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-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{Technical data page}}
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+This page discusses miscellaneous [[Rank-2 temperament|rank-2]] [[temperament]]s [[tempering out]] the [[breedsma]], {{monzo| -5 -1 -2 4 }} = 2401/2400. This is the amount by which two [[49/40]] intervals exceed [[3/2]], and by which two [[60/49]] intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system ([[12edo]], for example) which does not possess a neutral third cannot be tempering out the breedsma.
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-02-24 00:18:23 UTC</tt>.<br>
-: The original revision id was <tt>204565744</tt>.<br>
-: The revision comment was: <tt></tt><br>
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
-<h4>Original Wikitext content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">Breedsmic temperaments are rank two temperaments tempering out the breedsma, 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.
-It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.
+The breedsma is also the amount by which four stacked [[10/7]] intervals exceed 25/6: 10000/2401 × 2401/2400 = 10000/2400 = 25/6, which is two octaves above the classic chromatic semitone, [[25/24]]. We might note also that (49/40)(10/7) = 7/4 and (49/40)(10/7)<sup>2</sup> = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40~60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.
-==Hemififths==
+Temperaments discussed elsewhere include:
-Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with [[99edo]] and [[140edo]] providing good tunings, and [[239edo]] an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&amp;58 temperament and has wedgie &lt;&lt;2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.
+* ''[[Decimal]]'' (+25/24, 49/48 or 50/49) → [[Dicot family #Decimal|Dicot family]]
+* ''[[Beatles]]'' (+64/63 or 686/675) → [[Archytas clan #Beatles|Archytas clan]]
+* [[Squares]] (+81/80) → [[Meantone family #Squares|Meantone family]]
+* [[Myna]] (+126/125) → [[Starling temperaments #Myna|Starling temperaments]]
+* [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
+* ''[[Octacot]]'' (+245/243) → [[Tetracot family #Octacot|Tetracot family]]
+* ''[[Greenwood]]'' (+405/392 or 1323/1280) → [[Greenwoodmic temperaments #Greenwood|Greenwoodmic temperaments]]
+* ''[[Quasitemp]]'' (+875/864) → [[Keemic temperaments #Quasitemp|Keemic temperaments]]
+* ''[[Quadrasruta]]'' (+2048/2025) → [[Diaschismic family #Quadrasruta|Diaschismic family]]
+* ''[[Quadrimage]]'' (+3125/3072) → [[Magic family #Quadrimage|Magic family]]
+* ''[[Hemiwürschmidt]]'' (+3136/3125 or 6144/6125) → [[Hemimean clan #Hemiwürschmidt|Hemimean clan]]
+* [[Ennealimmal]] (+4375/4374) → [[Ragismic microtemperaments #Ennealimmal|Ragismic microtemperaments]]
+* ''[[Quadritikleismic]]'' (+15625/15552) → [[Kleismic family #Quadritikleismic|Kleismic family]]
+* [[Harry]] (+19683/19600) → [[Gravity family #Harry|Gravity family]]
+* ''[[Sesquiquartififths]]'' (+32805/32768) → [[Schismatic family #Sesquiquartififths|Schismatic family]]
+* ''[[Amicable]]'' (+1600000/1594323) → [[Amity family #Amicable|Amity family]]
+* ''[[Neptune]]'' (+48828125/48771072) → [[Gammic family #Neptune|Gammic family]]
+* ''[[Decoid]]'' (+67108864/66976875) → [[Quintosec family #Decoid|Quintosec family]]
+* ''[[Tertiseptisix]]'' (+390625000/387420489) → [[Quartonic family #Tertiseptisix|Quartonic family]]
+* ''[[Eagle]]'' (+10485760000/10460353203) → [[Vulture family #Eagle|Vulture family]]
-By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. [[99edo]] is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.
+== Hemififths ==
+{{Main| Hemififths }}
-Commas: 2401/2400, 5120/5103
+Hemififths may be described as the {{nowrap| 41 & 58 }} temperament, tempering out [[5120/5103]], the hemifamity comma, and [[10976/10935]], hemimage. It has a neutral third as a generator; its [[ploidacot]] is dicot. [[99edo]] and [[140edo]] provides good tunings, and [[239edo]] an even better one; and other possible tunings are 160<sup>(1/25)</sup>, giving just 5's, the 7- and 9-odd-limit minimax tuning, or 14<sup>(1/13)</sup>, giving just 7's. It requires 25 generator steps to get to the class for the harmonic 5, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17- and 24-note mos are suited. The full force of this highly accurate temperament can be found using the 41-note mos or even the 34-note 2mos{{clarify}}.
-and 9-limit minimax
+By adding [[243/242]] (which also means [[441/440]], [[540/539]] and [[896/891]]) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. 99edo is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding [[144/143]] brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be [[16/13]]. 99 remains a good tuning choice.
-[|1 0 0 0&gt;, |7/5, 0, 2/25, 0&gt;, |0 0 1 0&gt;, |8/5 0 13/25 0&gt;]
-Eigenvalues: 2, 5
-Algebraic generator: (2 + sqrt(2))/2
+[[Subgroup]]: 2.3.5.7
-===11-limit===
+[[Comma list]]: 2401/2400, 5120/5103
-Commas: 243/242, 441/440, 896/891
-POTE generator: ~11/9 = 351.521
+{{Mapping|legend=1| 1 1 -5 -1 | 0 2 25 13 }}
-Map: [&lt;1 1 -5 -1 2|, &lt;0 2 25 13 5|]
+: mapping generators: ~2, ~49/40
-EDOs: 7, 17, 41, 58, 99
-Badness: 0.0235
-===13-limit===
+[[Optimal tuning]]s:
-Commas: 144/143, 196/195, 243/242, 364/363
+* [[CTE]]: ~2 = 1200.0000, ~49/40 = 351.4464
+: [[error map]]: {{val| 0.0000 +0.9379 -0.1531 -0.0224 }}
+* [[POTE]]: ~2 = 1200.0000, ~49/40 = 351.4774
+: error map: {{val| 0.0000 +0.9999 +0.6221 +0.0307 }}
-POTE generator: ~11/9 = 351.573
+[[Minimax tuning]]:
+* [[7-odd-limit|7-]] and [[9-odd-limit]] minimax: ~49/40 = {{monzo| 1/5 0 1/25 }}
+: {{monzo list| 1 0 0 0 | 7/5 0 2/25 0 | 0 0 1 0 | 8/5 0 13/25 0 }}
+: [[Eigenmonzo basis|unchanged-interval (eigenmonzo) basis]]: 2.5
-Map: [&lt;1 1 -5 -1 2 4|, &lt;0 2 25 13 5 -1|]
+[[Algebraic generator]]: (2 + sqrt(2))/2
-EDOs: 7, 17, 41, 58, 99
-Badness: 0.0191
-==Tertiaseptal==
+{{Optimal ET sequence|legend=1| 41, 58, 99, 239, 338 }}
-Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.
-Commas: 2401/2400, 65625/65536
+[[Badness]] (Smith): 0.022243
-POTE generator: ~256/245 = 77.191
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
-Map: [&lt;1 3 2 3|, &lt;0 -22 5 -3|]
+Comma list: 243/242, 441/440, 896/891
-EDOs: 15, 16, 31, 109, 140, 171
-Badness: 0.0130
-===11-limit===
+Mapping: {{mapping| 1 1 -5 -1 2 | 0 2 25 13 5 }}
-Commas: 243/242, 441/440, 65625/65536
-POTE generator: ~256/245 = 77.227
+Optimal tunings:
+* CTE: ~2 = 1200.0000, ~11/9 = 351.4289
+* POTE: ~2 = 1200.0000, ~11/9 = 351.5206
-Map: [&lt;1 3 2 3 7|, &lt;0 -22 5 -3 -55|]
+{{Optimal ET sequence|legend=0| 17c, 41, 58, 99e }}
-EDOs: 15, 16, 31, 171, 202
-Badness: 0.0356
-==Harry==
+Badness (Smith): 0.023498
-Commas: 2401/2400, 19683/19600
-Harry adds cataharry, 19683/19600, to the set of commas. It may be described as the 58&amp;72 temperament, with wedgie &lt;&lt;12 34 20 26 -2 -49||. The period is half an octave, and the generator 21/20, with generator tunings of 9/130 or 14/202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices.
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
-Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is &lt;&lt;12 34 20 30 ...||.
+Comma list: 144/143, 196/195, 243/242, 364/363
-Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with &lt;&lt;12 34 20 30 52 ...|| as the octave wedgie. [[130edo]] is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.
+Mapping: {{mapping| 1 1 -5 -1 2 4 | 0 2 25 13 5 -1 }}
-[[POTE tuning|POTE generator]]: ~21/20 = 83.156
+Optimal tunings:
+* CTE: ~2 = 1200.0000, ~11/9 = 351.4331
+* POTE: ~2 = 1200.0000, ~11/9 = 351.5734
-Map: [&lt;2 4 7 7|, &lt;0 -6 -17 -10|]
+{{Optimal ET sequence|legend=0| 17c, 41, 58, 99ef, 157eff }}
-Wedgie: &lt;&lt;12 34 20 26 -2 -49||
-EDOs: 14, 58, 72, 130, 202, 534, 938
-Badness: 0.0341
-===11-limit===
+Badness (Smith): 0.019090
-Commas: 243/242, 441/440, 4000/3993
-[[POTE tuning|POTE generator]]: ~21/20 = 83.167
+=== Semihemi ===
+Subgroup: 2.3.5.7.11
-Map: [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]
+Comma list: 2401/2400, 3388/3375, 5120/5103
-EDOs: 14, 58, 72, 130, 202
-Badness: 0.0159
-===13-limit===
+Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}
-Commas: 243/242, 351/350, 441/440, 676/675
-[[POTE tuning|POTE generator]]: ~21/20 = 83.116
+: mapping generators: ~99/70, ~400/231
-Map: [&lt;2 4 7 7 9 11|, &lt;0 -6 -17 -10 -15 -26|]
+Optimal tunings:
-EDOs: 14, 58, 72, 130, 462
+* CTE: ~99/70 = 600.0000, ~49/40 = 351.4722
-Badness: 0.0130
+* POTE: ~99/70 = 600.0000, ~49/40 = 351.5047
-==Quasiorwell==
+{{Optimal ET sequence|legend=0| 58, 140, 198 }}
-In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&gt;. It has a wedgie &lt;&lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.
-Adding 3025/3024 extends to the 11-limit and gives &lt;&lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.</pre></div>
+Badness (Smith): 0.042487
-<h4>Original HTML content:</h4>
-<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Breedsmic temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;Breedsmic temperaments are rank two temperaments tempering out the breedsma, 2401/2400. This is the amount by which two 49/40 intervals exceed 3/2, and by which two 60/49 intervals fall short. Either of these represent a neutral third interval which is highly characteristic of breedsmic tempering; any tuning system (12edo, for example) which does not possess a neutral third cannot be tempering out the breedsma.&lt;br /&gt;
+==== 13-limit ====
-&lt;br /&gt;
+Subgroup: 2.3.5.7.11.13
-It is also the amount by which four stacked 10/7 intervals exceed 25/6: 10000/2401 * 2401/2400 = 10000/2400 = 25/6, which is two octaves above the chromatic semitone, 25/24. We might note also that 49/40 * 10/7 = 7/4 and 49/40 * (10/7)^2 = 5/2, relationships which will be significant in any breedsmic temperament. As a consequence of these facts, the 49/40+60/49 neutral third and the 7/5 and 10/7 intervals tend to have relatively low complexity in a breedsmic system.&lt;br /&gt;
-&lt;br /&gt;
+Comma list: 352/351, 676/675, 847/845, 1716/1715
-&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Hemififths"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Hemififths&lt;/h2&gt;
-Hemififths tempers out 5120/5103, the hemifamity comma, and 10976/10935, hemimage. It has a neutral third as a generator, with &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; and &lt;a class="wiki_link" href="/140edo"&gt;140edo&lt;/a&gt; providing good tunings, and &lt;a class="wiki_link" href="/239edo"&gt;239edo&lt;/a&gt; an even better one; and other possible tunings are (160)^(1/25), giving just 5s, the 7 and 9 limit minimax tuning, or 14^(1/13), giving just 7s. It may be called the 41&amp;amp;58 temperament and has wedgie &amp;lt;&amp;lt;2 25 13 35 15 -40||, which tells us that it requires 25 generator steps to get to the class for major thirds, whereas the 7 is half as complex, and hence hemififths makes for a good no-fives temperament, to which the 17 and 24 note MOS are suited. The full force of this highly accurate temperament can be found using the 41 note MOS or even the 34 note 2MOS.&lt;br /&gt;
+Mapping: {{mapping| 2 0 -35 -15 -47 -37 | 0 2 25 13 34 28 }}
-&lt;br /&gt;
-By adding 243/242 (which also means 441/440, 540/539 and 896/891) to the commas, hemififths extends to a less accurate 11-limit version, but one where 11/4 is only five generator steps. &lt;a class="wiki_link" href="/99edo"&gt;99edo&lt;/a&gt; is an excellent tuning; one which loses little of the accuracy of the 7-limit but improves the 11-limit a bit. Now adding 144/143 brings in the 13-limit with less accuracy yet, but with very low complexity, as the generator can be taken to be 16/13. 99 remains a good tuning choice.&lt;br /&gt;
+Optimal tunings:
-&lt;br /&gt;
+* CTE: ~99/70 = 600.0000, ~49/40 = 351.4674
-Commas: 2401/2400, 5120/5103&lt;br /&gt;
+* POTE: ~99/70 = 600.0000, ~49/40 = 351.5019
-&lt;br /&gt;
-and 9-limit minimax&lt;br /&gt;
+{{Optimal ET sequence|legend=0| 58, 140, 198, 536f }}
-[|1 0 0 0&amp;gt;, |7/5, 0, 2/25, 0&amp;gt;, |0 0 1 0&amp;gt;, |8/5 0 13/25 0&amp;gt;]&lt;br /&gt;
-Eigenvalues: 2, 5&lt;br /&gt;
+Badness (Smith): 0.021188
-&lt;br /&gt;
-Algebraic generator: (2 + sqrt(2))/2&lt;br /&gt;
+=== Quadrafifths ===
-&lt;br /&gt;
+This has been logged as ''semihemififths'' in Graham Breed's temperament finder, but ''quadrafifths'' arguably makes more sense because it straight-up splits the fifth in four.
-&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="x-Hemififths-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h3&gt;
-Commas: 243/242, 441/440, 896/891&lt;br /&gt;
+Subgroup: 2.3.5.7.11
-&lt;br /&gt;
-POTE generator: ~11/9 = 351.521&lt;br /&gt;
+Comma list: 2401/2400, 3025/3024, 5120/5103
-&lt;br /&gt;
-Map: [&amp;lt;1 1 -5 -1 2|, &amp;lt;0 2 25 13 5|]&lt;br /&gt;
+Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}
-EDOs: 7, 17, 41, 58, 99&lt;br /&gt;
-Badness: 0.0235&lt;br /&gt;
+: Mapping generators: ~2, ~243/220
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x-Hemififths-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h3&gt;
+Optimal tunings:
-Commas: 144/143, 196/195, 243/242, 364/363&lt;br /&gt;
+* CTE: ~2 = 1200.0000, ~243/220 = 175.7284
-&lt;br /&gt;
+* POTE: ~2 = 1200.0000, ~243/220 = 175.7378
-POTE generator: ~11/9 = 351.573&lt;br /&gt;
-&lt;br /&gt;
+{{Optimal ET sequence|legend=0| 41, 157, 198, 239, 676b, 915be }}
-Map: [&amp;lt;1 1 -5 -1 2 4|, &amp;lt;0 2 25 13 5 -1|]&lt;br /&gt;
-EDOs: 7, 17, 41, 58, 99&lt;br /&gt;
+Badness (Smith): 0.040170
-Badness: 0.0191&lt;br /&gt;
-&lt;br /&gt;
+==== 13-limit ====
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-Tertiaseptal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Tertiaseptal&lt;/h2&gt;
+Subgroup: 2.3.5.7.11.13
-Aside from the breedsma, tertiaseptal tempers out 65625/65536, the horwell comma, 703125/702464, the meter, and 2100875/2097152. It can be described as the 140&amp;amp;171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. &lt;a class="wiki_link" href="/171edo"&gt;171edo&lt;/a&gt; makes for an excellent tuning. The 15 or 16 note MOS can be used to explore no-threes harmony, and the 31 note MOS gives plenty of room for those as well.&lt;br /&gt;
-&lt;br /&gt;
+Comma list: 352/351, 847/845, 2401/2400, 3025/3024
-Commas: 2401/2400, 65625/65536&lt;br /&gt;
-&lt;br /&gt;
+Mapping: {{mapping| 1 1 -5 -1 8 10 | 0 4 50 26 -31 -43 }}
-POTE generator: ~256/245 = 77.191&lt;br /&gt;
-&lt;br /&gt;
+Optimal tunings:
-Map: [&amp;lt;1 3 2 3|, &amp;lt;0 -22 5 -3|]&lt;br /&gt;
+* CTE: ~2 = 1200.0000, ~72/65 = 175.7412
-EDOs: 15, 16, 31, 109, 140, 171&lt;br /&gt;
+* POTE: ~2 = 1200.0000, ~72/65 = 175.7470
-Badness: 0.0130&lt;br /&gt;
-&lt;br /&gt;
+{{Optimal ET sequence|legend=0| 41, 157, 198, 437f, 635bcff }}
-&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x-Tertiaseptal-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;11-limit&lt;/h3&gt;
-Commas: 243/242, 441/440, 65625/65536&lt;br /&gt;
+Badness (Smith): 0.031144
-&lt;br /&gt;
-POTE generator: ~256/245 = 77.227&lt;br /&gt;
+== Tertiaseptal ==
-&lt;br /&gt;
+{{Main| Tertiaseptal }}
-Map: [&amp;lt;1 3 2 3 7|, &amp;lt;0 -22 5 -3 -55|]&lt;br /&gt;
-EDOs: 15, 16, 31, 171, 202&lt;br /&gt;
+Aside from the breedsma, tertiaseptal tempers out [[65625/65536]], the horwell comma, [[703125/702464]], the meter, and [[2100875/2097152]], the rainy comma. It can be described as the 31 &amp; 171 temperament, and 256/245, 1029/1024 less than 21/20, serves as its generator. Three of these fall short of 8/7 by 2100875/2097152, and the generator can be taken as 1/3 of an 8/7 flattened by a fraction of a cent. [[171edo]] makes for an excellent tuning, although 171edo - [[31edo]] = [[140edo]] also makes sense, and in very high limits 140edo + 171edo = [[311edo]] is especially notable. The 15- or 16-note mos can be used to explore no-threes harmony, and the 31-note mos gives plenty of room for those as well.
-Badness: 0.0356&lt;br /&gt;
-&lt;br /&gt;
+[[Subgroup]]: 2.3.5.7
-&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;a name="x-Harry"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Harry&lt;/h2&gt;
-Commas: 2401/2400, 19683/19600&lt;br /&gt;
+[[Comma list]]: 2401/2400, 65625/65536
-&lt;br /&gt;
-Harry adds cataharry, 19683/19600, to the set of commas. It may be described as the 58&amp;amp;72 temperament, with wedgie &amp;lt;&amp;lt;12 34 20 26 -2 -49||. The period is half an octave, and the generator 21/20, with generator tunings of 9/130 or 14/202 being good choices. MOS of size 14, 16, 30, 44 or 58 are among the scale choices.&lt;br /&gt;
+{{Mapping|legend=1| 1 3 2 3 | 0 -22 5 -3 }}
-&lt;br /&gt;
-Harry becomes much more interesting as we move to the 11-limit, where we can add 243/242, 441/440 and 540/539 to the set of commas. 130 and especially 202 still make for good tuning choices, and the octave part of the wedgie is &amp;lt;&amp;lt;12 34 20 30 ...||.&lt;br /&gt;
+: Mapping generators: ~2, ~256/245
-&lt;br /&gt;
-Similar comments apply to the 13-limit, where we can add 351/350 and 364/363 to the commas, with &amp;lt;&amp;lt;12 34 20 30 52 ...|| as the octave wedgie. &lt;a class="wiki_link" href="/130edo"&gt;130edo&lt;/a&gt; is again a good tuning choice, but even better might be tuning 7s justly, which can be done via a generator of 83.1174 cents. 72 notes of harry gives plenty of room even for the 13-limit harmonies.&lt;br /&gt;
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~256/245 = 77.191
-&lt;br /&gt;
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~21/20 = 83.156&lt;br /&gt;
+{{Optimal ET sequence|legend=1| 31, 109, 140, 171 }}
-&lt;br /&gt;
-Map: [&amp;lt;2 4 7 7|, &amp;lt;0 -6 -17 -10|]&lt;br /&gt;
+[[Badness]]: 0.012995
-Wedgie: &amp;lt;&amp;lt;12 34 20 26 -2 -49||&lt;br /&gt;
-EDOs: 14, 58, 72, 130, 202, 534, 938&lt;br /&gt;
+=== 11-limit ===
-Badness: 0.0341&lt;br /&gt;
+Subgroup: 2.3.5.7.11
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x-Harry-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;11-limit&lt;/h3&gt;
+Comma list: 243/242, 441/440, 65625/65536
-Commas: 243/242, 441/440, 4000/3993&lt;br /&gt;
-&lt;br /&gt;
+Mapping: {{mapping| 1 3 2 3 7 | 0 -22 5 -3 -55 }}
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~21/20 = 83.167&lt;br /&gt;
-&lt;br /&gt;
+Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.227
-Map: [&amp;lt;2 4 7 7 9|, &amp;lt;0 -6 -17 -10 -15|]&lt;br /&gt;
-EDOs: 14, 58, 72, 130, 202&lt;br /&gt;
+Optimal ET sequence: {{Optimal ET sequence| 31, 109e, 140e, 171, 202 }}
-Badness: 0.0159&lt;br /&gt;
-&lt;br /&gt;
+Badness: 0.035576
-&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x-Harry-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;13-limit&lt;/h3&gt;
-Commas: 243/242, 351/350, 441/440, 676/675&lt;br /&gt;
+==== 13-limit ====
-&lt;br /&gt;
+Subgroup: 2.3.5.7.11.13
-&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~21/20 = 83.116&lt;br /&gt;
-&lt;br /&gt;
+Comma list: 243/242, 441/440, 625/624, 3584/3575
-Map: [&amp;lt;2 4 7 7 9 11|, &amp;lt;0 -6 -17 -10 -15 -26|]&lt;br /&gt;
-EDOs: 14, 58, 72, 130, 462&lt;br /&gt;
+Mapping: {{mapping| 1 3 2 3 7 1 | 0 -22 5 -3 -55 42 }}
-Badness: 0.0130&lt;br /&gt;
-&lt;br /&gt;
+Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.203
-&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-Quasiorwell"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Quasiorwell&lt;/h2&gt;
- In addition to 2401/2400, quasiorwell tempers out 29360128/29296875 = |22 -1 -10 1&amp;gt;. It has a wedgie &amp;lt;&amp;lt;38 -3 8 -93 -94 27||. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31&amp;amp;270 temperament, and as one might expect, 61/270 makes for an excellent tuning choice. Other possibilities are (7/2)^(1/8), giving just 7s, or 384^(1/38), giving pure fifths.&lt;br /&gt;
+Optimal ET sequence: {{Optimal ET sequence| 31, 109e, 140e, 171 }}
-&lt;br /&gt;
-Adding 3025/3024 extends to the 11-limit and gives &amp;lt;&amp;lt;38 -3 8 64 ...|| for the initial wedgie, and as expected, 270 remains an excellent tuning.&lt;/body&gt;&lt;/html&gt;</pre></div>
+Badness: 0.036876
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575
+Mapping: {{mapping| 1 3 2 3 7 1 1 | 0 -22 5 -3 -55 42 48 }}
+Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.201
+Optimal ET sequence: {{Optimal ET sequence| 31, 109eg, 140e, 171 }}
+Badness: 0.027398
+=== Tertia ===
+Subgroup:2.3.5.7.11
+Comma list: 385/384, 1331/1323, 1375/1372
+Mapping: {{mapping| 1 3 2 3 5 | 0 -22 5 -3 -24 }}
+Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.173
+Optimal ET sequence: {{Optimal ET sequence| 31, 109, 140, 171e, 311e }}
+Badness: 0.030171
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 352/351, 385/384, 625/624, 1331/1323
+Mapping: {{mapping| 1 3 2 3 5 1 | 0 -22 5 -3 -24 42 }}
+Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.158
+Optimal ET sequence: {{Optimal ET sequence| 31, 109, 140, 311e, 451ee }}
+Badness: 0.028384
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 352/351, 385/384, 561/560, 625/624, 715/714
+Mapping: {{mapping| 1 3 2 3 5 1 1 | 0 -22 5 -3 -24 42 48 }}
+Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.162
+Optimal ET sequence: {{Optimal ET sequence| 31, 109g, 140, 311e, 451ee }}
+Badness: 0.022416
+=== Tertiaseptia ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 6250/6237, 65625/65536
+Mapping: {{mapping| 1 3 2 3 -4 | 0 -22 5 -3 116 }}
+Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.169
+Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1695c, 2006bcd, 2317bcd, 2628bccde, 2939bccde, 3250bccde }}
+Badness: 0.056926
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400
+Mapping: {{mapping| 1 3 2 3 -4 1 | 0 -22 5 -3 116 42 }}
+Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.168
+Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1073, 1384cf, 1695cf, 2006bcdf }}
+Badness: 0.027474
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197
+Mapping: {{mapping| 1 3 2 3 -4 1 1 | 0 -22 5 -3 116 42 48 }}
+Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169
+Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}
+Badness: 0.018773
+==== 19-limit ====
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 595/594, 625/624, 833/832, 1156/1155, 1216/1215, 2200/2197
+Mapping: {{mapping| 1 3 2 3 -4 1 1 11 | 0 -22 5 -3 116 42 48 -105 }}
+Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169
+Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1384cfgg, 1695cfgg, 2006bcdfgg }}
+Badness: 0.017653
+==== 23-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23
+Comma list: 595/594, 625/624, 833/832, 875/874, 1105/1104, 1156/1155, 1216/1215
+Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 | 0 -22 5 -3 116 42 48 -105 117 }}
+Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.168
+Optimal ET sequence: {{Optimal ET sequence| 140, 311, 762g, 1073g, 1384cfgg }}
+Badness: 0.015123
+==== 29-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23.29
+Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155
+Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 | 0 -22 5 -3 116 42 48 -105 117 60 }}
+Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.167
+Optimal ET sequence: {{Optimal ET sequence| 140, 311, 762g, 1073g, 1384cfggj }}
+Badness: 0.012181
+==== 31-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31
+Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
+Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 | 0 -22 5 -3 116 42 48 -105 117 60 -94 }}
+Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169
+Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}
+Badness: 0.012311
+==== 37-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37
+Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014
+Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 0 | 0 -22 5 -3 116 42 48 -105 117 60 -94 81 }}
+Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.170
+Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}
+Badness: 0.010949
+==== 41-limit ====
+Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41
+Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930
+Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 0 6 | 0 -22 5 -3 116 42 48 -105 117 60 -94 81 -10 }}
+Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169
+Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}
+Badness: 0.009825
+=== Hemitert ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 3025/3024, 65625/65536
+Mapping: {{mapping| 1 3 2 3 6 | 0 -44 10 -6 -79 }}
+: Mapping generators: ~2, ~45/44
+Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.596
+Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 342 }}
+Badness: 0.015633
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095
+Mapping: {{mapping| 1 3 2 3 6 1 | 0 -44 10 -6 -79 84 }}
+Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.588
+Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 964f, 1275f, 1586cff }}
+Badness: 0.033573
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095
+Mapping: {{mapping| 1 3 2 3 6 1 1 | 0 -44 10 -6 -79 84 96 }}
+Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.589
+Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 653f, 964f }}
+Badness: 0.025298
+=== Semitert ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 9801/9800, 65625/65536
+Mapping: {{mapping| 2 6 4 6 1 | 0 -22 5 -3 46 }}
+: Mapping generators: ~99/70, ~256/245
+Optimal tuning (POTE): ~99/70 = 1\2, ~256/245 = 77.193
+Optimal ET sequence: {{Optimal ET sequence| 62e, 140, 202, 342 }}
+Badness: 0.025790
+== Quasiorwell ==
+In addition to 2401/2400, quasiorwell tempers out the quasiorwellisma, 29360128/29296875 = {{monzo| 22 -1 -10 1 }}. It has a generator 1024/875, which is 6144/6125 more than 7/6. It may be described as the 31 &amp; 270 temperament, and as one might expect, 61\270 makes for an excellent tuning choice. Other possibilities are (7/2)<sup>1/8</sup>, giving just 7's, or 384<sup>1/38</sup>, giving pure fifths.
+Adding 3025/3024 extends to the 11-limit and as expected, 270 remains an excellent tuning.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 29360128/29296875
+{{Mapping|legend=1| 1 31 0 9 | 0 -38 3 -8 }}
+: Mapping generators: ~2, ~875/512
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1024/875 = 271.107
+{{Optimal ET sequence|legend=1| 31, 177, 208, 239, 270, 571, 841, 1111 }}
+[[Badness]]: 0.035832
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 3025/3024, 5632/5625
+Mapping: {{mapping| 1 31 0 9 53 | 0 -38 3 -8 -64 }}
+Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.111
+Optimal ET sequence: {{Optimal ET sequence| 31, 208, 239, 270 }}
+Badness: 0.017540
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095
+Mapping: {{mapping| 1 31 0 9 53 -59 | 0 -38 3 -8 -64 81 }}
+Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.107
+Optimal ET sequence: {{Optimal ET sequence| 31, 239, 270, 571, 841, 1111 }}
+Badness: 0.017921
+== Neominor ==
+The generator for neominor temperament is tridecimal minor third [[13/11]], also known as ''Neo-gothic minor third''.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 177147/175616
+{{Mapping|legend=1| 1 3 12 8 | 0 -6 -41 -22 }}
+: Mapping generators: ~2, ~189/160
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~189/160 = 283.280
+{{Optimal ET sequence|legend=1| 72, 161, 233, 305 }}
+[[Badness]]: 0.088221
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 35937/35840
+Mapping: {{mapping| 1 3 12 8 7 | 0 -6 -41 -22 -15 }}
+Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 283.276
+Optimal ET sequence: {{Optimal ET sequence| 72, 161, 233, 305 }}
+Badness: 0.027959
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 169/168, 243/242, 364/363, 441/440
+Mapping: {{mapping| 1 3 12 8 7 7 | 0 -6 -41 -22 -15 -14 }}
+Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 283.294
+Optimal ET sequence: {{Optimal ET sequence| 72, 161f, 233f }}
+Badness: 0.026942
+== Emmthird ==
+The generator for emmthird is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 14348907/14336000
+{{Mapping|legend=1| 1 11 42 25 | 0 -14 -59 -33 }}
+: Mapping generators: ~2, ~2187/1372
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~2744/2187 = 392.988
+{{Optimal ET sequence|legend=1| 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d }}
+[[Badness]]: 0.016736
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 1792000/1771561
+Mapping: {{mapping| 1 11 42 25 27 | 0 -14 -59 -33 -35 }}
+Optimal tuning (POTE): ~2 = 1\1, ~1372/1089 = 392.991
+Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}
+Badness: 0.052358
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 364/363, 441/440, 2200/2197
+Mapping: {{mapping| 1 11 42 25 27 38 | 0 -14 -59 -33 -35 -51 }}
+Optimal tuning (POTE): ~2 = 1\1, ~180/143 = 392.989
+Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}
+Badness: 0.026974
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 243/242, 364/363, 441/440, 595/594, 2200/2197
+Mapping: {{mapping| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}
+Optimal tuning (POTE): ~2 = 1\1, ~64/51 = 392.985
+Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}
+Badness: 0.023205
+== Quinmite ==
+The generator for quinmite is quasi-tempered minor third [[25/21]], flatter than 6/5 by the starling comma, [[126/125]]. It is also generated by 1/5 of minor tenth 12/5, and its name is a play on the words "quintans" (Latin for "one fifth") and "minor tenth", given by [[Petr Pařízek]] in 2011<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref><ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo! Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 1959552/1953125
+{{Mapping|legend=1| 1 27 24 20 | 0 -34 -29 -23 }}
+: Mapping generators: ~2, ~42/25
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 302.997
+{{Optimal ET sequence|legend=1| 99, 202, 301, 400, 701, 1101c, 1802c, 2903cc }}
+[[Badness]]: 0.037322
+== Unthirds ==
+Despite the complexity of its mapping, unthirds is an important temperament to the structure of the [[11-limit]]; this is hinted at by unthirds' representation as the [[72edo|72]] & [[311edo|311]] temperament, the [[Temperament merging|join]] of two tuning systems well-known for their high accuracy in the 11-limit and [[41-limit]] respectively. It is generated by the interval of [[14/11]] ('''un'''decimal major '''third''', hence the name) tuned less than a cent flat, and the 23-note [[MOS]] this interval generates serves as a well temperament of, of all things, [[23edo]]. The 49-note MOS is needed to access the 3rd, 5th, 7th, and 11th harmonics, however.
+The commas it tempers out include the [[breedsma]] (2401/2400), the [[lehmerisma]] (3025/3024), the [[pine comma]] (4000/3993), the [[unisquary comma]] (12005/11979), the [[argyria]] (41503/41472), and 42875/42768, all of which appear individually in various 11-limit systems. It is also notable that there is a [[restriction]] of the temperament to the 2.5/3.7/3.11/3 [[fractional subgroup]] that tempers out 3025/3024 and 12005/11979, which is of considerably less complexity, and which is shared with [[sqrtphi]] (whose generator is tuned flat of 72edo's).
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 68359375/68024448
+{{Mapping|legend=1| 1 29 33 25 | 0 -42 -47 -34 }}
+: Mapping generators: ~2, ~6125/3888
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3969/3125 = 416.717
+{{Optimal ET sequence|legend=1| 72, 167, 239, 311, 694, 1005c }}
+[[Badness]]: 0.075253
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 3025/3024, 4000/3993
+Mapping: {{mapping| 1 29 33 25 25 | 0 -42 -47 -34 -33 }}
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.718
+Optimal ET sequence: {{Optimal ET sequence| 72, 167, 239, 311 }}
+Badness: 0.022926
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400
+Mapping: {{mapping| 1 29 33 25 25 99 | 0 -42 -47 -34 -33 -146 }}
+Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.716
+Optimal ET sequence: {{Optimal ET sequence| 72, 239f, 311, 694, 1005c }}
+Badness: 0.020888
+== Newt ==
+Newt has a generator of a neutral third (0.2 cents flat of [[49/40]]) and tempers out the [[garischisma]]. It can be described as the 41 & 270 temperament, and extends naturally to the no-17 19-limit, a.k.a. '''neonewt'''. [[270edo]] and [[311edo]] are obvious tuning choices, but [[581edo]] and especially [[851edo]] work much better.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 33554432/33480783
+{{Mapping|legend=1| 1 1 19 11 | 0 2 -57 -28 }}
+: mapping generators: ~2, ~49/40
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 351.113
+{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}
+[[Badness]]: 0.041878
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 3025/3024, 19712/19683
+Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}
+Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.115
+Optimal ET sequence: {{Optimal ET sequence| 41, 147ce, 188, 229, 270, 581, 851, 1121, 1972 }}
+Badness: 0.019461
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095
+Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
+Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.117
+Optimal ET sequence: {{Optimal ET sequence| 41, 147cef, 188f, 229, 270, 581, 851, 2283b, 3134b }}
+Badness: 0.013830
+=== 2.3.5.7.11.13.19 subgroup (neonewt) ===
+Subgroup: 2.3.5.7.11.13.19
+Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400
+Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}
+Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.117
+Optimal ET sequence: {{Optimal ET sequence| 41, 147cefh, 188f, 229, 270, 581, 851, 3134b, 3985b, 4836bb }}
+== Septidiasemi ==
+{{Main| Septidiasemi }}
+Aside from 2401/2400, [[septidiasemi]] tempers out 2152828125/2147483648 in the 7-limit. It is so named because the generator is a "septimal diatonic semitone" (0.15 cents flat of [[15/14]]). It is an excellent tuning for 2.3.5.7.13 and 2.3.5.7.13.17 subgroups rather than full 13- and 17-limit.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 2152828125/2147483648
+{{Mapping|legend=1| 1 25 -31 -8 | 0 -26 37 12 }}
+: Mapping generators: ~2, ~28/15
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 119.297
+{{Optimal ET sequence|legend=1| 10, 151, 161, 171, 3581bcdd, 3752bcdd, 3923bcdd, 4094bcdd, 4265bccdd, 4436bccdd, 4607bccdd }}
+[[Badness]]: 0.044115
+=== Sedia ===
+The ''sedia'' temperament (10&amp;161) is an 11-limit extension of the septidiasemi, which tempers out 243/242 and 441/440.
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 939524096/935859375
+Mapping: {{mapping| 1 25 -31 -8 62 | 0 -26 37 12 -65 }}
+Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.279
+Optimal ET sequence: {{Optimal ET sequence| 10, 151, 161, 171, 332 }}
+Badness: 0.090687
+==== 13-limit ====
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 441/440, 2200/2197, 3584/3575
+Mapping: {{mapping| 1 25 -31 -8 62 1 | 0 -26 37 12 -65 3 }}
+Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.281
+Optimal ET sequence: {{Optimal ET sequence| 10, 151, 161, 171, 332, 835eeff }}
+Badness: 0.045773
+==== 17-limit ====
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 243/242, 441/440, 833/832, 2200/2197, 3584/3575
+Mapping: {{mapping| 1 25 -31 -8 62 1 23 | 0 -26 37 12 -65 3 -21 }}
+Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 119.281
+Optimal ET sequence: {{Optimal ET sequence| 10, 151, 161, 171, 332, 503ef, 835eeff }}
+Badness: 0.027322
+== Maviloid ==
+{{See also| Ragismic microtemperaments #Parakleismic }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 1224440064/1220703125
+{{Mapping|legend=1| 1 31 34 26 | 0 -52 -56 -41 }}
+: Mapping generators: ~2, ~1296/875
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1296/875 = 678.810
+{{Optimal ET sequence|legend=1| 76, 99, 274, 373, 472, 571, 1043, 1614 }}
+[[Badness]]: 0.057632
+== Subneutral ==
+{{See also| Luna family }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 274877906944/274658203125
+{{Mapping|legend=1| 1 19 0 6 | 0 -60 8 -11 }}
+: Mapping generators: ~2, ~57344/46875
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~57344/46875 = 348.301
+{{Optimal ET sequence|legend=1| 31, …, 348, 379, 410, 441, 1354, 1795, 2236 }}
+[[Badness]]: 0.045792
+== Osiris ==
+{{See also| Metric microtemperaments #Geb }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 31381059609/31360000000
+{{Mapping|legend=1| 1 13 33 21 | 0 -32 -86 -51 }}
+: Mapping generators: ~2, ~2800/2187
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~2800/2187 = 428.066
+{{Optimal ET sequence|legend=1| 157, 171, 1012, 1183, 1354, 1525, 1696 }}
+[[Badness]]: 0.028307
+== Gorgik ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 28672/28125
+{{Mapping|legend=1| 1 5 1 3 | 0 -18 7 -1 }}
+: Mapping generators: ~2, ~8/7
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~8/7 = 227.512
+{{Optimal ET sequence|legend=1| 21, 37, 58, 153bc, 211bccd, 269bccd }}
+[[Badness]]: 0.158384
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 176/175, 2401/2400, 2560/2541
+Mapping: {{mapping| 1 5 1 3 1 | 0 -18 7 -1 13 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.500
+Optimal ET sequence: {{Optimal ET sequence| 21, 37, 58, 153bce, 211bccdee, 269bccdee }}
+Badness: 0.059260
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 176/175, 196/195, 364/363, 512/507
+Mapping: {{mapping| 1 5 1 3 1 2 | 0 -18 7 -1 13 9 }}
+Optimal tuning (POTE): ~2 = 1\1, ~8/7 = 227.493
+Optimal ET sequence: {{Optimal ET sequence| 21, 37, 58, 153bcef, 211bccdeeff }}
+Badness: 0.032205
+== Fibo ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 341796875/339738624
+{{Mapping|legend=1| 1 19 8 10 | 0 -46 -15 -19 }}
+: Mapping generators: ~2, ~125/96
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~125/96 = 454.310
+{{Optimal ET sequence|legend=1| 37, 66b, 103, 140, 243, 383, 1009cd, 1392ccd }}
+Badness: 0.100511
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 1375/1372, 43923/43750
+Mapping: {{mapping| 1 19 8 10 8 | 0 -46 -15 -19 -12 }}
+Optimal tuning (POTE): ~2 = 1\1, ~100/77 = 454.318
+Optimal ET sequence: {{Optimal ET sequence| 37, 66b, 103, 140, 243e }}
+Badness: 0.056514
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 385/384, 625/624, 847/845, 1375/1372
+Mapping: {{mapping| 1 19 8 10 8 9 | 0 -46 -15 -19 -12 -14 }}
+Optimal tuning (POTE): ~2 = 1\1, ~13/10 = 454.316
+Optimal ET sequence: {{Optimal ET sequence| 37, 66b, 103, 140, 243e }}
+Badness: 0.027429
+== Mintone ==
+In addition to 2401/2400, mintone tempers out 177147/175000 = {{monzo| -3 11 -5 -1 }} in the 7-limit; 243/242, 441/440, and 43923/43750 in the 11-limit. It has a generator tuned around 49/44. It may be described as the 58 &amp; 103 temperament, and as one might expect, 25\161 makes for an excellent tuning choice.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 177147/175000
+{{Mapping|legend=1| 1 5 9 7 | 0 -22 -43 -27 }}
+: Mapping generators: ~2, ~10/9
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~10/9 = 186.343
+{{Optimal ET sequence|legend=1| 45, 58, 103, 161, 586b, 747bc, 908bbc }}
+[[Badness]]: 0.125672
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 43923/43750
+Mapping: {{mapping| 1 5 9 7 12 | 0 -22 -43 -27 -55 }}
+Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.345
+Optimal ET sequence: {{Optimal ET sequence| 58, 103, 161, 425b, 586b, 747bc }}
+Badness: 0.039962
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 351/350, 441/440, 847/845
+Mapping: {{mapping| 1 5 9 7 12 11 | 0 -22 -43 -27 -55 -47 }}
+Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.347
+Optimal ET sequence: {{Optimal ET sequence| 58, 103, 161, 425b, 586bf }}
+Badness: 0.021849
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 243/242, 351/350, 441/440, 561/560, 847/845
+Mapping: {{mapping| 1 5 9 7 12 11 3 | 0 -22 -43 -27 -55 -47 7 }}
+Optimal tuning (POTE): ~2 = 1\1, ~10/9 = 186.348
+Optimal ET sequence: {{Optimal ET sequence| 58, 103, 161, 425b, 586bf }}
+Badness: 0.020295
+== Catafourth ==
+{{See also| Sensipent family }}
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 78732/78125
+{{Mapping|legend=1| 1 13 17 13 | 0 -28 -36 -25 }}
+: Mapping generators: ~2, ~250/189
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~250/189 = 489.235
+{{Optimal ET sequence|legend=1| 27, 76, 103, 130 }}
+Badness: 0.079579
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 78408/78125
+Mapping: {{mapping| 1 13 17 13 32 | 0 -28 -36 -25 -70 }}
+Optimal tuning (POTE): ~2 = 1\1, ~250/189 = 489.252
+Optimal ET sequence: {{Optimal ET sequence| 103, 130, 233, 363, 493e, 856be }}
+Badness: 0.036785
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 243/242, 351/350, 441/440, 10985/10976
+Mapping: {{mapping| 1 13 17 13 32 9 | 0 -28 -36 -25 -70 -13 }}
+Optimal tuning (POTE): ~2 = 1\1, ~65/49 = 489.256
+Optimal ET sequence: {{Optimal ET sequence| 103, 130, 233, 363 }}
+Badness: 0.021694
+== Cotritone ==
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 390625/387072
+{{Mapping|legend=1| 1 17 9 10 | 0 -30 -13 -14 }}
+: Mappping generators: ~2, ~10/7
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 583.385
+{{Optimal ET sequence|legend=1| 35, 37, 72, 109, 181, 253 }}
+[[Badness]]: 0.098322
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 385/384, 1375/1372, 4000/3993
+Mapping: {{mapping| 1 17 9 10 5 | 0 -30 -13 -14 -3 }}
+Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 583.387
+Optimal ET sequence: {{Optimal ET sequence| 35, 37, 72, 109, 181, 253 }}
+Badness: 0.032225
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 169/168, 364/363, 385/384, 625/624
+Mapping: {{mapping| 1 17 9 10 5 15 | 0 -30 -13 -14 -3 -22 }}
+Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 583.387
+Optimal ET sequence: {{Optimal ET sequence| 37, 72, 109, 181f }}
+Badness: 0.028683
+== Quasimoha ==
+: ''For the 5-limit version of this temperament, see [[High badness temperaments #Quasimoha]].''
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 3645/3584
+{{Mapping|legend=1| 1 1 9 6 | 0 2 -23 -11 }}
+: Mapping generators: ~2, ~49/40
+[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 348.603
+{{Optimal ET sequence|legend=1| 31, 117c, 148bc, 179bc }}
+[[Badness]]: 0.110820
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 243/242, 441/440, 1815/1792
+Mapping: {{mapping| 1 1 9 6 2 | 0 2 -23 -11 5 }}
+Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.639
+Optimal ET sequence: {{Optimal ET sequence| 31, 86ce, 117ce, 148bce }}
+Badness: 0.046181
+== Lockerbie ==
+: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Lockerbie]].''
+Lockerbie can be described as the {{nowrap| 103 & 270 }} temperament. Its generator is [[120/77]] or [[77/60]]. An obvious tuning is given by 270edo, but [[373edo]] and especially [[643edo]] work as well.
+The temperament derives its name from the {{w|Lockerbie|Scottish town}}, where a {{w|Pan Am Flight 103|flight numbered 103}} crashed with 270 casualties, and the temperament is defined as 103 & 270, hence the name. The name is proposed by Eliora, who favours it due to simplicity, ease of pronunciation and relation to numbers 103 and 270.
+Lockerbie also has a unique extension that adds the 41st harmonic such that the generator below 600 cents is also on the same step in 103 or 270 as [[41/32]], which means that [[616/615]] is tempered out.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, {{monzo| 24 13 -18 -1 }}
+{{Mapping|legend=1| 1 -25 -16 -13 | 0 74 51 44 }}
+: Mapping generators: ~2, ~3828125/2985984
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.0000, ~3828125/2985984 = 431.1071
+: [[error map]]: {{val| 0.0000 -0.0270 +0.1502 -0.1120 }}
+* [[CWE]]: ~2 = 1200.0000, ~3828125/2985984 = 431.1072
+: error map: {{val| 0.0000 -0.0205 +0.1547 -0.1081 }}
+{{Optimal ET sequence|legend=1| 103, 167, 270, 643, 913 }}
+[[Badness]] (Smith): 0.0597
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 3025/3024, 766656/765625
+Mapping: {{mapping| 1 -25 -16 -13 -26 | 0 74 51 44 82 }}
+Optimal tunings:
+* CTE: ~2 = 1200.0000, ~77/60 = 431.1082
+* CWE: ~2 = 1200.0000, ~77/60 = 431.1078
+{{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913, 1183e }}
+Badness (Smith): 0.0262
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 1001/1000, 1716/1715, 3025/3024, 4225/4224
+Mapping: {{mapping| 1 -25 -16 -13 -26 -6 | 0 74 51 44 82 27 }}
+Optimal tunings:
+* CTE: ~2 = 1200.0000, ~77/60 = 431.1085
+* CWE: ~2 = 1200.0000, ~77/60 = 431.1069
+{{Optimal ET sequence|legend=0| 103, 167, 270, 643, 913f }}
+Badness (Smith): 0.0160
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224
+Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 | 0 74 51 44 82 27 42 }}
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~77/60 = 431.107
+* CWE: ~2 = 1200.000, ~77/60 = 431.108
+{{Optimal ET sequence|legend=0| 103, 167, 270 }}
+Badness (Smith): 0.0210
+=== 2.3.5.7.11.13.17.41 subgroup ===
+Subgroup: 2.3.5.7.11.13.17.41
+Comma list: 616/615, 715/714, 936/935, 1001/1000, 1225/1224, 4225/4224
+Mapping: {{mapping| 1 -25 -16 -13 -26 -6 -11 5 | 0 74 51 44 82 27 42 1 }}
+Optimal tunings:
+* CTE: ~2 = 1200.000, ~41/32 = 431.107
+* CWE: ~2 = 1200.000, ~41/32 = 431.111
+{{Optimal ET sequence|legend=0| 103, 167, 270 }}
+== Hemigoldis ==
+: ''For the 5-limit version, see [[Diaschismic–gothmic equivalence continuum #Goldis]].''
+Though fairly complex in the [[7-limit]], hemigoldis does a lot better in badness metrics than pure 5-limit goldis, and yet again has many possible extensions to other primes. For example, two periods minus six generators yields a "tetracot second" which can be interpreted as ~[[21/19]] to add prime 19 or perhaps more accurately ~[[31/28]] to add prime 7, or even simply as ~[[32/29]] to add prime 29, though the other two have the benefit of clearly connecting to the 7-limit representation. Note that again [[89edo]] is a possible tuning for combining it with flat nestoria and not appearing in the optimal ET sequence.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, 549755813888/533935546875
+{{Mapping|legend=1| 1 21 -9 2 | 0 -24 14 1 }}
+: mapping generators: ~2, ~7/4
+[[Optimal tuning]] ([[CWE]]): ~2 = 1200.000, ~7/4 = 970.690
+{{Optimal ET sequence|legend=1| 21, 47b, 68, 157, 382bccd, 529bccd }}
+[[Badness]] (Sintel): 4.40
+== Surmarvelpyth ==
+''Surmarvelpyth'' is named for the generator fifth, 675/448 being 225/224 (marvel comma) sharp of 3/2. It can be described as the 311 & 431 temperament, starting with the 7-limit to the 19-limit.
+[[Subgroup]]: 2.3.5.7
+[[Comma list]]: 2401/2400, {{monzo| 93 -32 -17 -1 }}
+{{Mapping|legend=1| 1 43 -74 -25 | 0 -70 129 47 }}
+: Mapping generators: ~2, ~675/448
+[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~675/448 = 709.9719
+{{Optimal ET sequence|legend=1| 120, 191, 311, 742, 1053, 2848, 3901 }}
+[[Badness]]: 0.202249
+=== 11-limit ===
+Subgroup: 2.3.5.7.11
+Comma list: 2401/2400, 820125/819896, 2097152/2096325
+Mapping: {{mapping| 1 43 -74 -25 36 | 0 -70 129 47 -55 }}
+Optimal tuning (CTE): ~2 = 1\1, ~675/448 = 709.9720
+Optimal ET sequence: {{Optimal ET sequence| 120, 191, 311, 742, 1053, 1795 }}
+Badness: 0.052308
+=== 13-limit ===
+Subgroup: 2.3.5.7.11.13
+Comma list: 2401/2400, 4096/4095, 6656/6655, 24192/24167
+Mapping: {{mapping| 1 43 -74 -25 36 25 | 0 -70 129 47 -55 -36 }}
+Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9723
+Optimal ET sequence: {{Optimal ET sequence| 120, 191, 311, 742, 1053, 1795f }}
+Badness: 0.032503
+=== 17-limit ===
+Subgroup: 2.3.5.7.11.13.17
+Comma list: 2401/2400, 2601/2600, 4096/4095, 6656/6655, 8624/8619
+Mapping: {{mapping| 1 43 -74 -25 36 25 -103 | 0 -70 129 47 -55 -36 181 }}
+Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9722
+Optimal ET sequence: {{Optimal ET sequence| 120g, 191g, 311, 431, 742, 1795f }}
+Badness: 0.020995
+=== 19-limit ===
+Subgroup: 2.3.5.7.11.13.17.19
+Comma list: 2401/2400, 2601/2600, 2926/2925, 3136/3135, 3213/3211, 5985/5984
+Mapping: {{mapping| 1 43 -74 -25 36 25 -103 -49 | 0 -70 129 47 -55 -36 181 90 }}
+Optimal tuning (CTE): ~2 = 1\1, ~98/65 = 709.9722
+Optimal ET sequence: {{Optimal ET sequence| 120g, 191g, 311, 431, 742, 1795f }}
+Badness: 0.013771
+== Notes ==
+[[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]
+[[Category:Breedsmic temperaments| ]] <!-- main article -->
+[[Category:Breed| ]] <!-- key article -->
+[[Category:Rank 2]]

Breedsmic temperaments: Difference between revisions