<br /> <br /> == Vishnu ==<br /> [[Subgroup]]: 2.3.5<br /> <br /> [[Comma list]]: 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 | 0 -7 -3 }}<br /> <br /> : mapping generators: ~78125/55296, ~25/24<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~78125/55296 = 1\2, ~25/24 = 71.1556<br /> * [[POTE]]: ~78125/55296 = 1\2, ~25/24 = 71.143<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 84, 118, 270, 388, 506, 894, 1400, 3306c, 4706cc }}<br /> <br /> [[Badness]]: 0.031181<br /> <br /> == Septimal vishnu ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 4375/4374, 29360128/29296875<br /> <br /> {{Mapping|legend=1| 2 4 5 10 | 0 -7 -3 -37 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~10125/7168 = 1\2, ~25/24 = 71.1175<br /> * [[POTE]]: ~10125/7168 = 1\2, ~25/24 = 71.107<br /> <br /> {{Optimal ET sequence|legend=1| 34d, 84d, 118, 152, 270, 1232, 1502, 1772c, 2042bc, 2312bc, 2582bc, 4894bbccd }}<br /> <br /> [[Badness]]: 0.041912<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 3025/3024, 4375/4374, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 | 0 -7 -3 -37 -26 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 1\2, ~25/24 = 71.1142<br /> * POTE: ~99/70 = 1\2, ~25/24 = 71.105<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 34d, 84de, 118, 152, 270, 962, 1232, 1502, 2734bcd, 4236bbccdd }}<br /> <br /> Badness: 0.014180<br /> <br /> ==== Ananta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 3025/3024, 4096/4095, 4375/4374<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 1 | 0 -7 -3 -37 -26 54 }}<br /> <br /> Optimal tuning: <br /> * CTE: ~99/70 = 1\2, ~25/24 = 71.1173<br /> * POTE: ~99/70 = 1\2, ~25/24 = 71.117<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 118, 152, 270, 928, 1198, 1468 }}<br /> <br /> Badness: 0.023678<br /> <br /> ==== Acyuta ====<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1716/1715, 2080/2079, 3025/3024, 5632/5625<br /> <br /> Mapping: {{mapping| 2 4 5 10 10 17 | 0 -7 -3 -37 -26 -81 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 1\2, ~25/24 = 71.1079<br /> * POTE: ~99/70 = 1\2, ~25/24 = 71.101<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 118f, 152f, 270, 692, 962, 1654cd, 2616bcdf }}<br /> <br /> Badness: 0.015805<br /> <br /> == Vishnean ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 126/125, 540225/524288<br /> <br /> {{Mapping|legend=1| 2 4 5 5 | 0 -7 -3 5 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~735/512 = 1\2, ~25/24 = 71.4956<br /> * [[POTE]]: ~735/512 = 1\2, ~25/24 = 71.779<br /> <br /> {{Optimal ET sequence|legend=1| 16, 34, 50, 134dd }}<br /> <br /> [[Badness]]: 0.161398<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 126/125, 385/384, 1350/1331<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 | 0 -7 -3 5 -9 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~63/44 = 1\2, ~25/24 = 71.6218<br /> * POTE: ~63/44 = 1\2, ~25/24 = 71.924<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}<br /> <br /> Badness: 0.071990<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 105/104, 126/125, 144/143, 847/845<br /> <br /> Mapping: {{mapping| 2 4 5 5 8 8 | 0 -7 -3 5 -9 -5 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~55/39 = 1\2, ~25/24 = 71.6369<br /> * POTE: ~55/39 = 1\2, ~25/24 = 71.926<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 16, 34, 50 }}<br /> <br /> Badness: 0.040739<br /> <br /> == Narayana ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 65625/65536, 321489/320000<br /> <br /> {{Mapping|legend=1| 2 4 5 3 | 0 -7 -3 22 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~567/400 = 1\2, ~25/24 = 71.2706<br /> * [[POTE]]: ~567/400 = 1\2, ~25/24 = 71.265<br /> <br /> {{Optimal ET sequence|legend=1| 34, 84, 118, 202, 320, 522 }}<br /> <br /> [[Badness]]: 0.094295<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 441/440, 8019/8000, 65625/65536<br /> <br /> Mapping: {{mapping| 2 4 5 3 3 | 0 -7 -3 22 33 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 1\2, ~25/24 = 71.2609<br /> * POTE: ~99/70 = 1\2, ~25/24 = 71.248<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 34e, 84, 118, 202, 320 }}<br /> <br /> Badness: 0.045908<br /> <br /> == Quarvish ==<br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 2401/2400, 6115295232/6103515625<br /> <br /> {{Mapping|legend=1| 2 4 5 6 | 0 -28 -12 -13 }}<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~78125/55296 = 1\2, ~7/5 = 582.2115 (~110592/109375 = 17.7885)<br /> * [[POTE]]: ~78125/55296 = 1\2, ~7/5 = 582.213 (~110592/109375 = 17.787)<br /> <br /> {{Optimal ET sequence|legend=1| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> [[Badness]]: 0.045029<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 2401/2400, 9801/9800, 172032/171875<br /> <br /> Mapping: {{mapping| 2 4 5 6 6 | 0 -28 -12 -13 31 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~99/70 = 1\2, ~7/5 = 582.2122 (~99/98 = 17.7878)<br /> * POTE: ~99/70 = 1\2, ~7/5 = 582.213 (~99/98 = 17.787)<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 68, 134, 202, 270, 742, 1012 }}<br /> <br /> Badness: 0.019868<br /> <br /> == Decavish ==<br /> The decavish temperament (50 &amp;amp; 270) tempers out the wizma, {{monzo| -6 -8 2 5 }} = 420175/419904 and the [[linus comma]], {{monzo| 11 -10 -10 10 }} = 578509309952/576650390625.<br /> <br /> [[Subgroup]]: 2.3.5.7<br /> <br /> [[Comma list]]: 420175/419904, 2202927104/2197265625<br /> <br /> {{Mapping|legend=1| 10 6 19 14 | 0 7 3 10 }}<br /> <br /> : mapping generators: ~15/14, ~54/49<br /> <br /> [[Optimal tuning]]s: <br /> * [[CTE]]: ~15/14 = 1\10, ~54/49 = 168.8587 (~25/24 = 71.1413, or ~36/35 = 48.8587)<br /> * [[POTE]]: ~15/14 = 1\10, ~54/49 = 168.871 (~25/24 = 71.129, or ~36/35 = 48.871)<br /> <br /> {{Optimal ET sequence|legend=1| 50, …, 220, 270, 1400, 1670, 1940, 2210c, 2480c }}<br /> <br /> [[Badness]]: 0.114531<br /> <br /> === 11-limit ===<br /> Subgroup: 2.3.5.7.11<br /> <br /> Comma list: 9801/9800, 41503/41472, 172032/171875<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 | 0 7 3 10 -1 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)<br /> * POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.141, or ~36/35 = 48.859)<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 50, …, 220, 270, 860, 1130, 1400 }}<br /> <br /> Badness: 0.036938<br /> <br /> === 13-limit ===<br /> Subgroup: 2.3.5.7.11.13<br /> <br /> Comma list: 1001/1000, 4225/4224, 4459/4455, 6656/6655<br /> <br /> Mapping: {{mapping| 10 6 19 14 36 37 | 0 7 3 10 -1 0 }}<br /> <br /> Optimal tunings: <br /> * CTE: ~15/14 = 1\10, ~54/49 = 168.8583 (~25/24 = 71.1417, or ~36/35 = 48.8583)<br /> * POTE: ~15/14 = 1\10, ~54/49 = 168.859 (~25/24 = 71.151, or ~36/35 = 48.859)<br /> <br /> Optimal ET sequence: {{Optimal ET sequence| 50, 220, 270, 590, 860, 1130 }}<br /> <br /> Badness: 0.021906<br /> <br /> [[Category:Temperament families]]<br /> [[Category:Vishnuzmic family| ]] &lt;!-- main article --&gt;<br /> [[Category:Vishnuzmic| ]] &lt;!-- key article --&gt;<br /> [[Category:Rank 2]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_comma&diff=232372 Vishnu comma 2026-06-18T06:36:01Z <p>FloraC: </p> <hr /> <div>{{Infobox Interval<br /> | Ratio = 6115295232/6103515625<br /> | Name = vishnu comma, vishnuzma, semisuper comma<br /> | Color name = sg&lt;sup&gt;14&lt;/sup&gt;4, sasepbigu 4th<br /> | Comma = yes<br /> }}<br /> The '''vishnu comma''', '''vishnuzma''' or '''semisuper comma''' ([[ratio]]: 6 115 295 232 / 6 103 515 625, [[monzo]]: {{monzo| 23 6 -14 }}), is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 3.34 [[cent]]s. It is the amount by which a stack of seven [[25/24|classical chromatic semitones]] falls short of a [[4/3|just perfect fourth]], in other words the interval (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;. Equivalently, it is the amount by which a stack of fourteen [[5/4|classical major thirds]] misses the [[729/512|Pythagorean augmented fourth]]. <br /> <br /> == Temperaments ==<br /> [[Tempering out]] this comma leads to the 5-limit [[vishnu]] temperament. <br /> <br /> See [[Vishnu family]] for the [[family]] of rank-2 temperaments where it is tempered out.<br /> <br /> == Etymology ==<br /> This comma was first named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''semisuper'', for one possible generator of the temperament was a &quot;semisuper fourth&quot;&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic &amp; co'']&lt;/ref&gt;. ''Semisuper comma'' appeared shortly after&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']&lt;/ref&gt;. It is not clear yet how and why the later names ''vishnu'' (for the temperament) and ''vishnuzma'' (for the comma) were added. <br /> <br /> == References ==<br /> <br /> [[Category:Vishnu]]<br /> [[Category:Commas with unknown etymology]]</div> FloraC https://en.xen.wiki/index.php?title=Category:Vishnu&diff=232371 Category:Vishnu 2026-06-18T06:35:24Z <p>FloraC: FloraC moved page Category:Vishnuzmic to Category:Vishnu without leaving a redirect: The temp&#039;s name is *vishnu*</p> <hr /> <div>[[Category:Categories by temperament]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnuzma&diff=232370 Vishnuzma 2026-06-18T06:34:45Z <p>FloraC: FloraC moved page Vishnuzma to Vishnu comma: See last edit summary</p> <hr /> <div>#REDIRECT [[Vishnu comma]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_comma&diff=232369 Vishnu comma 2026-06-18T06:34:44Z <p>FloraC: FloraC moved page Vishnuzma to Vishnu comma: See last edit summary</p> <hr /> <div>{{Infobox Interval<br /> | Ratio = 6115295232/6103515625<br /> | Name = vishnuzma, semisuper comma<br /> | Color name = sg&lt;sup&gt;14&lt;/sup&gt;4, sasepbigu 4th<br /> | Comma = yes<br /> }}<br /> The '''vishnu comma''', '''vishnuzma''' or '''semisuper comma''' ([[ratio]]: 6 115 295 232 / 6 103 515 625, [[monzo]]: {{monzo| 23 6 -14 }}), is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 3.34 [[cent]]s. It is the amount by which a stack of seven [[25/24|classical chromatic semitones]] falls short of a [[4/3|just perfect fourth]], in other words the interval (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;. Equivalently, it is the amount by which a stack of fourteen [[5/4|classical major thirds]] misses the [[729/512|Pythagorean augmented fourth]]. <br /> <br /> == Temperaments ==<br /> [[Tempering out]] this comma leads to the 5-limit [[vishnu]] temperament. <br /> <br /> See [[Vishnu family]] for the [[family]] of rank-2 temperaments where it is tempered out.<br /> <br /> == Etymology ==<br /> This comma was first named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''semisuper'', for one possible generator of the temperament was a &quot;semisuper fourth&quot;&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic &amp; co'']&lt;/ref&gt;. ''Semisuper comma'' appeared shortly after&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']&lt;/ref&gt;. It is not clear yet how and why the later names ''vishnu'' (for the temperament) and ''vishnuzma'' (for the comma) were added. <br /> <br /> == References ==<br /> <br /> [[Category:Vishnu]]<br /> [[Category:Commas with unknown etymology]]</div> FloraC https://en.xen.wiki/index.php?title=Vishnu_comma&diff=232368 Vishnu comma 2026-06-18T06:34:15Z <p>FloraC: The temp&#039;s name is *vishnu*, so *vishnu comma* is arguably standard</p> <hr /> <div>{{Infobox Interval<br /> | Ratio = 6115295232/6103515625<br /> | Name = vishnuzma, semisuper comma<br /> | Color name = sg&lt;sup&gt;14&lt;/sup&gt;4, sasepbigu 4th<br /> | Comma = yes<br /> }}<br /> The '''vishnu comma''', '''vishnuzma''' or '''semisuper comma''' ([[ratio]]: 6 115 295 232 / 6 103 515 625, [[monzo]]: {{monzo| 23 6 -14 }}), is an [[unnoticeable comma|unnoticeable]] [[5-limit]] [[comma]] measuring about 3.34 [[cent]]s. It is the amount by which a stack of seven [[25/24|classical chromatic semitones]] falls short of a [[4/3|just perfect fourth]], in other words the interval (4/3)/(25/24)&lt;sup&gt;7&lt;/sup&gt;. Equivalently, it is the amount by which a stack of fourteen [[5/4|classical major thirds]] misses the [[729/512|Pythagorean augmented fourth]]. <br /> <br /> == Temperaments ==<br /> [[Tempering out]] this comma leads to the 5-limit [[vishnu]] temperament. <br /> <br /> See [[Vishnu family]] for the [[family]] of rank-2 temperaments where it is tempered out.<br /> <br /> == Etymology ==<br /> This comma was first named by [[Gene Ward Smith]] in 2001 in terms of the corresponding temperament, ''semisuper'', for one possible generator of the temperament was a &quot;semisuper fourth&quot;&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_2121.html Yahoo! Tuning Group | ''Shismic &amp; co'']&lt;/ref&gt;. ''Semisuper comma'' appeared shortly after&lt;ref&gt;[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_5025.html Yahoo! Tuning Group | ''5-limit comma names'']&lt;/ref&gt;. It is not clear yet how and why the later names ''vishnu'' (for the temperament) and ''vishnuzma'' (for the comma) were added. <br /> <br /> == References ==<br /> <br /> [[Category:Vishnu]]<br /> [[Category:Commas with unknown etymology]]</div> FloraC