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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]] [[regular temperament|temperaments]] [[tempering out]] [[225/224]], the marvel comma or septimal kleisma.  
: This revision was by author [[User:Gedankenwelt|Gedankenwelt]] and made on <tt>2013-07-10 19:16:54 UTC</tt>.<br>
: The original revision id was <tt>441020614</tt>.<br>
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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">[[toc]]
This page discusses some of the temperaments tempering out |-5 2 2 -1&gt; =[[225_224| 225/224]], the [[Marvel family|marvel]] comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are [[Meantone family|meantone]], [[Miracle|miracle]], [[Magic family|magic]], [[Pajara|pajara]], [[Orwell|orwell]], [[Kleismic family|catakleismic]], [[Garibaldi temperament|garibaldi]], [[Augmented family|august]], [[Pythagorean family|compton]], [[Dicot family|sharp]], [[Escapade family|escapade]] and [[Pelogic family|mavila]].


Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.
Temperaments considered in families and clans are:
* ''[[Pelogic]]'' (+21/20 or 135/128) → [[Mavila family #Pelogic|Mavila family]]
* [[Meantone]] (+81/80 or 126/125) → [[Meantone family #Septimal meantone|Meantone family]]
* [[Garibaldi]] (+3125/3087) → [[Schismatic family #Garibaldi|Schismatic family]]
* [[Pajara]] (+50/49 or 64/63) → [[Diaschismic family #Pajara|Diaschismic family]]
* ''[[Sharpie]]'' (+25/24 or 28/27) → [[Dicot family #Sharpie|Dicot family]]
* ''[[Immune]]'' (+781250/750141) → [[Immunity family #Immune|Immunity family]]
* ''[[August]]'' (+36/35 or 128/125) → [[Augmented family #August|Augmented family]]
* ''[[Fog]]'' (+156250/151263) → [[Misty family #Fog|Misty family]]
* [[Bunya]] (+15625/15309) → [[Tetracot family #Bunya|Tetracot family]]
* [[Negri]] (+49/48) → [[Semaphoresmic clan #Negri|Semaphoresmic clan]]
* [[Magic]] (+245/243) → [[Magic family #Magic|Magic family]]
* ''[[Passive]]'' (+256/245) → [[Passion family #Passive|Passion family]]
* ''[[Quintapole]]'' (+7812500/7411887) → [[Quintaleap family #Quintapole|Quintaleap family]]
* ''[[Houborizic]]'' (+1250000/1240029) → [[Amity family #Houborizic|Amity family]]
* ''[[Qintosec]]'' (+2560000/2470629) → [[Quintosec family #Qintosec|Quintosec family]]
* [[Miracle]] (+1029/1024) → [[Gamelismic clan #Miracle|Gamelismic clan]]
* [[Catakleismic]] (+4375/4374) → [[Kleismic family #Catakleismic|Kleismic family]]
* ''[[Marvo]]'' (+78125000/78121827) → [[Gravity family #Marvo|Gravity family]]
* [[Orwell]] (+1728/1715) → [[Semicomma family #Orwell|Semicomma family]]
* ''[[Snipes]]'' (+6125/5832)  → [[Wesley family #Snipes|Wesley family]]
* ''[[Demibuzzard]]'' (+65536/64827) → [[Buzzardsmic clan #Demibuzzard|Buzzardsmic clan]]
* ''[[Escapist]]'' (+65625/65536) → [[Escapade family #Escapist|Escapade family]]
* ''[[Decic]]'' (+16807/16384) → [[Cloudy clan #Decic|Cloudy clan]]
* ''[[Amavil]]'' (+17496/16807) → [[Mabila family #Amavil|Mabila family]]
* ''[[Betic]]'' (+1071875/1062882) → [[Sycamore family #Betic|Sycamore family]]
* ''[[Hendeca]]'' (+122880/117649) → [[11th-octave temperaments #Hendeca|11th-octave temperaments]]
* [[Compton]] (+250047/250000) → [[Compton family #Compton|Compton family]]
* ''[[Raccoon]]'' (+41943040/40353607) → [[Vavoom family #Raccoon|Vavoom family]]
* ''[[Maquila]]'' (+30233088/28824005) → [[Maquila family #Septimal maquila|Maquila family]]
* ''[[Gammy]]'' (+94143178827/91913281250) → [[Gammic family #Gammy|Gammic family]]
 
Considered below are wizard, tritonic, septimin, merman, slender, triton, marvolo, enneaportent, gracecordial, alphorn, misneb, untriton, naiadical, quintannic, gwazy, and tertiosec, in the order of increasing [[badness]].
 
Since {{nowrap|(5/4)<sup>2</sup> {{=}} (225/224)⋅(14/9)}}, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.


The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.
The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.


Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.)
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is {{nowrap|(16/9)/(5/4) {{=}} 64/45}}. Setting this equal to 10/7 gives {{nowrap|(10/7)/(64/45) {{=}} 225/224}}.)
 
== Wizard ==
{{Main| Wizard }}
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Wizard]].''
 
Wizard has a [[semi-octave]] period and is generated by an interval that can be treated as [[~]][[17/15]]. The semi-octave complement of this interval is ~[[5/4]]. Wizard can be described as {{nowrap| 22 & 72 }}. Its [[ploidacot]] is diploid alpha-hexacot, so six generator steps plus a semi-octave period gives the [[3/1|perfect twelfth]]. [[72edo]], [[94edo]], and especially [[166edo]] are good tunings for it.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 118098/117649
 
{{Mapping|legend=1| 2 1 5 2 | 0 6 -1 10 }}
: mapping generators: ~1225/864, ~245/216
 
[[Optimal tuning]]s:
* [[WE]]: ~1225/864 = 600.3438{{c}}, ~245/216 = 216.8680{{c}}
: [[error map]]: {{val| +0.688 -0.403 -1.463 +0.541 }}
* [[CWE]]: ~1225/864 = 600.0000{{c}}, ~245/216 = 216.7977{{c}}
: error map: {{val| 0.000 -1.169 -3.111 -0.849 }}
 
{{Optimal ET sequence|legend=1| 22, 50, 72, 238c, 310c, 382c, 454bccd }}
 
[[Badness]] (Sintel): 1.03
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 4000/3993
 
Mapping: {{mapping| 2 1 5 2 8 | 0 6 -1 10 -3 }}
 
Optimal tunings:
* WE: ~99/70 = 600.3051{{c}}, ~25/22 = 216.8782{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.7961{{c}}
 
{{Optimal ET sequence|legend=0| 22, 50, 72, 166, 238c, 310c }}
 
Badness (Sintel): 0.613
 
==== Lizard ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 351/350, 364/363, 385/384
 
Mapping: {{mapping| 2 1 5 2 8 11 | 0 6 -1 10 -3 -10 }}
 
Optimal tunings:
* WE: ~55/39 = 600.4824{{c}}, ~25/22 = 216.7852{{c}}
* CWE: ~55/39 = 600.0000{{c}}, ~25/22 = 216.6247{{c}}
 
{{Optimal ET sequence|legend=0| 22, 50, 72 }}
 
Badness (Sintel): 0.900
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 221/220, 273/272, 289/288, 351/350, 375/374
 
Mapping: {{mapping| 2 1 5 2 8 11 6 | 0 6 -1 10 -3 -10 6 }}
 
Optimal tunings:
* WE: ~17/12 = 600.5032{{c}}, ~17/15 = 216.8002{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.6361{{c}}
 
{{Optimal ET sequence|legend=0| 22, 50, 72 }}
 
Badness (Sintel): 0.741
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342
 
Mapping: {{mapping| 2 1 5 2 8 11 6 2 | 0 6 -1 10 -3 -10 6 18 }}
 
Optimal tunings:
* WE: ~17/12 = 600.4698{{c}}, ~17/15 = 216.6925{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.5434{{c}}
 
{{Optimal ET sequence|legend=0| 22h, 50, 72, 122g, 194dfg }}
 
Badness (Sintel): 0.955
 
==== Gizzard ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 325/324, 385/384, 1573/1568
 
Mapping: {{mapping| 2 1 5 2 8 -2 | 0 6 -1 10 -3 26 }}
 
Optimal tunings:
* WE: ~99/70 = 600.2896{{c}}, ~25/22 = 216.9343{{c}}
* CWE: ~99/70 = 600.0000{{c}}, ~25/22 = 216.8501{{c}}
 
{{Optimal ET sequence|legend=0| 22f, 72, 166, 238cf }}
 
Badness (Sintel): 0.837
 
===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 289/288, 325/324, 375/374, 385/384
 
Mapping: {{mapping| 2 1 5 2 8 -2 6 | 0 6 -1 10 -3 26 6 }}
 
Optimal tunings:
* WE: ~17/12 = 600.3227{{c}}, ~17/15 = 216.9414{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8469{{c}}
 
{{Optimal ET sequence|legend=0| 22f, 72, 166g, 238cfg }}
 
Badness (Sintel): 0.694
 
===== 19-limit =====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 225/224, 325/324, 375/374, 385/384, 400/399, 595/594
 
Mapping: {{mapping| 2 1 5 2 8 -2 6 15 | 0 6 -1 10 -3 26 6 -18 }}
 
Optimal tunings:
* WE: ~17/12 = 600.2637{{c}}, ~17/15 = 216.9570{{c}}
* CWE: ~17/12 = 600.0000{{c}}, ~17/15 = 216.8687{{c}}
 
{{Optimal ET sequence|legend=0| 72, 94, 166g }}
 
Badness (Sintel): 0.901
 
=== Mage ===
Subgroup: 2.3.5.7.11
 
Comma list: 99/98, 176/175, 1331/1296
 
Mapping: {{mapping| 2 1 5 2 4 | 0 6 -1 10 8 }}
 
Optimal tunings:
* WE: ~77/54 = 600.6486{{c}}, ~55/48 = 217.1099{{c}}
* CWE: ~77/54 = 600.0000{{c}}, ~55/48 = 216.9841{{c}}
 
{{Optimal ET sequence|legend=0| 22, 50e, 72ee }}
 
Badness (Sintel): 1.91
 
== Tritonic ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritonic]].''
 
Tritonic tempers out [[50421/50000]] and may be described as the {{nowrap| 29 & 31 }} temperament. It splits the [[6/1|6th]] [[harmonic]] into five generators of [[~]][[10/7]] [[tritone]]s, hence the name. Its [[ploidacot]] is beta-pentacot. [[60edo]] may be used as a tuning, which in the 11-limit entails the 60e val.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 50421/50000
 
{{Mapping|legend=1| 1 -1 8 9 | 0 5 -11 -12 }}
: mapping generators: ~2, ~10/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.3539{{c}}, ~10/7 = 620.4131{{c}}
: [[error map]]: {{val| +1.354 -1.243 -0.027 -1.598 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 619.6778{{c}}
: error map: {{val| 0.000 -3.566 -2.769 -4.959 }}
 
{{Optimal ET sequence|legend=1| 29, 31, 60, 91, 122, 213bcd }}
 
[[Badness]] (Sintel): 1.20
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 121/120, 225/224, 441/440
 
Mapping: {{mapping| 1 -1 8 9 5 | 0 5 -11 -12 -3 }}
 
Optimal tunings:
* WE: ~2 = 1201.7116{{c}}, ~10/7 = 620.6166{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6890{{c}}
 
{{Optimal ET sequence|legend=0| 29, 31, 60e, 91e, 213bcdeee }}
 
Badness (Sintel): 0.782
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 121/120, 196/195, 275/273
 
Mapping: {{mapping| 1 -1 8 9 5 13 | 0 5 -11 -12 -3 -18 }}
 
Optimal tunings:
* WE: ~2 = 1201.5355{{c}}, ~10/7 = 620.6855{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8469{{c}}
 
{{Optimal ET sequence|legend=0| 29, 31, 60e }}
 
Badness (Sintel): 0.950
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 105/104, 121/120, 154/153, 196/195, 273/272
 
Mapping: {{mapping| 1 -1 8 9 5 13 17 | 0 5 -11 -12 -3 -18 -25 }}
 
Optimal tunings:
* WE: ~2 = 1201.5260{{c}}, ~10/7 = 620.7330{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.8986{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
 
Badness (Sintel): 0.973
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 77/76, 105/104, 121/120, 153/152, 196/195, 273/272
 
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 | 0 5 -11 -12 -3 -18 -25 -15 }}
 
Optimal tunings:
* WE: ~2 = 1201.3100{{c}}, ~10/7 = 620.6509{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9328{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
 
Badness (Sintel): 1.03
 
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 77/76, 105/104, 115/114, 121/120, 153/152, 161/160, 196/195
 
Mapping: {{mapping| 1 -1 8 9 5 13 17 12 4 | 0 5 -11 -12 -3 -18 -25 -15 1 }}
 
Optimal tunings:
* WE: ~2 = 1201.4074{{c}}, ~10/7 = 620.7185{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.9548{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 31, 60e }}
 
Badness (Sintel): 1.04
 
=== Tritoni ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 27783/27500
 
Mapping: {{mapping| 1 -1 8 9 -11 | 0 5 -11 -12 28 }}
 
Optimal tunings:
* WE: ~2 = 1201.0888{{c}}, ~10/7 = 620.1733{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 619.6146{{c}}
 
{{Optimal ET sequence|legend=0| 31, 91, 122, 153d }}
 
Badness (Sintel): 1.50
 
== Septimin ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Septimin]].''
 
Septimin may be described as the {{nowrap| 41 & 50 }} temperament. It is generated by a septimal minor third ([[7/6]]), which gives rise to the name, but the generator can be taken to be the [[octave complement]], [[12/7]], such that eleven of them [[octave reduction|octave reduced]] give the [[3/2|perfect fifth]]; its [[ploidacot]] is thus eta-hendecacot. [[91edo]] may be recommended as a tuning.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 84035/82944
 
{{Mapping|legend=1| 1 -7 7 -5 | 0 11 -6 10 }}
: mapping generators: ~2, ~12/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.2452{{c}}, ~12/7 = 937.3394{{c}}
: [[error map]]: {{val| +1.245 +0.062 -1.633 -1.658 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~12/7 = 936.4036{{c}}
: error map: {{val| 0.000 -1.516 -4.735 -4.790 }}
 
{{Optimal ET sequence|legend=1| 41, 91, 132d }}
 
[[Badness]] (Sintel): 1.38
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 245/242, 385/384
 
Mapping: {{mapping| 1 -7 7 -5 -2 | 0 11 -6 10 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.8059{{c}}, ~12/7 = 936.9952{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3906{{c}}
 
{{Optimal ET sequence|legend=0| 41, 91, 223cdef }}
 
Badness (Sintel): 1.04
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 105/104, 144/143, 196/195, 245/242
 
Mapping: {{mapping| 1 -7 7 -5 -2 -8 | 0 11 -6 10 7 15 }}
 
Optimal tunings:
* WE: ~2 = 1200.5990{{c}}, ~12/7 = 936.7670{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~12/7 = 936.3196{{c}}
 
{{Optimal ET sequence|legend=0| 41, 91 }}
 
Badness (Sintel): 0.955
 
== Merman ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Merman]].''
 
Merman may be described as the {{nowrap| 41 & 43 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, seven generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is gamma-heptacot.
 
The name was likely derived from {{w|Triton (mythology)|''Triton''}}, which was in turn derived from ''tritonic''.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 2500000/2470629
 
{{Mapping|legend=1| 1 -2 10 11 | 0 7 -15 -16 }}
: mapping generators: ~2, ~10/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3898{{c}}, ~10/7 = 614.6413{{c}}
: [[error map]]: {{val| +0.390 -0.435 -1.630 +1.634 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 614.4073{{c}}
: error map: {{val| 0.000 -1.104 -2.423 +0.657 }}
 
{{Optimal ET sequence|legend=1| 41, 84, 125 }}
 
[[Badness]] (Sintel): 1.39
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 1344/1331
 
Mapping: {{mapping| 1 -2 10 11 5 | 0 7 -15 -16 -3 }}
 
Optimal tunings:
* WE: ~2 = 1199.9578{{c}}, ~10/7 = 614.3720{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3943{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84, 125e }}
 
Badness (Sintel): 1.20
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 144/143, 225/224, 364/363, 441/440
 
Mapping: {{mapping| 1 -2 10 11 5 -5 | 0 7 -15 -16 -3 17 }}
 
Optimal tunings:
* WE: ~2 = 1199.7422{{c}}, ~10/7 = 614.2110{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.3442{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84, 125e, 209ef, 293ef }}
 
Badness (Sintel): 1.14
 
=== Mermaid ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 532400/531441
 
Mapping: {{mapping| 1 -2 10 11 -16 | 0 7 -15 -16 38 }}
 
Optimal tunings:
* WE: ~2 = 1199.4973{{c}}, ~10/7 = 614.7004{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4470{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84e, 125, 166 }}
 
Badness (Sintel): 1.46
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 325/324, 385/384, 10648/10647
 
Mapping: {{mapping| 1 -2 10 11 22 32 | 0 7 -15 -16 38 58 }}
 
Optimal tunings:
* WE: ~2 = 1200.5126{{c}}, ~10/7 = 614.7152{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 614.4562{{c}}
 
{{Optimal ET sequence|legend=0| 41, 84ef, 125f, 166 }}
 
Badness (Sintel): 1.47
 
== Slender ==
Slender tempers out the [[hewuermera comma]] in addition to the marvel comma, and may be described as the {{nowrap| 31 & 32 }} temperament. This temperament has a generator of [[49/48]], three of which equal marvel's [[16/15]][[~]][[15/14]], and ten generators give [[5/4]]. Its [[ploidacot]] is omega-13-cot.
 
The name was likely derived from ''slendro diesis'', one of the names for the interval 49/48.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 589824/588245
 
{{Mapping|legend=1| 1 2 2 3 | 0 -13 10 -6 }}
: mapping generators: ~2, ~49/48
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.3816{{c}}, ~49/48 = 38.4256{{c}}
: [[error map]]: {{val| +0.382 -0.725 -1.295 +1.765 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/48 = 38.4079{{c}}
: error map: {{val| 0.000 -1.257 -2.235 +0.727 }}
 
{{Optimal ET sequence|legend=1| 31, 94, 125, 406c }}
 
[[Badness]] (Sintel): 1.44
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 1331/1323
 
Mapping: {{mapping| 1 2 2 3 4 | 0 -13 10 -6 -17 }}
 
Optimal tunings:
* WE: ~2 = 1199.4983{{c}}, ~49/48 = 38.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3775{{c}}
 
{{Optimal ET sequence|legend=0| 31, 63, 94, 125 }}
 
Badness (Sintel): 0.838
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 275/273, 385/384, 1331/1323
 
Mapping: {{mapping| 1 2 2 3 4 3 | 0 -13 10 -6 -17 22 }}
 
Optimal tunings:
* WE: ~2 = 1200.1728{{c}}, ~49/48 = 38.3192{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~49/48 = 38.3129{{c}}
 
{{Optimal ET sequence|legend=0| 31, 63, 94 }}
 
Badness (Sintel): 1.07
 
== Triton ==
: ''For the 5-limit version, see [[Syntonic–kleismic equivalence continuum #Stump]].''
 
Triton may be described as the {{nowrap| 19 & 21 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, three generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is alpha-tricot.
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 1029/1000
 
{{Mapping|legend=1| 1 0 6 7 | 0 3 -7 -8 }}
: mapping generators: ~2, ~10/7
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1203.3828{{c}}, ~10/7 = 632.9137{{c}}
: [[error map]]: {{val| +3.383 -3.214 +3.587 -8.457 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 630.9827{{c}}
: error map: {{val| 0.000 -9.007 -3.192 -16.687 }}
 
{{Optimal ET sequence|legend=1| 2, 17d, 19, 78bd, 97bd }}
 
[[Badness]] (Sintel): 1.50
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 45/44, 56/55, 1029/1000
 
Mapping: {{mapping| 1 0 6 7 4 | 0 3 -7 -8 -1 }}
 
Optimal tunings:
* WE: ~2 = 1201.3875{{c}}, ~10/7 = 631.5852{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 630.8007{{c}}
 
{{Optimal ET sequence|legend=0| 2, 17d, 19 }}
 
Badness (Sintel): 1.51
 
== Marvolo ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 156250000/155649627
 
{{Mapping|legend=1| 1 2 1 1 | 0 -6 19 26 }}
: mapping generators: ~2, ~21/20
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.7714{{c}}, ~21/20 = 83.4014{{c}}
: [[error map]]: {{val| +0.772 -0.820 -0.916 +0.381 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~21/20 = 83.3640{{c}}
: error map: {{val| 0.000 -2.139 -2.398 -1.362 }}
 
{{Optimal ET sequence|legend=1| 29, 43, 72, 619bbccd, 691bbccd }}
 
[[Badness]] (Sintel): 2.11
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 441/440, 4000/3993
 
Mapping: {{mapping| 1 2 1 1 2 | 0 -6 19 26 21 }}
 
Optimal tunings:
* WE: ~2 = 1200.7075{{c}}, ~21/20 = 83.3888{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3564{{c}}
 
{{Optimal ET sequence|legend=0| 29, 43, 72 }}
 
Badness (Sintel): 0.958
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 225/224, 364/363, 441/440
 
Mapping: {{mapping| 1 2 1 1 2 3 | 0 -6 19 26 21 10 }}
 
Optimal tunings:
* WE: ~2 = 1200.9467{{c}}, ~21/20 = 83.3956{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3516{{c}}
 
{{Optimal ET sequence|legend=0| 29, 43, 72 }}
 
Badness (Sintel): 0.887
 
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 169/168, 221/220, 225/224, 364/363, 441/440
 
Mapping: {{mapping| 1 2 1 1 2 3 2 | 0 -6 19 26 21 10 30 }}
 
Optimal tunings:
* WE: ~2 = 1200.9606{{c}}, ~21/20 = 83.4030{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3594{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
 
Badness (Sintel): 0.760
 
=== 19-limit ===
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 169/168, 210/209, 221/220, 225/224, 364/363, 441/440
 
Mapping: {{mapping| 1 2 1 1 2 3 2 3 | 0 -6 19 26 21 10 30 18 }}
 
Optimal tunings:
* WE: ~2 = 1200.7625{{c}}, ~21/20 = 83.3895{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~21/20 = 83.3551{{c}}
 
{{Optimal ET sequence|legend=0| 29g, 43, 72 }}
 
Badness (Sintel): 0.895
 
== Enneaportent ==
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 40353607/40310784
 
{{Mapping|legend=1| 9 0 28 11 | 0 2 -1 2 }}
: mapping generators: ~2592/2401, ~12005/6912
 
[[Optimal tuning]]s:
* [[WE]]: ~2592/2401 = 133.4174{{c}}, ~12005/6912 = 950.7667{{c}} (~1728/1715 = 16.8452{{c}})
: [[error map]]: {{val| +0.756 -0.422 -1.395 +0.298 }}
* [[CWE]]: ~2592/2401 = 133.3333{{c}}, ~12005/6912 = 950.2969{{c}} (~1728/1715 = 16.9636{{c}})
: error map: {{val| 0.000 -1.361 -3.277 -1.565 }}
 
{{Optimal ET sequence|legend=1| 9, 54, 63, 72, 495bccd, 567bcccd }}
 
[[Badness]] (Sintel): 2.37
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 12005/11979
 
Mapping: {{mapping| 9 0 28 11 24 | 0 2 -1 2 1 }}
 
Optimal tunings:
* WE: ~121/112 = 133.4071{{c}}, ~210/121 = 950.7131{{c}} (~99/98 = 16.8633{{c}})
* CWE: ~121/112 = 133.3333{{c}}, ~210/121 = 950.2994{{c}} (~99/98 = 16.9661{{c}})
 
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
 
Badness (Sintel): 1.01
 
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
 
Comma list: 169/168, 225/224, 364/363, 1716/1715
 
Mapping: {{mapping| 9 0 28 11 24 19 | 0 2 -1 2 1 2 }}
 
Optimal tunings:
* WE: ~14/13 = 133.4245{{c}}, ~26/15 = 950.9362{{c}} (~105/104 = 16.9650{{c}})
* CWE: ~14/13 = 133.3333{{c}}, ~26/15 = 950.4364{{c}} (~99/98 = 17.1031{{c}})
 
{{Optimal ET sequence|legend=0| 9, 54, 63, 72 }}
 
Badness (Sintel): 0.922
 
== Gracecordial ==
: ''For the 5-limit version, see [[Schismic–Pythagorean equivalence continuum #Gracecordial (5-limit)]].''
 
[[Subgroup]]: 2.3.5.7
 
[[Comma list]]: 225/224, 781250000/771895089
 
{{Mapping|legend=1| 1 0 34 63 | 0 1 -20 -38 }}
: mapping generators: ~2, ~3
 
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1200.4904{{c}}, ~3/2 = 701.1103{{c}}
: [[error map]]: {{val| +0.490 -0.354 -1.655 +1.241 }}
* [[CWE]]: ~2 = 1200.3333{{c}}, ~3/2 = 700.8112{{c}}
: error map: {{val| 0.000 -1.144 -2.537 +0.349 }}
 
{{Optimal ET sequence|legend=1| 12, …, 113, 125, 238c, 363c }}
 
[[Badness]] (Sintel): 2.44
 
=== 11-limit ===
Subgroup: 2.3.5.7.11
 
Comma list: 225/224, 385/384, 236328125/234365481
 
Mapping: {{mapping| 1 0 34 63 -90 | 0 1 -20 -38 59 }}
 
Optimal tunings:
* WE: ~2 = 1200.5571{{c}}, ~3/2 = 701.1589{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8328{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 113, 125, 238c }}
 
Badness (Sintel): 2.96
 
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
 
Comma list: 225/224, 325/324, 385/384, 831875/830466
 
Mapping: {{mapping| 1 0 34 63 -90 -66 | 0 1 -20 -38 59 44 }}
 
Optimal tunings:
* WE: ~2 = 1200.6282{{c}}, ~3/2 = 701.2080{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8421{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
 
Badness (Sintel): 2.16
 
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17
 
Comma list: 225/224, 273/272, 325/324, 385/384, 4928/4913
 
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 | 0 1 -20 -38 59 44 7 }}
 
Optimal tunings:
* WE: ~2 = 1200.5058{{c}}, ~3/2 = 701.1360{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8414{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
 
Badness (Sintel): 1.96
 
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19
 
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 1445/1444
 
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 | 0 1 -20 -38 59 44 7 -3 }}
 
Optimal tunings:
* WE: ~2 = 1200.4418{{c}}, ~3/2 = 701.0999{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8425{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cf }}
 
Badness (Sintel): 1.71
 
==== 23-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23
 
Comma list: 225/224, 273/272, 324/323, 325/324, 385/384, 460/459, 529/528
 
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 | 0 1 -20 -38 59 44 7 -3 30 }}
 
Optimal tunings:
* WE: ~2 = 1200.4641{{c}}, ~3/2 = 701.1145{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8444{{c}}
 
{{Optimal ET sequence|legend=0| 12e, 113, 238cfi }}
 
Badness (Sintel): 1.57
 
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29
 
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 494/493


=Negri=
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 | 0 1 -20 -38 59 44 7 -3 30 34 }}
[[Comma]]s: 49/48, 225/224


[[POTE tuning|POTE temperament]]: ~15/14 = 125.608
Optimal tunings:  
* WE: ~2 = 1200.4400{{c}}, ~3/2 = 701.0986{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8428{{c}}


[[Map]]: [&lt;1 2 2 3|, &lt;0 -4 3 -2|]
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
[[Wedgie]]: &lt;&lt;4 -3 2 -14 -8 13||
EDOs: [[9edo|9]], [[10edo|10]], [[19edo|19]], [[86edo|86]]


==11-limit==
Badness (Sintel): 1.50
Commas: 45/44, 49/48, 56/55


[[POTE tuning|POTE generator]]: ~15/14 = 126.474
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


Map: [&lt;1 2 2 3 4|, &lt;0 -4 3 -2 -5|]
Comma list: 225/224, 273/272, 290/289, 324/323, 325/324, 385/384, 460/459, 465/464, 494/493
EDOs: 9, 10, 19
[[Badness]]: 0.0262


==13-limit==
Mapping: {{mapping| 1 0 34 63 -90 -66 -7 9 -43 -49 -79 | 0 1 -20 -38 59 44 7 -3 30 34 53 }}
Commas: 45/44, 49/48, 56/55, 78/77


[[POTE tuning|POTE generator]]: ~14/13 = 126.431
Optimal tunings:  
* WE: ~2 = 1200.4178{{c}}, ~3/2 = 701.0822{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8396{{c}}


Map: [&lt;1 2 2 3 4 4|, &lt;0 -4 3 -2 -5 -3|]
{{Optimal ET sequence|legend=0| 12e, 113, 125f, 238cfi }}
EDOs: 9, 10, 19


=Negril=
Badness (Sintel): 1.53
Commas: 49/48, 100/99, 225/224


POTE generator: ~15/14 = 124.767
=== Gracecord ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 2 2 3 2|, &lt;0 -4 3 -2 14|]
Comma list: 225/224, 441/440, 109375/107811
EDOs: 19, [[29edo|29]], [[48edo|48df]], [[77edo|77cdf]]
Badness: 0.0387


==13-limit==
Mapping: {{mapping| 1 0 34 63 89 | 0 1 -20 -38 -54 }}
Commas: 49/48, 65/64, 91/90, 875/858


POTE generator: ~15/14 = 124.716
Optimal tunings:  
* WE: ~2 = 1200.6064{{c}}, ~3/2 = 701.2398{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8718{{c}}


Map: [&lt;1 2 2 3 2 4|, &lt;0 -4 3 -2 14 -3|]
{{Optimal ET sequence|legend=0| 12, …, 101cd, 113 }}
EDOs: 9, 10, 19, 29, 48, 77
Badness: 0.0244


=Negric=
Badness (Sintel): 2.21
Commas: 33/32, 49/48, 77/75


POTE generator: ~15/14 = 127.039
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 2 2 3 3|, &lt;0 -4 3 -2 4|]
Comma list: 225/224, 364/363, 441/440, 6125/6084
EDOs: 9, 19, [[85edo|85]]
Badness: 0.0306


==13-limit==
Mapping: {{mapping| 1 0 34 63 89 113 | 0 1 -20 -38 -54 -69 }}
Commas: 33/32, 49/48, 65/64, 91/90


POTE generator: ~15/14 = 127.039
Optimal tunings:  
* WE: ~2 = 1200.6225{{c}}, ~3/2 = 701.2539{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8781{{c}}


Map: [&lt;1 2 2 3 3 4|, &lt;0 -4 3 -2 4 -3|]
{{Optimal ET sequence|legend=0| 12f, …, 101cdf, 113 }}
EDOs: 9, 19, 85
Badness: 0.0202


=Negroni=
Badness (Sintel): 1.83
Commas: 49/48, 55/54, 225/224


POTE generator: ~15/14 = 124.539
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


Map: [&lt;1 2 2 3 5|, &lt;0 -4 3 -2 -15|]
Comma list: 225/224, 364/363, 441/440, 595/594, 2000/1989
EDOs: 10, 19e, 29, 77cde
Badness: 0.0353


==13-limit==
Mapping: {{mapping| 1 0 34 63 89 113 -7 | 0 1 -20 -38 -54 -69 7 }}
Commas: 49/48, 55/54, 65/64, 91/90


POTE generator: ~15/14 = 124.545
Optimal tunings:  
* WE: ~2 = 1200.3308{{c}}, ~3/2 = 701.0632{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8654{{c}}


Map: [&lt;1 2 2 3 5 4|, &lt;0 -4 3 -2 -15 -3|]
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
EDOs: 10, 19e, 29, 77cdef
Badness: 0.0216


=Wizard=
Badness (Sintel): 1.87
Comma: 2197265625/2147483648


POTE generator: ~5/4 = 383.212
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


Map: [&lt;2 1 5|, &lt;0 6 -1|]
Comma list: 210/209, 225/224, 324/323, 364/363, 400/399, 665/663
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc
Badness: 0.3864


==7-limit==
Mapping: {{mapping| 1 0 34 63 89 113 -7 9 | 0 1 -20 -38 -54 -69 7 -3 }}
Commas: 225/224, 118098/117649


[[POTE tuning|POTE temperament]]: 383.256
Optimal tunings:  
* WE: ~2 = 1200.2658{{c}}, ~3/2 = 701.0213{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~3/2 = 700.8629{{c}}


Map: [&lt;2 1 5 2|, &lt;0 6 -1 10|]
{{Optimal ET sequence|legend=0| 12f, 101cdf, 113 }}
Wedgie: &lt;&lt;12 -2 20 -31 -2 52||
EDOs: [[22edo|22]], [[50edo|50]], [[72edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238c]], [[310edo|310c]], [[382edo|382c]]
Badness: 0.0408


==11-limit==
Badness (Sintel): 1.68
Commas: 225/224, 385/384, 4000/3993


[[POTE tuning|POTE temperament]]: 383.232
== Alphorn ==
[[Subgroup]]: 2.3.5.7


Map: [&lt;2 1 5 2 8|, &lt;0 6 -1 10 -3|]
[[Comma list]]: 225/224, 5764801/5668704
EDOs: 22, 50, 72, 94, [[166edo|166]], [[238edo|238c]], [[310edo|310c]]
Badness: 0.0185


==Lizard==
{{Mapping|legend=1| 1 -7 5 -9 | 0 16 -5 22 }}
Commas: 225/224, 351/350, 364/363, 385/384
: mapping generators: ~2, ~35/24


[[POTE tuning|POTE temperament]]: 383.389
[[Optimal tuning]]s:
* [[WE]]: ~2 = 1201.3004{{c}}, ~35/24 = 644.4767{{c}}
: [[error map]]: {{val| +1.300 +0.569 -2.195 -2.043 }}
* [[CWE]]: ~2 = 1200.3333{{c}}, ~35/24 = 643.8137{{c}}
: error map: {{val| 0.000 -0.936 -5.382 -4.924 }}


Map: [&lt;2 1 5 2 8 11|, &lt;0 6 -1 10 -3 -10|]
{{Optimal ET sequence|legend=1| 13d, 28d, 41, 151cd, 192cdd, 233ccdd }}
EDOs: 22, 50, 72, 122, 194df
Badness: 0.0218


===17-limit===
[[Badness]] (Sintel): 3.27
Commas: 221/220, 273/272, 289/288, 351/350, 375/374


[[POTE tuning|POTE temperament]]: 383.381
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;2 1 5 2 8 11 6|, &lt;0 6 -1 10 -3 -10 6|]
Comma list: 225/224, 385/384, 12250/11979
EDOs: 22, 50, 72, 122g, 194dfg
Badness: 0.0145


===19-limit===
Mapping: {{mapping| 1 -7 5 -9 4 | 0 16 -5 22 -1 }}
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342


[[POTE tuning|POTE generator]]: ~5/4 = 383.477
Optimal tunings:  
* WE: ~2 = 1200.5123{{c}}, ~16/11 = 644.1307{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~16/11 = 643.8662{{c}}


Map: [&lt;2 1 5 2 8 11 6 2|, &lt;0 6 -1 10 -3 -10 6 18|]
{{Optimal ET sequence|legend=0| 13d, 28d, 41 }}
EDOs: 22h, 50, 72, [[122edo|122g]], [[194edo|194dfg]]
Badness: 0.0157


==Gizzard==
Badness (Sintel): 2.43
Commas: 225/224, 385/384, 325/324, 1573/1568


POTE generator: ~5/4 = 383.170
== Misneb ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Misneb]].''


Map: [&lt;2 1 5 2 8 -2|, &lt;0 6 -1 10 -3 26|]
[[Subgroup]]: 2.3.5.7
EDOs: [[22edo|22]], [[26edo|72]], [[94edo|94]], [[166edo|166]], [[238edo|238cf]]
Badness: 0.0203


===17-limit===
[[Comma list]]: 225/224, 4194304/4117715
Commas: 225/224, 289/288, 325/324, 375/374, 385/384


POTE generator: ~5/4 = 383.175
{{Mapping|legend=1| 1 -12 15 1 | 0 15 -14 2 }}
: mapping generators: ~2, ~15/8


Map: [&lt;2 1 5 2 8 -2 6|, &lt;0 6 -1 10 -3 26 6|]
[[Optimal tuning]]s:  
EDOs: 22f, 72, 94, [[166edo|166g]], [[238edo|238cfg]]
* [[WE]]: ~2 = 1199.7642{{c}}, ~15/8 = 1086.5513{{c}}
Badness: 0.0136
: [[error map]]: {{val| -0.236 -0.856 -1.569 +4.041 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~15/8 = 1086.7633{{c}}
: error map: {{val| 0.000 -0.506 -0.999 +4.701 }}


===19-limit===
{{Optimal ET sequence|legend=1| 21, 32, 53 }}
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399


POTE generator: ~5/4 = 383.138
[[Badness]] (Sintel): 3.57


Map: [&lt;2 1 5 2 8 -2 6 15|, &lt;0 6 -1 10 -3 26 6 -18|]
=== 11-limit ===
EDOs: 22f, 72, 94, 166g
Subgroup: 2.3.5.7.11
Badness: 0.0148


==Mage==
Comma list: 99/98, 176/175, 1310720/1294139
Commas: 99/98, 176/175, 1331/1296


POTE generator: ~55/48 = 216.876
Mapping: {{mapping| 1 -12 15 1 27 | 0 15 -14 2 -26 }}


Map: [&lt;2 1 5 2 4|, &lt;0 6 -1 10 8|]
Optimal tunings:  
EDOs: 22, 72e, 94e
* WE: ~2 = 1200.1654{{c}}, ~15/8 = 1086.8269{{c}}
Badness: 0.0578
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6766{{c}}


=Triton=
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
Commas: 225/224, 1029/1000


[[POTE tuning|POTE temperament]]: ~7/5 = 568.865
Badness (Sintel): 2.82


Map: [&lt;1 0 6 7|, &lt;0 3 -7 -8|]
==== 13-limit ====
Wedgie: &lt;&lt;3 -7 -8 -18 -21 1||
Subgroup: 2.3.5.7.11.13
EDOs: 17d, 19, 78bd, 97bd
Badness: 0.0592


==11-limit==
Comma list: 99/98, 176/175, 640/637, 847/845
Commas: 45/44, 56/55, 1029/1000


POTE generator: ~7/5 = 569.144
Mapping: {{mapping| 1 -12 15 1 27 20 | 0 15 -14 2 -26 -18 }}


Map: [&lt;1 0 6 7 4|, &lt;0 3 -7 -8 -1|]
Optimal tunings:  
EDOs: 19, 59bde, 78bde, 97bde
* WE: ~2 = 1200.1687{{c}}, ~15/8 = 1086.8295{{c}}
Badness: 0.0457
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.6757{{c}}


=Tritonic=
{{Optimal ET sequence|legend=0| 21, 32e, 53, 127 }}
Comnma: 553584375/536870912


POTE generator: ~45/32 = 580.219
Badness (Sintel): 1.88


Map: [&lt;1 4 -3|, &lt;0 -5 11|]
=== Musneb ===
EDOs: 29, 31, 60, 91
Subgroup: 2.3.5.7.11
Badness: 0.3785


==7-limit==
Comma list: 225/224, 385/384, 66550/64827
Commas: 225/224, 50421/50000


[[POTE tuning|POTE temperament]]: 580.286
Mapping: {{mapping| 1 3 1 3 6 | 0 -15 14 -2 -27 }}


Map: [&lt;1 4 -3 -3|, &lt;0 -5 11 12|]
Optimal tunings:  
Wedgie: &lt;&lt;5 -11 -12 -29 -33 3||
* WE: ~2 = 1200.0839{{c}}, ~15/8 = 1086.9343{{c}}
EDOs: [[29edo|29]], [[31edo|31]], [[60edo|60]], [[91edo|91]], [[122edo|122]], 213bcd
* CWE: ~2 = 1200.0000{{c}}, ~15/8 = 1086.8593{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 21e, 32, 53 }}
Commas: 121/120, 225/224, 441/440


[[POTE tuning|POTE generator]]: ~7/5 = 580.267
Badness (Sintel): 2.89


Map: [&lt;1 4 -3 -3 2|, &lt;0 -5 11 12 3|]
== Untriton ==
EDOs: 29, 31, 60e
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Untriton]].''
Badness: 0.0237


==13-limit==
Named by [[Petr Pařízek]] in 2011<ref name="petr's long post">[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_101780.html Yahoo! Tuning Group | ''Suggested names for the unclasified temperaments'']</ref>, untriton may be described as the {{nowrap| 51 & 53 }} temperament. Like [[#Tritonic|tritonic]], it is generated by a [[~]][[10/7]] [[tritone]], but here, nine generator steps give the [[interval class]] of [[3/1|3]]. The [[ploidacot]] for this temperament is delta-enneacot.
Commas: 105/104, 121/120, 196/195, 275/273


POTE generator: ~7/5 = 580.108
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 4 -3 -3 2 -5|, &lt;0 -5 11 12 3 18|]
[[Comma list]]: 225/224, 125000000/121060821
EDOs: 29, 31, 60e, 151cde
Badness: 0.0230


==Tritoni==
{{Mapping|legend=1| 1 -3 12 13 | 0 9 -19 -20 }}
Commas: 225/224, 385/384, 27783/27500
: mapping generators: ~2, ~10/7


POTE generator: ~7/5 = 580.389
[[Optimal tuning]]s:  
* [[WE]]: ~2 = 1199.8275{{c}}, ~10/7 = 611.2710{{c}}
: [[error map]]: {{val| -0.172 +0.002 -2.533 +3.511 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10/7 = 611.3614{{c}}
: error map: {{val| 0.000 +0.298 -2.181 +3.946 }}


Map: [&lt;1 4 -3 -3 17|, &lt;0 -5 11 12 -28|]
{{Optimal ET sequence|legend=1| 51, 53 }}
EDOs: 31, 91, 122
Badness: 0.0455


=Merman=
[[Badness]] (Sintel): 3.64
Comma: 1121008359375/1099511627776


POTE generator: ~45/32 = 585.634
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 5 -5|, &lt;0 -7 15|]
Comma list: 121/120, 225/224, 22000/21609
EDOs: 41, 84, 125, 209, 334c, 543bc
Badness: 0.4538


==7-limit==
Mapping: {{mapping| 1 -3 12 13 6 | 0 9 -19 -20 -5 }}
Commas: 225/224, 2500000/2470629


POTE generator: ~7/5 = 585.585
Optimal tunings:  
* WE: ~2 = 1200.3591{{c}}, ~10/7 = 611.5569{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3690{{c}}


Map: [&lt;1 5 -5 -5|, &lt;0 -7 15 16|]
{{Optimal ET sequence|legend=0| 51, 53 }}
Wedgie: &lt;&lt;7 -15 -16 -40 -45 5||
EDOs: 41, 84, 125
Badness: 0.0551


==11-limit==
Badness (Sintel): 2.46
Commas: 225/224, 441/440, 1344/1331


POTE generator: ~7/5 = 585.606
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 5 -5 -5 2|, &lt;0 -7 15 16 3]]
Comma list: 121/120, 225/224, 275/273, 1040/1029
EDOs: 41, 84, 125e
Badness: 0.0364


==13-limit==
Mapping: {{mapping| 1 -3 12 13 6 20 | 0 9 -19 -20 -5 -32 }}
Commas: 144/143, 225/224, 364/363, 441/440


POTE generator: ~7/5 = 585.657
Optimal tunings:  
* WE: ~2 = 1200.4078{{c}}, ~10/7 = 611.5536{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~10/7 = 611.3392{{c}}


Map: [&lt;1 5 -5 -5 2 12|, &lt;0 -7 15 16 3 -17|]
{{Optimal ET sequence|legend=0| 51f, 53 }}
EDOs: 41, 84, 125e, 209ef, 293ef
Badness: 0.0275


=Septimin=
Badness (Sintel): 1.96
Comma: 35595703125/34359738368


POTE generator: ~75/64 = 263.658
== Naiadical ==
Named by [[Xenllium]] in 2026, naiadical may be described as the {{nowrap| 21 & 29 }} temperament.  


Map: [&lt;1 4 1|, &lt;0 -11 6|]
[[Subgroup]]: 2.3.5.7
EDOs: 9, 32, 41, 91, 132, 223c, 355bc
Badness: 0.6709


==7-limit==
[[Comma list]]: 225/224, 823543/800000
Commas: 225/224, 84035/82944


[[POTE tuning|POTE temperament]]: 263.632
{{Mapping|legend=1| 1 -4 11 9 | 0 9 -14 -10 }}
: mapping generators: ~2, ~32/21


Map: [&lt;1 4 1 5|, &lt;0 -11 6 -10|]
[[Optimal tuning]]s:  
Wedgie: &lt;&lt;11 -6 10 -35 -15 40||
* [[WE]]: ~2 = 1202.1198{{c}}, ~32/21 = 745.4675{{c}}
EDOs: 9, [[32edo|32]], 41, 91, [[132edo|132]]
: [[error map]]: {{val| +2.120 -1.227 +0.459 -4.423 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~32/21 = 744.1318{{c}}
: error map: {{val| 0.000 -4.769 -4.159 -10.144 }}


==11-limit==
{{Optimal ET sequence|legend=1| 21, 29, 50, 79d, 129cdd, 179bcddd }}
Commas: 225/224, 385/384, 2401/2376


[[POTE tuning|POTE temperament]]: 263.634
[[Badness]] (Sintel): 3.67


Map: [&lt;1 4 1 5 5|, &lt;0 -11 6 -10 -7|]
=== 11-limit ===
EDOs: 9, 32, 41, 91, 223cdef
Subgroup: 2.3.5.7.11


==13-limit==
Comma list: 225/224, 245/242, 1617/1600
Commas: 105/104, 144/143, 196/195, 245/242


[[POTE tuning|POTE temperament]]: 263.700
Mapping: {{Mapping| 1 -4 11 9 14 | 0 9 -14 -10 -17 }}


Map: [&lt;1 4 1 5 5 7|, &lt;0 -11 6 -10 -7 -15|]
Optimal tunings:  
EDOs: 9, 41, 91
* WE: ~2 = 1201.9008{{c}}, ~21/16 = 745.3867{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~32/21 = 744.1777{{c}}


=Slender=
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
Commas: 225/224, 589824/588245


[[POTE tuning|POTE temperament]]: ~49/48 = 38.413
Badness (Sintel): 2.00


Map: [&lt;1 2 2 3|, &lt;0 -13 10 -6|]
=== 13-limit ===
Wedgie: &lt;&lt;13 -10 6 -46 -27 42||
Subgroup: 2.3.5.7.11.13
EDOs: 31, 94, 125
Badness: 0.0569


==11-limit==
Comma list: 105/104, 196/195, 245/242, 1001/1000
Commas: 225/224, 385/384, 1331/1323


[[POTE tuning|POTE temperament]]: ~49/48 = 38.387
Mapping: {{Mapping| 1 -4 11 9 14 13 | 0 9 -14 -10 -17 -15 }}


Map: [&lt;1 2 2 3 4|, &lt;0 -13 10 -6 -17|]
Optimal tunings:  
EDOs: 31, 63, 94, 125
* WE: ~2 = 1201.7863{{c}}, ~20/13 = 745.3344{{c}}
Badness: 25.342
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1931{{c}}


==13-limit==
{{Optimal ET sequence|legend=0| 21, 29, 50, 79d }}
Commas: 225/224, 275/273, 385/384, 1331/1323


POTE generator: ~49/48 = 38.314
Badness (Sintel): 1.43


Map: [&lt;1 2 2 3 4 3|, &lt;0 -13 10 -6 -17 22|]
=== 17-limit ===
EDOs: 31, 63, 94
Subgroup: 2.3.5.7.11.13.17
Badness: 25.913


=Marvo=
Comma list: 105/104, 170/169, 196/195, 221/220, 245/242
Commas: 225/224, 78125000/78121827


[[POTE tuning|POTE temperament]]: ~27/20 = 516.694
Mapping: {{Mapping| 1 -4 11 9 14 13 14 | 0 9 -14 -10 -17 -15 -16 }}


Map: [&lt;1 5 12 29|, &lt;0 -6 -17 -46|]
Optimal tunings:  
Wedgie: &lt;&lt;6, 17, 46, 13, 56 59||
* WE: ~2 = 1201.9208{{c}}, ~20/13 = 745.3976{{c}}
EDOs: 65, 72
* CWE: ~2 = 1200.0000{{c}}, ~20/13 = 744.1669{{c}}


==11-limit==
{{Optimal ET sequence|legend=0| 21, 29g, 50, 79dg }}
Commas: 225/224, 243/242, 4000/3993


[[POTE tuning|POTE temperament]]: ~27/20 = 516.699
Badness (Sintel): 1.26


Map: [&lt;1 5 12 29 12|, &lt;0 -6 -17 -46 -15|]
== Quintannic ==
EDOs: 65, 72, 281, 497
Named by [[Scott Dakota]], quintannic may be described as the {{nowrap| 43 & 60 }} temperament.


==13-limit==
[[Subgroup]]: 2.3.5.7
Commas: 243/242, 225/224, 351/350, 1625/1617


POTE generator: ~27/20 = 516.730
[[Comma list]]: 225/224, 9805926501/9765625000


Map: [&lt;1 5 12 29 12 39|, &lt;0 -6 -17 -46 -15 -62|]
{{Mapping|legend=1| 1 1 5 7 | 0 5 -23 -36 }}
EDOs: 72, 137, 209, 281f, 490bcf
: mapping generators: ~2, ~10000/9261
Badness: 0.0269


=Marvolo=  
[[Optimal tuning]]s:
Commas: 225/224, 156250000/155649627
* [[WE]]: ~2 = 1200.9803{{c}}, ~10000/9261 = 139.9522{{c}}
: [[error map]]: {{val| +0.980 -1.214 -0.313 -0.243 }}
* [[CWE]]: ~2 = 1200.0000{{c}}, ~10000/9261 = 139.8184{{c}}
: error map: {{val| 0.000 -2.863 -2.136 -2.287 }}


POTE generator: ~21/20 = 83.348
{{Optimal ET sequence|legend=1| 43, 60, 103, 266bcd, 369bcd }}


Map: [&lt;1 2 1 1|, &lt;0 -6 19 26|]
[[Badness]] (Sintel): 3.81
Wedgie: &lt;&lt;6 -19 -26 -44 -58 -7||
EDOs: 29, 43, 72, 619bcd, 691bcd
Badness: 0.0833


==11-limit==  
=== 11-limit ===
Commas: 225/224, 441/440, 4000/3993
Subgroup: 2.3.5.7.11


POTE generator: ~21/20 = 83.340
Comma list: 225/224, 441/440, 43923/43750


Map: [&lt;1 2 1 1 2|, &lt;0 -6 19 26 21|]
Mapping: {{mapping| 1 1 5 7 8 | 0 5 -23 -36 -39 }}
EDOs: 29, 43, 72
Badness: 0.0290


==13-limit==
Optimal tunings:
Commas: 169/168, 225/224, 364/363, 441/440
* WE: ~2 = 1201.0031{{c}}, ~320/297 = 139.9435{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~320/297 = 139.8053{{c}}


POTE generator: ~21/20 = 83.330
{{Optimal ET sequence|legend=0| 43, 60e, 103, 369bcdeee, 472bbcddeee }}


Map: [&lt;1 2 1 1 2 3|, &lt;0 -6 19 26 21 10|]
Badness (Sintel): 1.74
EDOs: 29, 43, 72
Badness: 0.0215


=Amavil=  
=== 13-limit ===
Commas: 225/224, 17496/16807
Subgroup: 2.3.5.7.11.13


POTE generator: ~48/35 = 529.979
Comma list: 225/224, 441/440, 1001/1000, 1188/1183


Map: [&lt;1 6 1 9|, &lt;0 -10 3 -14|]
Mapping: {{mapping| 1 1 5 7 8 3 | 0 5 -23 -36 -39 6 }}
Wedgie: &lt;&lt;10 -3 14 -28 -6 41||
EDOs: 9, 34d, 43, 77d
Badness: 0.1096


==11-limit==
Optimal tunings:
Commas: 99/98, 176/175, 864/847
* WE: ~2 = 1200.8354{{c}}, ~13/12 = 139.9095{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.7997{{c}}


POTE generator: ~15/11 = 529.974
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


Map: [&lt;1 6 1 9 7|, &lt;0 -10 3 -14 -8|]
Badness (Sintel): 1.35
EDOs: 9, 34d, 43, 77de
Badness: 0.0426


==13-limit==  
=== 17-limit ===
Commas: 78/77, 99/98, 144/143, 176/175
Subgroup: 2.3.5.7.11.13.17


POTE generator: ~15/11 = 529.951
Comma list: 225/224, 273/272, 375/374, 441/440, 891/884


Map: [&lt;1 6 1 9 7 9|, &lt;0 -10 3 -14 -8 -12|]
Mapping: {{mapping| 1 1 5 7 8 3 7 | 0 5 -23 -36 -39 6 -25 }}
EDOs: 9, 34d, 43, 77de
Badness: 0.0258


=Enneaportent=  
Optimal tunings:
Commas: 225/224, 40353607/40310784
* WE: ~2 = 1200.7402{{c}}, ~13/12 = 139.9015{{c}}
* CWE: ~2 = 1200.0000{{c}}, ~13/12 = 139.8038{{c}}


POTE generator: ~5/4 = 383.165
{{Optimal ET sequence|legend=0| 43, 60e, 103 }}


Map: [&lt;9 0 28 11|, &lt;0 2 -1 2|]
Badness (Sintel): 1.17
Wedgie: &lt;&lt;18 -9 18 -56 -22 67||
EDOs: 9, 54, 63, 72, 495bcd
Badness: 0.0937


==11-limit==  
== Gwazy ==
Commas: 225/224, 385/384, 12005/11979
: ''For the 5-limit version, see [[Very high accuracy temperaments #Kwazy]].''


POTE generator: ~5/4 = 383.146
Named by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, gwazy may be described as the {{nowrap| 22 & 74 }} temperament.  


Map: [&lt;9 0 28 11 24|, &lt;0 2 -1 2 1|]
[[Subgroup]]: 2.3.5.7
EDOs: 9, 54, 63, 72, 423cd, 495bcd
Badness: 0.0304


==13-limit==
[[Comma list]]: 225/224, 5971968/5764801
Commas: 169/168 225/224 364/363 1716/1715


POTE generator: ~5/4 = 383.047
{{Mapping|legend=1| 2 1 6 4 | 0 8 -5 6 }}
: mapping generators: ~2401/1728, ~35/32


Map: [&lt;9 0 28 11 24 19|, &lt;0 2 -1 2 1 2|]
[[Optimal tuning]]s:
EDOs: 9, 54, 63, 72, 279cf
* [[WE]]: ~2401/1728 = 599.7132{{c}}, ~35/32 = 162.5806{{c}}
Badness: 0.0223
: [[error map]]: {{val| -0.574 -1.597 -0.937 +5.510 }}
* [[CWE]]: ~2401/1728 = 600.0000{{c}}, ~35/32 = 162.6388{{c}}
: error map: {{val| 0.000 -0.844 +0.492 +7.007 }}


=Submajor=
{{Optimal ET sequence|legend=1| 22, 74, 96, 118d }}
Comma: 69198046875/68719476736


POTE generator: ~10125/8192 = 362.321
[[Badness]] (Sintel): 4.53


Map: [&lt;1 4 -1|, &lt;0 -8 11|]
=== 11-limit ===
EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc
Subgroup: 2.3.5.7.11
Badness: 0.1302


==7-limit==
Comma list: 99/98, 176/175, 65536/65219
Commas: 225/224, 51200/50421


POTE generator: ~49/40 = 362.255
Mapping: {{mapping| 2 1 6 4 8 | 0 8 -5 6 -4 }}


Map: [&lt;1 4 -1 1|, &lt;0 -8 11 6|]
Optimal tunings:  
Wedgie: &lt;&lt;8 -11 -6 -36 -32 17||
* WE: ~363/256 = 599.8517{{c}}, ~11/10 = 162.5518{{c}}
EDOs: 10, 33, 43, 53
* CWE: ~363/256 = 600.0000{{c}}, ~11/10 = 162.5863{{c}}
Badness: 0.0605


==11-limit==
{{Optimal ET sequence|legend=0| 22, 74, 96 }}
Commas: 225/224, 385/384, 6655/6561


POTE generator: ~27/22 = 362.101
Badness (Sintel): 2.26


Map: [&lt;1 4 -1 1 11|, &lt;0 -8 11 6 -25|]
== Tertiosec ==
EDOs: 10, 53, 116, 169de, 285cde
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tertiosec]].''
Badness: 0.0506


==13-limit==
Tertiosec may be described as the {{nowrap| 21 & 75 }} temperament. It was initially named ''tertiomar'' by [[Petr Pařízek]] in 2011<ref name="petr's long post"/>, but was changed to ''tertiosec'' in 2012<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning/topicId_104268.html Yahoo! Tuning Group | ''2D temperament names, part I -- reclassified temperaments from message #101780'']</ref>.
Commas: 169/168, 225/224, 275/273, 385/384


POTE generator: ~16/13 = 362.105
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 4 -1 1 11 4|, &lt;0 -8 11 6 -25 -1|]
[[Comma list]]: 225/224, 14495514624/13841287201
EDOs: 10, 53, 116, 169de, 285cdef
Badness: 0.0277


==Interpental==
{{Mapping|legend=1| 3 -1 12 7 | 0 8 -7 2 }}
Commas: 99/98, 176/175, 51200/50421
: mapping generators: ~3072/2401, ~2048/1715


POTE generator: ~49/40 = 362.418
[[Optimal tuning]]s:
* [[WE]]: ~3072/2401 = 399.8257{{c}}, ~2048/1715 = 287.5920{{c}}
: [[error map]]: {{val| -0.523 -1.044 -1.549 +5.138 }}
* [[CWE]]: ~3072/2401 = 400.0000{{c}}, ~2048/1715 = 287.7088{{c}}
: error map: {{val| 0.000 -0.284 -0.276 +6.592 }}


Map: [&lt;1 4 -1 1 -5|, &lt;0 -8 11 6 28|]
{{Optimal ET sequence|legend=1| 21, 54, 75, 96, 171d }}
EDOs: 43, 53, 96, 149d
Badness: 0.0518


===13-limit===
[[Badness]] (Sintel): 10.9
Commas: 99/98, 169/168, 176/175, 640/637


POTE generator: ~16/13 = 362.402
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 4 -1 1 -5 4|, &lt;0 -8 11 6 28 -1|]
Comma list: 225/224, 3840/3773, 12005/11979
EDOs: 43, 53, 96, 149d
Badness: 0.0297


=Alphorn=
Mapping: {{mapping| 3 -1 12 7 14 | 0 8 -7 2 -5 }}
Commas: 225/224, 5764801/5668704


POTE generator: ~48/35 = 556.221
Optimal tunings:
* WE: ~44/35 = 399.6550{{c}}, ~33/28 = 287.5803{{c}}
* CWE: ~44/35 = 400.0000{{c}}, ~33/28 = 287.8224{{c}}


Map: [&lt;1 9 0 13|, &lt;0 -16 5 -22|]
{{Optimal ET sequence|legend=0| 21, 54, 75e }}
Wedgie: &lt;&lt;16 -5 22 -45 -10 65||
EDOs: 28d, 41, 151cd, 192cd, 233cd
Badness: 0.1293


==11-limit==
Badness (Sintel): 5.74
Commas: 225/224, 385/384, 12250/11979


POTE generator: ~11/8 = 556.144
== References ==


Map: [&lt;1 9 0 13 3|, &lt;0 -16 5 -22 1|]
[[Category:Temperament collections]]
EDOs: 41, 315cde
[[Category:Marvel temperaments| ]] <!-- main article -->
Badness: 0.0735</pre></div>
[[Category:Rank 2]]
<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;Marvel temperaments&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextTocRule:114:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:114 --&gt;&lt;!-- ws:start:WikiTextTocRule:115: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negri"&gt;Negri&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:115 --&gt;&lt;!-- ws:start:WikiTextTocRule:116: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negri-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:116 --&gt;&lt;!-- ws:start:WikiTextTocRule:117: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negri-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:117 --&gt;&lt;!-- ws:start:WikiTextTocRule:118: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negril"&gt;Negril&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:118 --&gt;&lt;!-- ws:start:WikiTextTocRule:119: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negril-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:119 --&gt;&lt;!-- ws:start:WikiTextTocRule:120: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negric"&gt;Negric&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:120 --&gt;&lt;!-- ws:start:WikiTextTocRule:121: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negric-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:121 --&gt;&lt;!-- ws:start:WikiTextTocRule:122: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Negroni"&gt;Negroni&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:122 --&gt;&lt;!-- ws:start:WikiTextTocRule:123: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Negroni-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:123 --&gt;&lt;!-- ws:start:WikiTextTocRule:124: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Wizard"&gt;Wizard&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:124 --&gt;&lt;!-- ws:start:WikiTextTocRule:125: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:125 --&gt;&lt;!-- ws:start:WikiTextTocRule:126: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:126 --&gt;&lt;!-- ws:start:WikiTextTocRule:127: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-Lizard"&gt;Lizard&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:127 --&gt;&lt;!-- ws:start:WikiTextTocRule:128: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Lizard-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:128 --&gt;&lt;!-- ws:start:WikiTextTocRule:129: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Lizard-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:129 --&gt;&lt;!-- ws:start:WikiTextTocRule:130: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-Gizzard"&gt;Gizzard&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:130 --&gt;&lt;!-- ws:start:WikiTextTocRule:131: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Gizzard-17-limit"&gt;17-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:131 --&gt;&lt;!-- ws:start:WikiTextTocRule:132: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Wizard-Gizzard-19-limit"&gt;19-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:132 --&gt;&lt;!-- ws:start:WikiTextTocRule:133: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Wizard-Mage"&gt;Mage&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:133 --&gt;&lt;!-- ws:start:WikiTextTocRule:134: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Triton"&gt;Triton&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:134 --&gt;&lt;!-- ws:start:WikiTextTocRule:135: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Triton-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:135 --&gt;&lt;!-- ws:start:WikiTextTocRule:136: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Tritonic"&gt;Tritonic&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:136 --&gt;&lt;!-- ws:start:WikiTextTocRule:137: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:137 --&gt;&lt;!-- ws:start:WikiTextTocRule:138: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:138 --&gt;&lt;!-- ws:start:WikiTextTocRule:139: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:139 --&gt;&lt;!-- ws:start:WikiTextTocRule:140: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Tritonic-Tritoni"&gt;Tritoni&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:140 --&gt;&lt;!-- ws:start:WikiTextTocRule:141: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Merman"&gt;Merman&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:141 --&gt;&lt;!-- ws:start:WikiTextTocRule:142: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Merman-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:142 --&gt;&lt;!-- ws:start:WikiTextTocRule:143: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Merman-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:143 --&gt;&lt;!-- ws:start:WikiTextTocRule:144: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Merman-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:144 --&gt;&lt;!-- ws:start:WikiTextTocRule:145: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Septimin"&gt;Septimin&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:145 --&gt;&lt;!-- ws:start:WikiTextTocRule:146: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimin-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:146 --&gt;&lt;!-- ws:start:WikiTextTocRule:147: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimin-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:147 --&gt;&lt;!-- ws:start:WikiTextTocRule:148: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Septimin-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:148 --&gt;&lt;!-- ws:start:WikiTextTocRule:149: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Slender"&gt;Slender&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:149 --&gt;&lt;!-- ws:start:WikiTextTocRule:150: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Slender-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:150 --&gt;&lt;!-- ws:start:WikiTextTocRule:151: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Slender-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:151 --&gt;&lt;!-- ws:start:WikiTextTocRule:152: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Marvo"&gt;Marvo&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:152 --&gt;&lt;!-- ws:start:WikiTextTocRule:153: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvo-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:153 --&gt;&lt;!-- ws:start:WikiTextTocRule:154: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvo-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:154 --&gt;&lt;!-- ws:start:WikiTextTocRule:155: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Marvolo"&gt;Marvolo&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:155 --&gt;&lt;!-- ws:start:WikiTextTocRule:156: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvolo-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:156 --&gt;&lt;!-- ws:start:WikiTextTocRule:157: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Marvolo-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:157 --&gt;&lt;!-- ws:start:WikiTextTocRule:158: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Amavil"&gt;Amavil&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:158 --&gt;&lt;!-- ws:start:WikiTextTocRule:159: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amavil-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:159 --&gt;&lt;!-- ws:start:WikiTextTocRule:160: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Amavil-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:160 --&gt;&lt;!-- ws:start:WikiTextTocRule:161: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Enneaportent"&gt;Enneaportent&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:161 --&gt;&lt;!-- ws:start:WikiTextTocRule:162: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Enneaportent-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:162 --&gt;&lt;!-- ws:start:WikiTextTocRule:163: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Enneaportent-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:163 --&gt;&lt;!-- ws:start:WikiTextTocRule:164: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Submajor"&gt;Submajor&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:164 --&gt;&lt;!-- ws:start:WikiTextTocRule:165: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-7-limit"&gt;7-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:165 --&gt;&lt;!-- ws:start:WikiTextTocRule:166: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:166 --&gt;&lt;!-- ws:start:WikiTextTocRule:167: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:167 --&gt;&lt;!-- ws:start:WikiTextTocRule:168: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Submajor-Interpental"&gt;Interpental&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:168 --&gt;&lt;!-- ws:start:WikiTextTocRule:169: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Submajor-Interpental-13-limit"&gt;13-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:169 --&gt;&lt;!-- ws:start:WikiTextTocRule:170: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Alphorn"&gt;Alphorn&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:170 --&gt;&lt;!-- ws:start:WikiTextTocRule:171: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Alphorn-11-limit"&gt;11-limit&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:171 --&gt;&lt;!-- ws:start:WikiTextTocRule:172: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:172 --&gt;This page discusses some of the temperaments tempering out |-5 2 2 -1&amp;gt; =&lt;a class="wiki_link" href="/225_224"&gt; 225/224&lt;/a&gt;, the &lt;a class="wiki_link" href="/Marvel%20family"&gt;marvel&lt;/a&gt; comma or septimal kleisma. These include negri, wizard, tritonic, septimin, slender, triton, merman and marvo. Considered elsewhere are &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone&lt;/a&gt;, &lt;a class="wiki_link" href="/Miracle"&gt;miracle&lt;/a&gt;, &lt;a class="wiki_link" href="/Magic%20family"&gt;magic&lt;/a&gt;, &lt;a class="wiki_link" href="/Pajara"&gt;pajara&lt;/a&gt;, &lt;a class="wiki_link" href="/Orwell"&gt;orwell&lt;/a&gt;, &lt;a class="wiki_link" href="/Kleismic%20family"&gt;catakleismic&lt;/a&gt;, &lt;a class="wiki_link" href="/Garibaldi%20temperament"&gt;garibaldi&lt;/a&gt;, &lt;a class="wiki_link" href="/Augmented%20family"&gt;august&lt;/a&gt;, &lt;a class="wiki_link" href="/Pythagorean%20family"&gt;compton&lt;/a&gt;, &lt;a class="wiki_link" href="/Dicot%20family"&gt;sharp&lt;/a&gt;, &lt;a class="wiki_link" href="/Escapade%20family"&gt;escapade&lt;/a&gt; and &lt;a class="wiki_link" href="/Pelogic%20family"&gt;mavila&lt;/a&gt;.&lt;br /&gt;
&lt;br /&gt;
Since (5/4)^2 = 225/224 * 14/9, these temperaments tend to have a relatively small complexity for 5/4. They also possess a version of the augmented triad where each third approximates either 5/4 or 9/7. Since this is a chord of meantone temperament in wide use in Western common practice harmony long before 12edo established itself as the standard tuning, it is arguably more authentic to tune it as two stacked major thirds and a diminished fourth, which is what it is in meantone, than as the modern version of three stacked very sharp major thirds.&lt;br /&gt;
&lt;br /&gt;
The melodic signature of marvel temperaments is that 16/15 and 15/14 are tempered to be equal. Hence 8/7 can be divided into two equal parts.&lt;br /&gt;
&lt;br /&gt;
Marvel tempering allows for a tritone substitution whereby the dominant seventh chord formed by adding 16/9 above the root shares its tritone with a 4:5:6:7 tetrad. (The tritone of the dominant seventh is (16/9)/(5/4)=64/45. Setting this equal to 10/7 gives (10/7)/(64/45)=225/224.)&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Negri"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Negri&lt;/h1&gt;
&lt;a class="wiki_link" href="/Comma"&gt;Comma&lt;/a&gt;s: 49/48, 225/224&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~15/14 = 125.608&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Map"&gt;Map&lt;/a&gt;: [&amp;lt;1 2 2 3|, &amp;lt;0 -4 3 -2|]&lt;br /&gt;
&lt;a class="wiki_link" href="/Wedgie"&gt;Wedgie&lt;/a&gt;: &amp;lt;&amp;lt;4 -3 2 -14 -8 13||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/9edo"&gt;9&lt;/a&gt;, &lt;a class="wiki_link" href="/10edo"&gt;10&lt;/a&gt;, &lt;a class="wiki_link" href="/19edo"&gt;19&lt;/a&gt;, &lt;a class="wiki_link" href="/86edo"&gt;86&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Negri-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;11-limit&lt;/h2&gt;
Commas: 45/44, 49/48, 56/55&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~15/14 = 126.474&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -4 3 -2 -5|]&lt;br /&gt;
EDOs: 9, 10, 19&lt;br /&gt;
&lt;a class="wiki_link" href="/Badness"&gt;Badness&lt;/a&gt;: 0.0262&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Negri-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;13-limit&lt;/h2&gt;
Commas: 45/44, 49/48, 56/55, 78/77&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~14/13 = 126.431&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 4|, &amp;lt;0 -4 3 -2 -5 -3|]&lt;br /&gt;
EDOs: 9, 10, 19&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Negril"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Negril&lt;/h1&gt;
Commas: 49/48, 100/99, 225/224&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.767&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 2|, &amp;lt;0 -4 3 -2 14|]&lt;br /&gt;
EDOs: 19, &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/48edo"&gt;48df&lt;/a&gt;, &lt;a class="wiki_link" href="/77edo"&gt;77cdf&lt;/a&gt;&lt;br /&gt;
Badness: 0.0387&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Negril-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 65/64, 91/90, 875/858&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.716&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 2 4|, &amp;lt;0 -4 3 -2 14 -3|]&lt;br /&gt;
EDOs: 9, 10, 19, 29, 48, 77&lt;br /&gt;
Badness: 0.0244&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Negric"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Negric&lt;/h1&gt;
Commas: 33/32, 49/48, 77/75&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 127.039&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 3|, &amp;lt;0 -4 3 -2 4|]&lt;br /&gt;
EDOs: 9, 19, &lt;a class="wiki_link" href="/85edo"&gt;85&lt;/a&gt;&lt;br /&gt;
Badness: 0.0306&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Negric-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;13-limit&lt;/h2&gt;
Commas: 33/32, 49/48, 65/64, 91/90&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 127.039&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 3 4|, &amp;lt;0 -4 3 -2 4 -3|]&lt;br /&gt;
EDOs: 9, 19, 85&lt;br /&gt;
Badness: 0.0202&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Negroni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Negroni&lt;/h1&gt;
Commas: 49/48, 55/54, 225/224&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.539&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 5|, &amp;lt;0 -4 3 -2 -15|]&lt;br /&gt;
EDOs: 10, 19e, 29, 77cde&lt;br /&gt;
Badness: 0.0353&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Negroni-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;13-limit&lt;/h2&gt;
Commas: 49/48, 55/54, 65/64, 91/90&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/14 = 124.545&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 5 4|, &amp;lt;0 -4 3 -2 -15 -3|]&lt;br /&gt;
EDOs: 10, 19e, 29, 77cdef&lt;br /&gt;
Badness: 0.0216&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Wizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Wizard&lt;/h1&gt;
Comma: 2197265625/2147483648&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.212&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5|, &amp;lt;0 6 -1|]&lt;br /&gt;
EDOs: 22, 50, 72, 166, 238c, 310c, 548bc&lt;br /&gt;
Badness: 0.3864&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Wizard-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 118098/117649&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.256&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2|, &amp;lt;0 6 -1 10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;12 -2 20 -31 -2 52||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/50edo"&gt;50&lt;/a&gt;, &lt;a class="wiki_link" href="/72edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238c&lt;/a&gt;, &lt;a class="wiki_link" href="/310edo"&gt;310c&lt;/a&gt;, &lt;a class="wiki_link" href="/382edo"&gt;382c&lt;/a&gt;&lt;br /&gt;
Badness: 0.0408&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Wizard-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.232&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8|, &amp;lt;0 6 -1 10 -3|]&lt;br /&gt;
EDOs: 22, 50, 72, 94, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238c&lt;/a&gt;, &lt;a class="wiki_link" href="/310edo"&gt;310c&lt;/a&gt;&lt;br /&gt;
Badness: 0.0185&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Wizard-Lizard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Lizard&lt;/h2&gt;
Commas: 225/224, 351/350, 364/363, 385/384&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.389&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 11|, &amp;lt;0 6 -1 10 -3 -10|]&lt;br /&gt;
EDOs: 22, 50, 72, 122, 194df&lt;br /&gt;
Badness: 0.0218&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Wizard-Lizard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;17-limit&lt;/h3&gt;
Commas: 221/220, 273/272, 289/288, 351/350, 375/374&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 383.381&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 11 6|, &amp;lt;0 6 -1 10 -3 -10 6|]&lt;br /&gt;
EDOs: 22, 50, 72, 122g, 194dfg&lt;br /&gt;
Badness: 0.0145&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Wizard-Lizard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;19-limit&lt;/h3&gt;
Commas: 153/152, 210/209, 221/220, 225/224, 273/272, 343/342&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~5/4 = 383.477&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 11 6 2|, &amp;lt;0 6 -1 10 -3 -10 6 18|]&lt;br /&gt;
EDOs: 22h, 50, 72, &lt;a class="wiki_link" href="/122edo"&gt;122g&lt;/a&gt;, &lt;a class="wiki_link" href="/194edo"&gt;194dfg&lt;/a&gt;&lt;br /&gt;
Badness: 0.0157&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Wizard-Gizzard"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Gizzard&lt;/h2&gt;
Commas: 225/224, 385/384, 325/324, 1573/1568&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.170&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 -2|, &amp;lt;0 6 -1 10 -3 26|]&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/22edo"&gt;22&lt;/a&gt;, &lt;a class="wiki_link" href="/26edo"&gt;72&lt;/a&gt;, &lt;a class="wiki_link" href="/94edo"&gt;94&lt;/a&gt;, &lt;a class="wiki_link" href="/166edo"&gt;166&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238cf&lt;/a&gt;&lt;br /&gt;
Badness: 0.0203&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Wizard-Gizzard-17-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;17-limit&lt;/h3&gt;
Commas: 225/224, 289/288, 325/324, 375/374, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.175&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 -2 6|, &amp;lt;0 6 -1 10 -3 26 6|]&lt;br /&gt;
EDOs: 22f, 72, 94, &lt;a class="wiki_link" href="/166edo"&gt;166g&lt;/a&gt;, &lt;a class="wiki_link" href="/238edo"&gt;238cfg&lt;/a&gt;&lt;br /&gt;
Badness: 0.0136&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc17"&gt;&lt;a name="Wizard-Gizzard-19-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;19-limit&lt;/h3&gt;
Commas: 225/224, 385/384, 325/324, 595/594, 375/374, 400/399&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.138&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 8 -2 6 15|, &amp;lt;0 6 -1 10 -3 26 6 -18|]&lt;br /&gt;
EDOs: 22f, 72, 94, 166g&lt;br /&gt;
Badness: 0.0148&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Wizard-Mage"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Mage&lt;/h2&gt;
Commas: 99/98, 176/175, 1331/1296&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~55/48 = 216.876&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;2 1 5 2 4|, &amp;lt;0 6 -1 10 8|]&lt;br /&gt;
EDOs: 22, 72e, 94e&lt;br /&gt;
Badness: 0.0578&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc19"&gt;&lt;a name="Triton"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Triton&lt;/h1&gt;
Commas: 225/224, 1029/1000&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~7/5 = 568.865&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 6 7|, &amp;lt;0 3 -7 -8|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;3 -7 -8 -18 -21 1||&lt;br /&gt;
EDOs: 17d, 19, 78bd, 97bd&lt;br /&gt;
Badness: 0.0592&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Triton-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;11-limit&lt;/h2&gt;
Commas: 45/44, 56/55, 1029/1000&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 569.144&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 0 6 7 4|, &amp;lt;0 3 -7 -8 -1|]&lt;br /&gt;
EDOs: 19, 59bde, 78bde, 97bde&lt;br /&gt;
Badness: 0.0457&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc21"&gt;&lt;a name="Tritonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Tritonic&lt;/h1&gt;
Comnma: 553584375/536870912&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~45/32 = 580.219&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3|, &amp;lt;0 -5 11|]&lt;br /&gt;
EDOs: 29, 31, 60, 91&lt;br /&gt;
Badness: 0.3785&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Tritonic-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 50421/50000&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 580.286&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3|, &amp;lt;0 -5 11 12|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;5 -11 -12 -29 -33 3||&lt;br /&gt;
EDOs: &lt;a class="wiki_link" href="/29edo"&gt;29&lt;/a&gt;, &lt;a class="wiki_link" href="/31edo"&gt;31&lt;/a&gt;, &lt;a class="wiki_link" href="/60edo"&gt;60&lt;/a&gt;, &lt;a class="wiki_link" href="/91edo"&gt;91&lt;/a&gt;, &lt;a class="wiki_link" href="/122edo"&gt;122&lt;/a&gt;, 213bcd&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Tritonic-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;11-limit&lt;/h2&gt;
Commas: 121/120, 225/224, 441/440&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE generator&lt;/a&gt;: ~7/5 = 580.267&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3 2|, &amp;lt;0 -5 11 12 3|]&lt;br /&gt;
EDOs: 29, 31, 60e&lt;br /&gt;
Badness: 0.0237&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Tritonic-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 121/120, 196/195, 275/273&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 580.108&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3 2 -5|, &amp;lt;0 -5 11 12 3 18|]&lt;br /&gt;
EDOs: 29, 31, 60e, 151cde&lt;br /&gt;
Badness: 0.0230&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Tritonic-Tritoni"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Tritoni&lt;/h2&gt;
Commas: 225/224, 385/384, 27783/27500&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 580.389&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -3 -3 17|, &amp;lt;0 -5 11 12 -28|]&lt;br /&gt;
EDOs: 31, 91, 122&lt;br /&gt;
Badness: 0.0455&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="Merman"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Merman&lt;/h1&gt;
Comma: 1121008359375/1099511627776&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~45/32 = 585.634&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5|, &amp;lt;0 -7 15|]&lt;br /&gt;
EDOs: 41, 84, 125, 209, 334c, 543bc&lt;br /&gt;
Badness: 0.4538&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc27"&gt;&lt;a name="Merman-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 2500000/2470629&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.585&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5 -5|, &amp;lt;0 -7 15 16|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;7 -15 -16 -40 -45 5||&lt;br /&gt;
EDOs: 41, 84, 125&lt;br /&gt;
Badness: 0.0551&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc28"&gt;&lt;a name="Merman-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 441/440, 1344/1331&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.606&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5 -5 2|, &amp;lt;0 -7 15 16 3]]&lt;br /&gt;
EDOs: 41, 84, 125e&lt;br /&gt;
Badness: 0.0364&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Merman-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;13-limit&lt;/h2&gt;
Commas: 144/143, 225/224, 364/363, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~7/5 = 585.657&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 -5 -5 2 12|, &amp;lt;0 -7 15 16 3 -17|]&lt;br /&gt;
EDOs: 41, 84, 125e, 209ef, 293ef&lt;br /&gt;
Badness: 0.0275&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc30"&gt;&lt;a name="Septimin"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Septimin&lt;/h1&gt;
Comma: 35595703125/34359738368&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~75/64 = 263.658&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1|, &amp;lt;0 -11 6|]&lt;br /&gt;
EDOs: 9, 32, 41, 91, 132, 223c, 355bc&lt;br /&gt;
Badness: 0.6709&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc31"&gt;&lt;a name="Septimin-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 84035/82944&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.632&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1 5|, &amp;lt;0 -11 6 -10|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;11 -6 10 -35 -15 40||&lt;br /&gt;
EDOs: 9, &lt;a class="wiki_link" href="/32edo"&gt;32&lt;/a&gt;, 41, 91, &lt;a class="wiki_link" href="/132edo"&gt;132&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:64:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc32"&gt;&lt;a name="Septimin-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:64 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 2401/2376&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.634&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1 5 5|, &amp;lt;0 -11 6 -10 -7|]&lt;br /&gt;
EDOs: 9, 32, 41, 91, 223cdef&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:66:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc33"&gt;&lt;a name="Septimin-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:66 --&gt;13-limit&lt;/h2&gt;
Commas: 105/104, 144/143, 196/195, 245/242&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: 263.700&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 1 5 5 7|, &amp;lt;0 -11 6 -10 -7 -15|]&lt;br /&gt;
EDOs: 9, 41, 91&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:68:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc34"&gt;&lt;a name="Slender"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:68 --&gt;Slender&lt;/h1&gt;
Commas: 225/224, 589824/588245&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~49/48 = 38.413&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3|, &amp;lt;0 -13 10 -6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;13 -10 6 -46 -27 42||&lt;br /&gt;
EDOs: 31, 94, 125&lt;br /&gt;
Badness: 0.0569&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:70:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc35"&gt;&lt;a name="Slender-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:70 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 1331/1323&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~49/48 = 38.387&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4|, &amp;lt;0 -13 10 -6 -17|]&lt;br /&gt;
EDOs: 31, 63, 94, 125&lt;br /&gt;
Badness: 25.342&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:72:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc36"&gt;&lt;a name="Slender-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:72 --&gt;13-limit&lt;/h2&gt;
Commas: 225/224, 275/273, 385/384, 1331/1323&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/48 = 38.314&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 2 3 4 3|, &amp;lt;0 -13 10 -6 -17 22|]&lt;br /&gt;
EDOs: 31, 63, 94&lt;br /&gt;
Badness: 25.913&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:74:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc37"&gt;&lt;a name="Marvo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:74 --&gt;Marvo&lt;/h1&gt;
Commas: 225/224, 78125000/78121827&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~27/20 = 516.694&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 29|, &amp;lt;0 -6 -17 -46|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6, 17, 46, 13, 56 59||&lt;br /&gt;
EDOs: 65, 72&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:76:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc38"&gt;&lt;a name="Marvo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:76 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 243/242, 4000/3993&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/POTE%20tuning"&gt;POTE temperament&lt;/a&gt;: ~27/20 = 516.699&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 29 12|, &amp;lt;0 -6 -17 -46 -15|]&lt;br /&gt;
EDOs: 65, 72, 281, 497&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:78:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc39"&gt;&lt;a name="Marvo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:78 --&gt;13-limit&lt;/h2&gt;
Commas: 243/242, 225/224, 351/350, 1625/1617&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/20 = 516.730&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 5 12 29 12 39|, &amp;lt;0 -6 -17 -46 -15 -62|]&lt;br /&gt;
EDOs: 72, 137, 209, 281f, 490bcf&lt;br /&gt;
Badness: 0.0269&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:80:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc40"&gt;&lt;a name="Marvolo"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:80 --&gt;Marvolo&lt;/h1&gt;
Commas: 225/224, 156250000/155649627&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.348&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 1 1|, &amp;lt;0 -6 19 26|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;6 -19 -26 -44 -58 -7||&lt;br /&gt;
EDOs: 29, 43, 72, 619bcd, 691bcd&lt;br /&gt;
Badness: 0.0833&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:82:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc41"&gt;&lt;a name="Marvolo-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:82 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 441/440, 4000/3993&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.340&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 1 1 2|, &amp;lt;0 -6 19 26 21|]&lt;br /&gt;
EDOs: 29, 43, 72&lt;br /&gt;
Badness: 0.0290&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:84:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc42"&gt;&lt;a name="Marvolo-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:84 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 364/363, 441/440&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~21/20 = 83.330&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 2 1 1 2 3|, &amp;lt;0 -6 19 26 21 10|]&lt;br /&gt;
EDOs: 29, 43, 72&lt;br /&gt;
Badness: 0.0215&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:86:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc43"&gt;&lt;a name="Amavil"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:86 --&gt;Amavil&lt;/h1&gt;
Commas: 225/224, 17496/16807&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~48/35 = 529.979&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 1 9|, &amp;lt;0 -10 3 -14|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;10 -3 14 -28 -6 41||&lt;br /&gt;
EDOs: 9, 34d, 43, 77d&lt;br /&gt;
Badness: 0.1096&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:88:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc44"&gt;&lt;a name="Amavil-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:88 --&gt;11-limit&lt;/h2&gt;
Commas: 99/98, 176/175, 864/847&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/11 = 529.974&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 1 9 7|, &amp;lt;0 -10 3 -14 -8|]&lt;br /&gt;
EDOs: 9, 34d, 43, 77de&lt;br /&gt;
Badness: 0.0426&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:90:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc45"&gt;&lt;a name="Amavil-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:90 --&gt;13-limit&lt;/h2&gt;
Commas: 78/77, 99/98, 144/143, 176/175&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~15/11 = 529.951&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 6 1 9 7 9|, &amp;lt;0 -10 3 -14 -8 -12|]&lt;br /&gt;
EDOs: 9, 34d, 43, 77de&lt;br /&gt;
Badness: 0.0258&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:92:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc46"&gt;&lt;a name="Enneaportent"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:92 --&gt;Enneaportent&lt;/h1&gt;
Commas: 225/224, 40353607/40310784&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.165&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 0 28 11|, &amp;lt;0 2 -1 2|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;18 -9 18 -56 -22 67||&lt;br /&gt;
EDOs: 9, 54, 63, 72, 495bcd&lt;br /&gt;
Badness: 0.0937&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:94:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc47"&gt;&lt;a name="Enneaportent-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:94 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 12005/11979&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.146&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 0 28 11 24|, &amp;lt;0 2 -1 2 1|]&lt;br /&gt;
EDOs: 9, 54, 63, 72, 423cd, 495bcd&lt;br /&gt;
Badness: 0.0304&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:96:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc48"&gt;&lt;a name="Enneaportent-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:96 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168 225/224 364/363 1716/1715&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~5/4 = 383.047&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;9 0 28 11 24 19|, &amp;lt;0 2 -1 2 1 2|]&lt;br /&gt;
EDOs: 9, 54, 63, 72, 279cf&lt;br /&gt;
Badness: 0.0223&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:98:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc49"&gt;&lt;a name="Submajor"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:98 --&gt;Submajor&lt;/h1&gt;
Comma: 69198046875/68719476736&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~10125/8192 = 362.321&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1|, &amp;lt;0 -8 11|]&lt;br /&gt;
EDOs: 10, 33, 43, 53, 202, 255, 308, 361, 414, 775, 1189bc&lt;br /&gt;
Badness: 0.1302&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:100:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc50"&gt;&lt;a name="Submajor-7-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:100 --&gt;7-limit&lt;/h2&gt;
Commas: 225/224, 51200/50421&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/40 = 362.255&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1|, &amp;lt;0 -8 11 6|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;8 -11 -6 -36 -32 17||&lt;br /&gt;
EDOs: 10, 33, 43, 53&lt;br /&gt;
Badness: 0.0605&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:102:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc51"&gt;&lt;a name="Submajor-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:102 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 6655/6561&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~27/22 = 362.101&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 11|, &amp;lt;0 -8 11 6 -25|]&lt;br /&gt;
EDOs: 10, 53, 116, 169de, 285cde&lt;br /&gt;
Badness: 0.0506&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:104:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc52"&gt;&lt;a name="Submajor-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:104 --&gt;13-limit&lt;/h2&gt;
Commas: 169/168, 225/224, 275/273, 385/384&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 362.105&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 11 4|, &amp;lt;0 -8 11 6 -25 -1|]&lt;br /&gt;
EDOs: 10, 53, 116, 169de, 285cdef&lt;br /&gt;
Badness: 0.0277&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:106:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc53"&gt;&lt;a name="Submajor-Interpental"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:106 --&gt;Interpental&lt;/h2&gt;
Commas: 99/98, 176/175, 51200/50421&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~49/40 = 362.418&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 -5|, &amp;lt;0 -8 11 6 28|]&lt;br /&gt;
EDOs: 43, 53, 96, 149d&lt;br /&gt;
Badness: 0.0518&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:108:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc54"&gt;&lt;a name="Submajor-Interpental-13-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:108 --&gt;13-limit&lt;/h3&gt;
Commas: 99/98, 169/168, 176/175, 640/637&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~16/13 = 362.402&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 4 -1 1 -5 4|, &amp;lt;0 -8 11 6 28 -1|]&lt;br /&gt;
EDOs: 43, 53, 96, 149d&lt;br /&gt;
Badness: 0.0297&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:110:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc55"&gt;&lt;a name="Alphorn"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:110 --&gt;Alphorn&lt;/h1&gt;
Commas: 225/224, 5764801/5668704&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~48/35 = 556.221&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 9 0 13|, &amp;lt;0 -16 5 -22|]&lt;br /&gt;
Wedgie: &amp;lt;&amp;lt;16 -5 22 -45 -10 65||&lt;br /&gt;
EDOs: 28d, 41, 151cd, 192cd, 233cd&lt;br /&gt;
Badness: 0.1293&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:112:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc56"&gt;&lt;a name="Alphorn-11-limit"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:112 --&gt;11-limit&lt;/h2&gt;
Commas: 225/224, 385/384, 12250/11979&lt;br /&gt;
&lt;br /&gt;
POTE generator: ~11/8 = 556.144&lt;br /&gt;
&lt;br /&gt;
Map: [&amp;lt;1 9 0 13 3|, &amp;lt;0 -16 5 -22 1|]&lt;br /&gt;
EDOs: 41, 315cde&lt;br /&gt;
Badness: 0.0735&lt;/body&gt;&lt;/html&gt;</pre></div>
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