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__FORCETOC__
{{Technical data page}}
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.


'''Breedsmic temperaments''' are rank two temperaments tempering out the [[breedsma]], |-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.
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.


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.
Temperaments discussed elsewhere include:
* ''[[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]]


=Hemififths=
== Hemififths ==
:''See also [[Hemififths]]''
{{Main| Hemififths }}


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.
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}}.


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.
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.


==5-limit==
[[Subgroup]]: 2.3.5.7
Comma: 858993459200/847288609443


POTE generator: ~655360/531441 = 351.476
[[Comma list]]: 2401/2400, 5120/5103


Map: [&lt;1 1 -5|, &lt;0 2 25|]
{{Mapping|legend=1| 1 1 -5 -1 | 0 2 25 13 }}


EDOs: 41, 58, 99, 239, 338, 915b, 1253bc
: mapping generators: ~2, ~49/40


Badness: 0.3728
[[Optimal tuning]]s:  
* [[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 }}


==7-limit==
[[Minimax tuning]]:
Commas: 2401/2400, 5120/5103
* [[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


7 and 9-limit minimax
[[Algebraic generator]]: (2 + sqrt(2))/2


[|1 0 0 0&gt;, |7/5, 0, 2/25, 0&gt;, |0 0 1 0&gt;, |8/5 0 13/25 0&gt;]
{{Optimal ET sequence|legend=1| 41, 58, 99, 239, 338 }}


Eigenvalues: 2, 5
[[Badness]] (Smith): 0.022243


Algebraic generator: (2 + sqrt(2))/2
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 1 -5 -1|, &lt;0 2 25 13|]
Comma list: 243/242, 441/440, 896/891


EDOs: [[41edo|41]], [[58edo|58]], [[99edo|99]], [[239edo|239]], [[338edo|338]]
Mapping: {{mapping| 1 1 -5 -1 2 | 0 2 25 13 5 }}


Badness: 0.0222
Optimal tunings:  
* CTE: ~2 = 1200.0000, ~11/9 = 351.4289
* POTE: ~2 = 1200.0000, ~11/9 = 351.5206


==11-limit==
{{Optimal ET sequence|legend=0| 17c, 41, 58, 99e }}
Commas: 243/242, 441/440, 896/891


POTE generator: ~11/9 = 351.521
Badness (Smith): 0.023498


Map: [&lt;1 1 -5 -1 2|, &lt;0 2 25 13 5|]
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


EDOs: 7ccd, 17c, 41, 58, 99e
Comma list: 144/143, 196/195, 243/242, 364/363


Badness: 0.0235
Mapping: {{mapping| 1 1 -5 -1 2 4 | 0 2 25 13 5 -1 }}


==13-limit==
Optimal tunings:
Commas: 144/143, 196/195, 243/242, 364/363
* CTE: ~2 = 1200.0000, ~11/9 = 351.4331
* POTE: ~2 = 1200.0000, ~11/9 = 351.5734


POTE generator: ~11/9 = 351.573
{{Optimal ET sequence|legend=0| 17c, 41, 58, 99ef, 157eff }}


Map: [&lt;1 1 -5 -1 2 4|, &lt;0 2 25 13 5 -1|]
Badness (Smith): 0.019090


EDOs: 7ccd, 17c, 41, 58, 99ef
=== Semihemi ===
Subgroup: 2.3.5.7.11


Badness: 0.0191
Comma list: 2401/2400, 3388/3375, 5120/5103


=Semihemi=
Mapping: {{mapping| 2 0 -35 -15 -47 | 0 2 25 13 34 }}
Commas: 2401/2400, 3388/3375, 9801/9800


POTE generator: ~49/40 = 351.505
: mapping generators: ~99/70, ~400/231


Map: [&lt;2 0 -35 -15 -47|, &lt;0 2 25 13 34|]
Optimal tunings:  
* CTE: ~99/70 = 600.0000, ~49/40 = 351.4722
* POTE: ~99/70 = 600.0000, ~49/40 = 351.5047


EDOs: 58, 140, 198, 734bc, 932bcd, 1130bcd
{{Optimal ET sequence|legend=0| 58, 140, 198 }}


Badness: 0.042487
Badness (Smith): 0.042487


==13-limit==
==== 13-limit ====
Commas: 352/351, 676/675, 847/845, 1716/1715
Subgroup: 2.3.5.7.11.13


POTE generator: ~49/40 = 351.502
Comma list: 352/351, 676/675, 847/845, 1716/1715


Map: [&lt;2 0 -35 -15 -47 -37|, &lt;0 2 25 13 34 28|]
Mapping: {{mapping| 2 0 -35 -15 -47 -37 | 0 2 25 13 34 28 }}


EDOs: 58, 140, 198, 536f, 734bcf, 932bcdf
Optimal tunings:  
* CTE: ~99/70 = 600.0000, ~49/40 = 351.4674
* POTE: ~99/70 = 600.0000, ~49/40 = 351.5019


Badness: 0.0212
{{Optimal ET sequence|legend=0| 58, 140, 198, 536f }}


=Tertiaseptal=
Badness (Smith): 0.021188
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 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. 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
=== Quadrafifths ===
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.


POTE generator: ~256/245 = 77.191
Subgroup: 2.3.5.7.11


Map: [&lt;1 3 2 3|, &lt;0 -22 5 -3|]
Comma list: 2401/2400, 3025/3024, 5120/5103


EDOs: 15, 16, 31, 109, 140, 171
Mapping: {{mapping| 1 1 -5 -1 8 | 0 4 50 26 -31 }}


Badness: 0.0130
: Mapping generators: ~2, ~243/220


==11-limit==
Optimal tunings:
Commas: 243/242, 441/440, 65625/65536
* CTE: ~2 = 1200.0000, ~243/220 = 175.7284
* POTE: ~2 = 1200.0000, ~243/220 = 175.7378


POTE generator: ~256/245 = 77.227
{{Optimal ET sequence|legend=0| 41, 157, 198, 239, 676b, 915be }}


Map: [&lt;1 3 2 3 7|, &lt;0 -22 5 -3 -55|]
Badness (Smith): 0.040170


EDOs: 15, 16, 31, 171, 202
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0356
Comma list: 352/351, 847/845, 2401/2400, 3025/3024


==13-limit==
Mapping: {{mapping| 1 1 -5 -1 8 10 | 0 4 50 26 -31 -43 }}
Commas: 243/242, 441/440, 625/624, 3584/3575


POTE generator: ~117/112 = 77.203
Optimal tunings:
* CTE: ~2 = 1200.0000, ~72/65 = 175.7412
* POTE: ~2 = 1200.0000, ~72/65 = 175.7470


Map: [&lt;1 3 2 3 7 1|, &lt;0 -22 5 -3 -55 42|]
{{Optimal ET sequence|legend=0| 41, 157, 198, 437f, 635bcff }}


EDOs: 31, 140e, 171
Badness (Smith): 0.031144


Badness: 0.0369
== Tertiaseptal ==
{{Main| Tertiaseptal }}


==17-limit==
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.
Commas: 243/242, 375/374, 441/440, 625/624, 3584/3575


POTE generator: ~68/65 = 77.201
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 3 2 3 7 1 1|, &lt;0 -22 5 -3 -55 42 48|]
[[Comma list]]: 2401/2400, 65625/65536


EDOs: 31, 140e, 171
{{Mapping|legend=1| 1 3 2 3 | 0 -22 5 -3 }}


Badness: 0.0274
: Mapping generators: ~2, ~256/245


==Tertia==
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~256/245 = 77.191
Commas: 385/384, 1331/1323, 1375/1372


POTE generator: ~22/21 = 77.173
{{Optimal ET sequence|legend=1| 31, 109, 140, 171 }}


Map: [&lt;1 3 2 3 5|, &lt;0 -22 5 -3 -24|]
[[Badness]]: 0.012995


EDOs: 31, 109, 140, 171e, 311e
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.0302
Comma list: 243/242, 441/440, 65625/65536


=Hemitert=
Mapping: {{mapping| 1 3 2 3 7 | 0 -22 5 -3 -55 }}
Commas: 2401/2400 3025/3024 65625/65536


POTE generator: ~45/44 = 38.596
Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.227


Map: [&lt;1 3 2 3 6|, &lt;0 -44 10 -6 -79|]
Optimal ET sequence: {{Optimal ET sequence| 31, 109e, 140e, 171, 202 }}


EDOs: 31, 280, 311, 342, 2021cde, 3731cde
Badness: 0.035576


Badness: 0.0156
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


=Harry=
Comma list: 243/242, 441/440, 625/624, 3584/3575
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.
Mapping: {{mapping| 1 3 2 3 7 1 | 0 -22 5 -3 -55 42 }}


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 ...||.
Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.203


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.
Optimal ET sequence: {{Optimal ET sequence| 31, 109e, 140e, 171 }}


[[POTE_tuning|POTE generator]]: ~21/20 = 83.156
Badness: 0.036876


Map: [&lt;2 4 7 7|, &lt;0 -6 -17 -10|]
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


Wedgie: &lt;&lt;12 34 20 26 -2 -49||
Comma list: 243/242, 375/374, 441/440, 625/624, 3584/3575


EDOs: 14c, 58, 72, 130, 202, 534, 938
Mapping: {{mapping| 1 3 2 3 7 1 1 | 0 -22 5 -3 -55 42 48 }}


Badness: 0.0341
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.201


==11-limit==
Optimal ET sequence: {{Optimal ET sequence| 31, 109eg, 140e, 171 }}
Commas: 243/242, 441/440, 4000/3993


[[POTE_tuning|POTE generator]]: ~21/20 = 83.167
Badness: 0.027398


Map: [&lt;2 4 7 7 9|, &lt;0 -6 -17 -10 -15|]
=== Tertia ===
Subgroup:2.3.5.7.11


EDOs: 14c, 58, 72, 130, 202
Comma list: 385/384, 1331/1323, 1375/1372


Badness: 0.0159
Mapping: {{mapping| 1 3 2 3 5 | 0 -22 5 -3 -24 }}


==13-limit==
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.173
Commas: 243/242, 351/350, 441/440, 676/675


POTE generator: ~21/20 = 83.116
Optimal ET sequence: {{Optimal ET sequence| 31, 109, 140, 171e, 311e }}


Map: [&lt;2 4 7 7 9 11|, &lt;0 -6 -17 -10 -15 -26|]
Badness: 0.030171


EDOs: 58, 72, 130, 462
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


Badness: 0.0130
Comma list: 352/351, 385/384, 625/624, 1331/1323


==17-limit==
Mapping: {{mapping| 1 3 2 3 5 1 | 0 -22 5 -3 -24 42 }}
Commas: 221/220, 243/242, 289/288, 351/350, 441/440


POTE generator: ~21/20 = 83.168
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.158


Map: [&lt;2 4 7 7 9 11 9|, &lt;0 -6 -17 -10 -15 -26 -6|]
Optimal ET sequence: {{Optimal ET sequence| 31, 109, 140, 311e, 451ee }}


EDOs: 58, 72, 130, 202g
Badness: 0.028384


Badness: 0.0127
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


=Quasiorwell=
Comma list: 352/351, 385/384, 561/560, 625/624, 715/714
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.
Mapping: {{mapping| 1 3 2 3 5 1 1 | 0 -22 5 -3 -24 42 48 }}


Commas: 2401/2400, 29360128/29296875
Optimal tuning (POTE): ~2 = 1\1, ~22/21 = 77.162


POTE generator: ~1024/875 = 271.107
Optimal ET sequence: {{Optimal ET sequence| 31, 109g, 140, 311e, 451ee }}


Map: [&lt;1 31 0 9|, &lt;0 -38 3 -8|]
Badness: 0.022416


EDOs: [[31edo|31]], [[177edo|177]], [[208edo|208]], [[239edo|239]], [[270edo|270]], [[571edo|571]], [[841edo|841]], [[1111edo|1111]]
=== Tertiaseptia ===
Subgroup: 2.3.5.7.11


Badness: 0.0358
Comma list: 2401/2400, 6250/6237, 65625/65536


==11-limit==
Mapping: {{mapping| 1 3 2 3 -4 | 0 -22 5 -3 116 }}
Commas: 2401/2400, 3025/3024, 5632/5625


POTE generator: ~90/77 = 271.111
Optimal tuning (POTE): ~2 = 1\1, ~256/245 = 77.169


Map: [&lt;1 31 0 9 53|, &lt;0 -38 3 -8 -64|]
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1695c, 2006bcd, 2317bcd, 2628bccde, 2939bccde, 3250bccde }}


EDOs: [[31edo|31]], [[208edo|208]], [[239edo|239]], [[270edo|270]]
Badness: 0.056926


Badness: 0.0175
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


==13-limit==
Comma list: 625/624, 2080/2079, 2200/2197, 2401/2400
Commas: 1001/1000, 1716/1715, 3025/3024, 4096/4095


POTE generator: ~90/77 = 271.107
Mapping: {{mapping| 1 3 2 3 -4 1 | 0 -22 5 -3 116 42 }}


Map: [&lt;1 31 0 9 53 -59|, &lt;0 -38 3 -8 -64 81|]
Optimal tuning (POTE): ~2 = 1\1, ~117/112 = 77.168


EDOs: [[31edo|31]], [[239edo|239]], [[270edo|270]], [[571edo|571]], [[841edo|841]], [[1111edo|1111]]
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1073, 1384cf, 1695cf, 2006bcdf }}


Badness: 0.0179
Badness: 0.027474


=Decoid=
==== 17-limit ====
In addition to 2401/2400, decoid tempers out 67108864/66976875 to temper 15/14 into one degree of [[10edo]]. Either 8/7 or 16/15 can be used its generator. It may be described as the 10&amp;270 temperament, and as one might expect, 181\940 or 233\1210 makes for an excellent tuning choice. It is also described as an extension of the [[Qintosec family|qintosec temperament]].
Subgroup: 2.3.5.7.11.13.17


Commas: 2401/2400, 67108864/66976875
Comma list: 595/594, 625/624, 833/832, 1156/1155, 2200/2197


POTE generator: ~8/7 = 231.099
Mapping: {{mapping| 1 3 2 3 -4 1 1 | 0 -22 5 -3 116 42 48 }}


Map: [&lt;10 0 47 36|, &lt;0 2 -3 -1|]
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169


Wedgie: &lt;&lt;20 -30 -10 -94 -72 61||
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}


EDOs: 10, 120, 130, 270
Badness: 0.018773


Badness: 0.0339
==== 19-limit ====
Subgroup: 2.3.5.7.11.13.17.19


==11-limit==
Comma list: 595/594, 625/624, 833/832, 1156/1155, 1216/1215, 2200/2197
Commas: 2401/2400, 5832/5825, 9801/9800


POTE generator: ~8/7 = 231.070
Mapping: {{mapping| 1 3 2 3 -4 1 1 11 | 0 -22 5 -3 116 42 48 -105 }}


Map: [&lt;10 0 47 36 98|, &lt;0 2 -3 -1 -8|]
Optimal tuning (POTE): ~2 = 1\1, ~68/65 = 77.169


EDOs: 130, 270, 670, 940, 1210
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311, 1384cfgg, 1695cfgg, 2006bcdfgg }}


Badness: 0.0187
Badness: 0.017653


==13-limit==
==== 23-limit ====
Commas: 676/675, 1001/1000, 1716/1715, 4225/4224
Subgroup: 2.3.5.7.11.13.17.19.23


POTE generator: ~8/7 = 231.083
Comma list: 595/594, 625/624, 833/832, 875/874, 1105/1104, 1156/1155, 1216/1215


Map: [&lt;10 0 47 36 98 37|, &lt;0 2 -3 -1 -8 0|]
Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 | 0 -22 5 -3 116 42 48 -105 117 }}


EDOs: 130, 270, 940, 1480
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.168


Badness: 0.0135
Optimal ET sequence: {{Optimal ET sequence| 140, 311, 762g, 1073g, 1384cfgg }}


=Neominor=
Badness: 0.015123
Commas: 2401/2400, 177147/175616


POTE generator: ~189/160 = 283.280
==== 29-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29


Map: [&lt;1 3 12 8|, &lt;0 -6 -41 -22|]
Comma list: 595/594, 625/624, 784/783, 833/832, 875/874, 1015/1014, 1105/1104, 1156/1155


Weggie: &lt;&lt;6 41 22 51 18 -64||
Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 | 0 -22 5 -3 116 42 48 -105 117 60 }}


EDOs: 72, 161, 233, 305
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.167


Badness: 0.0882
Optimal ET sequence: {{Optimal ET sequence| 140, 311, 762g, 1073g, 1384cfggj }}


==11-limit==
Badness: 0.012181
Commas: 243/242, 441/440, 35937/35840


POTE: ~33/28 = 283.276
==== 31-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31


Map: [&lt;1 3 12 8 7|, &lt;0 -6 -41 -22 -15|]
Comma list: 595/594, 625/624, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014


EDOs: 72, 161, 233, 305
Mapping: {{mapping| 1 3 2 3 -4 1 1 11 -3 1 11 | 0 -22 5 -3 116 42 48 -105 117 60 -94 }}


Badness: 0.0280
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169


==13-limit==
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}
Commas: 169/168, 243/242, 364/363, 441/440


POTE generator: ~13/11 = 283.294
Badness: 0.012311


Map: [&lt;1 3 12 8 7 7|, &lt;0 -6 -41 -22 -15 -14|]
==== 37-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37


EDOs: 72, 161f, 233f
Comma list: 595/594, 625/624, 703/702, 714/713, 784/783, 833/832, 875/874, 900/899, 931/930, 1015/1014


Badness: 0.0269
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 }}


=Emmthird=
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.170
The generator for emmthird temperament is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.


Commas: 2401/2400, 14348907/14336000
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}


POTE generator: ~2744/2187 = 392.988
Badness: 0.010949


Map: [&lt;1 11 42 25|,  &lt;0 -14 -59 -33|]
==== 41-limit ====
Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41


Wedgie: &lt;&lt;14 59 33 61 13 -89||
Comma list: 595/594, 625/624, 697/696, 703/702, 714/713, 784/783, 820/819, 833/832, 875/874, 900/899, 931/930


EDOs: 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d
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 }}


Badness: 0.0167
Optimal tuning (POTE): ~2 = 1\1, ~23/22 = 77.169


=Quinmite=
Optimal ET sequence: {{Optimal ET sequence| 140, 171, 311 }}
Commas: 2401/2400, 1959552/1953125


POTE generator: ~25/21 = 302.997
Badness: 0.009825


Map: [&lt;1 27 24 20|, &lt;0 -34 -29 -23|]
=== Hemitert ===
Subgroup: 2.3.5.7.11


Wedgie: &lt;&lt;34 29 23 -33 -59 -28||
Comma list: 2401/2400, 3025/3024, 65625/65536


EDOs: 95, 99, 202, 301, 400, 701, 1001c, 1802c, 2903c
Mapping: {{mapping| 1 3 2 3 6 | 0 -44 10 -6 -79 }}


Badness: 0.0373
: Mapping generators: ~2, ~45/44


=Unthirds=
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.596
Commas: 2401/2400, 68359375/68024448


POTE generator: ~3969/3125 = 416.717
Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 342 }}


Map: [&lt;1 29 33 25|, &lt;0 -42 -47 -34|]
Badness: 0.015633


Wedgie: &lt;&lt;42 47 34 -23 -64 -53||
==== 13-limit ====
Subgroup: 2.3.5.7.11.13


EDOs: 72, 167, 239, 311, 694, 1005c
Comma list: 625/624, 1575/1573, 2401/2400, 4096/4095


Badness: 0.0753
Mapping: {{mapping| 1 3 2 3 6 1 | 0 -44 10 -6 -79 84 }}


==11-limit==
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.588
Commas: 2401/2400, 3025/3024, 4000/3993


POTE generator: ~14/11 = 416.718
Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 964f, 1275f, 1586cff }}


Map: [&lt;1 29 33 25 25|, &lt;0 -42 -47 -34 -33|]
Badness: 0.033573


EDOs: 72, 167, 239, 311, 1316c
==== 17-limit ====
Subgroup: 2.3.5.7.11.13.17


Badness: 0.0229
Comma list: 625/624, 833/832, 1225/1224, 1575/1573, 4096/4095


==13-limit==
Mapping: {{mapping| 1 3 2 3 6 1 1 | 0 -44 10 -6 -79 84 96 }}
Commas: 625/624, 1575/1573, 2080/2079, 2401/2400


POTE generator: ~14/11 = 416.716
Optimal tuning (POTE): ~2 = 1\1, ~45/44 = 38.589


Map: [&lt;1 29 33 25 25 99|, &lt;0 -42 -47 -34 -33 -146|]
Optimal ET sequence: {{Optimal ET sequence| 31, 280, 311, 653f, 964f }}


EDOs: 72, 311, 694, 1005c, 1699cd
Badness: 0.025298


Badness: 0.0209
=== Semitert ===
Subgroup: 2.3.5.7.11


=Newt=
Comma list: 2401/2400, 9801/9800, 65625/65536
Commas: 2401/2400, 33554432/33480783


POTE generator: ~49/40 = 351.113
Mapping: {{mapping| 2 6 4 6 1 | 0 -22 5 -3 46 }}


Map: [&lt;1 1 19 11|, &lt;0 2 -57 -28|]
: Mapping generators: ~99/70, ~256/245


Wedgie: &lt;&lt;2 -57 -28 -95 -50 95||
Optimal tuning (POTE): ~99/70 = 1\2, ~256/245 = 77.193


EDOs: 41, 188, 229, 270, 1121, 1391, 1661, 1931, 2201, 6333bc
Optimal ET sequence: {{Optimal ET sequence| 62e, 140, 202, 342 }}


Badness: 0.0419
Badness: 0.025790


==11-limit==
== Quasiorwell ==
Commas: 2401/2400, 3025/3024, 19712/19683
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.


POTE generator: ~49/40 = 351.115
Adding 3025/3024 extends to the 11-limit and as expected, 270 remains an excellent tuning.


Map: [&lt;1 1 19 11 -10|, &lt;0 2 -57 -28 46|]
[[Subgroup]]: 2.3.5.7


EDOs: 41, 188, 229, 270, 581, 851, 1121, 1972, 3093b, 4214b
[[Comma list]]: 2401/2400, 29360128/29296875


Badness: 0.0195
{{Mapping|legend=1| 1 31 0 9 | 0 -38 3 -8 }}


==13-limit==
: Mapping generators: ~2, ~875/512
Commas: 2080/2079, 2401/2400, 3025/3024, 4096/4095


POTE genertaor: ~49/40 = 351.117
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~1024/875 = 271.107


Map: [&lt;1 1 19 11 -10 -20|, &lt;0 2 -57 -28 46 81|]
{{Optimal ET sequence|legend=1| 31, 177, 208, 239, 270, 571, 841, 1111 }}


EDOs: 41, 229, 270, 581, 851, 2283b, 3134b
[[Badness]]: 0.035832


Badness: 0.0138
=== 11-limit ===
Subgroup: 2.3.5.7.11


=Amicable=
Comma list: 2401/2400, 3025/3024, 5632/5625
Commas: 2401/2400, 1600000/1594323


POTE generator: ~21/20 = 84.880
Mapping: {{mapping| 1 31 0 9 53 | 0 -38 3 -8 -64 }}


Map: [&lt;1 3 6 5|, &lt;0 -20 -52 -31|]
Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.111


Wedgie: &lt;&lt;20 52 31 36 -7 -74||
Optimal ET sequence: {{Optimal ET sequence| 31, 208, 239, 270 }}


EDOs: 99, 212, 311, 410, 1131, 1541b
Badness: 0.017540


Badness: 0.0455
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=Septidiasemi=
Comma list: 1001/1000, 1716/1715, 3025/3024, 4096/4095
Commas: 2401/2400, 2152828125/2147483648


POTE generator: ~15/14 = 119.297
Mapping: {{mapping| 1 31 0 9 53 -59 | 0 -38 3 -8 -64 81 }}


Map: [&lt;1 25 -31 -8|, &lt;0 -26 37 12|]
Optimal tuning (POTE): ~2 = 1\1, ~90/77 = 271.107


Wedgie: &lt;&lt;26 -37 -12 -119 -92 76||
Optimal ET sequence: {{Optimal ET sequence| 31, 239, 270, 571, 841, 1111 }}


EDOs: 10, 151, 161, 171, 3581bcd, 3752bcd, 3923bcd, 4094bcd, 4265bcd, 4436bcd, 4607bcd
Badness: 0.017921


Badness: 0.0441
== Neominor ==
The generator for neominor temperament is tridecimal minor third [[13/11]], also known as ''Neo-gothic minor third''.


=Maviloid=
[[Subgroup]]: 2.3.5.7
Commas: 2401/2400, 1224440064/1220703125


POTE generator: ~1296/875 = 678.810
[[Comma list]]: 2401/2400, 177147/175616


Map: [&lt;1 31 34 26|, &lt;0 -52 -56 -41|]
{{Mapping|legend=1| 1 3 12 8 | 0 -6 -41 -22 }}


Wedgie: &lt;&lt;52 56 41 -32 -81 -62||
: Mapping generators: ~2, ~189/160


EDOs: 76, 99, 274, 373, 472, 571, 1043, 1614
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~189/160 = 283.280


Badness: 0.0576
{{Optimal ET sequence|legend=1| 72, 161, 233, 305 }}


=Subneutral=
[[Badness]]: 0.088221
Commas: 2401/2400, 274877906944/274658203125


POTE generator: ~57344/46875 = 348.301
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 19 0 6}, &lt;0 -60 8 -11|]
Comma list: 243/242, 441/440, 35937/35840


Wedgie: &lt;&lt;60 -8 11 -152 -151 48||
Mapping: {{mapping| 1 3 12 8 7 | 0 -6 -41 -22 -15 }}


EDOs: 31, 348, 379, 410, 441, 1354, 1795, 2236
Optimal tuning (POTE): ~2 = 1\1, ~33/28 = 283.276


Badness: 0.0458
Optimal ET sequence: {{Optimal ET sequence| 72, 161, 233, 305 }}


=Osiris=
Badness: 0.027959
Commas: 2401/2400, 31381059609/31360000000


POTE generator: ~2800/2187 = 428.066
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


Map: [&lt;1 13 33 21|, &lt;0 -32 -86 -51|]
Comma list: 169/168, 243/242, 364/363, 441/440


Wedgie: &lt;&lt;32 86 51 62 -9 -123||
Mapping: {{mapping| 1 3 12 8 7 7 | 0 -6 -41 -22 -15 -14 }}


EDOs: 157, 171, 1012, 1183, 1354, 1525, 1696, 6955d
Optimal tuning (POTE): ~2 = 1\1, ~13/11 = 283.294


Badness: 0.0283
Optimal ET sequence: {{Optimal ET sequence| 72, 161f, 233f }}


=Gorgik=
Badness: 0.026942
Commas: 2401/2400, 28672/28125


POTE generator: ~8/7 = 227.512
== Emmthird ==
The generator for emmthird is the hemimage third, sharper than 5/4 by the hemimage comma, 10976/10935.


Map: [&lt;1 5 1 3|, &lt;0 -18 7 -1|]
[[Subgroup]]: 2.3.5.7


Wedgie: &lt;&lt;18 -7 1 -53 -49 22||
[[Comma list]]: 2401/2400, 14348907/14336000


EDOs: 21, 37, 58, 153bc, 211bcd, 269bcd
{{Mapping|legend=1| 1 11 42 25 | 0 -14 -59 -33 }}


Badness: 0.1584
: Mapping generators: ~2, ~2187/1372


==11-limit==
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~2744/2187 = 392.988
Commas: 176/175, 2401/2400, 2560/2541


POTE generator: ~8/7 = 227.500
{{Optimal ET sequence|legend=1| 58, 113, 171, 742, 913, 1084, 1255, 2681d, 3936d }}


Map: [&lt;1 5 1 3 1|, &lt;0 -18 7 -1 13|]
[[Badness]]: 0.016736


EDOs: 21, 37, 58, 153bce, 211bcde, 269bcde
=== 11-limit ===
Subgroup: 2.3.5.7.11


Badness: 0.059
Comma list: 243/242, 441/440, 1792000/1771561


==13-limit==
Mapping: {{mapping| 1 11 42 25 27 | 0 -14 -59 -33 -35 }}
Commas: 176/175, 196/195, 364/363, 512/507


POTE generator: ~8/7 = 227.493
Optimal tuning (POTE): ~2 = 1\1, ~1372/1089 = 392.991


Map: [&lt;1 5 1 3 1 2|, &lt;0 -18 7 -1 13 9|]
Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}


EDOs: 21, 37, 58, 153bcef, 211bcdef
Badness: 0.052358


Badness: 0.0322
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


=Fibo=
Comma list: 243/242, 364/363, 441/440, 2200/2197
Commas: 2401/2400, 341796875/339738624


POTE generator: ~125/96 = 454.310
Mapping: {{mapping| 1 11 42 25 27 38 | 0 -14 -59 -33 -35 -51 }}


Map: [&lt;1 19 8 10|, &lt;0 -46 -15 -19|]
Optimal tuning (POTE): ~2 = 1\1, ~180/143 = 392.989


Wedgie: &lt;&lt;46 15 19 -83 -99 2||
Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}


EDOs: 37, 103, 140, 243, 383, 1009cd, 1392cd
Badness: 0.026974


Badness: 0.1005
=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17


==11-limit==
Comma list: 243/242, 364/363, 441/440, 595/594, 2200/2197
Commas: 385/384, 1375/1372, 43923/43750


POTE generator: ~100/77 = 454.318
Mapping: {{mapping| 1 -3 -17 -8 -8 -13 9 | 0 14 59 33 35 51 -15 }}


Map: [&lt;1 19 8 10 8|, &lt;0 -46 -15 -19 -12|]
Optimal tuning (POTE): ~2 = 1\1, ~64/51 = 392.985


EDOs: 37, 103, 140, 243e
Optimal ET sequence: {{Optimal ET sequence| 58, 113, 171 }}


Badness: 0.0565
Badness: 0.023205


==13-limit==
== Quinmite ==
Commas: 385/384, 625/624, 847/845, 1375/1372
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>.


POTE generator: ~13/10 = 454.316
[[Subgroup]]: 2.3.5.7


Map: [&lt;1 19 8 10 8 9|, &lt;0 -46 -15 -19 -12 -14|]
[[Comma list]]: 2401/2400, 1959552/1953125


EDOs: 37, 103, 140, 243e
{{Mapping|legend=1| 1 27 24 20 | 0 -34 -29 -23 }}


Badness: 0.0274
: Mapping generators: ~2, ~42/25


=Mintone=
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~25/21 = 302.997
In addition to 2401/2400, mintone tempers out 177147/175000 = |-3 11 -5 -1&gt; 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.


==7-limit==
{{Optimal ET sequence|legend=1| 99, 202, 301, 400, 701, 1101c, 1802c, 2903cc }}
Commas: 2401/2400, 177147/175000


POTE generator: ~10/9 = 186.343
[[Badness]]: 0.037322


Map: [&lt;1 5 9 7|, &lt;0 -22 -43 -27|]
== 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.


EDOs: 45, 58, 103, 161, 586b, 747bc, 908bc
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).


Badness: 0.12567
[[Subgroup]]: 2.3.5.7


==11-limit==
[[Comma list]]: 2401/2400, 68359375/68024448
Commas: 243/242, 441/440, 43923/43750


POTE generator: ~10/9 = 186.345
{{Mapping|legend=1| 1 29 33 25 | 0 -42 -47 -34 }}


Map: [&lt;1 5 9 7 12|, &lt;0 -22 -43 -27 -55|]
: Mapping generators: ~2, ~6125/3888


EDOs: 58, 103, 161, 425b, 586b, 747bc
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3969/3125 = 416.717


Badness: 0.0400
{{Optimal ET sequence|legend=1| 72, 167, 239, 311, 694, 1005c }}


==13-limit==
[[Badness]]: 0.075253
Commas: 243/242, 351/350, 441/440, 847/845


POTE generator: ~10/9 = 186.347
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 5 9 7 12 11|, &lt;0 -22 -43 -27 -55 -47|]
Comma list: 2401/2400, 3025/3024, 4000/3993


EDOs: 58, 103, 161
Mapping: {{mapping| 1 29 33 25 25 | 0 -42 -47 -34 -33 }}


Badness: 0.0218
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.718


==17-limit==
Optimal ET sequence: {{Optimal ET sequence| 72, 167, 239, 311 }}
Commas: 243/242, 351/350, 441/440, 561/560, 847/845


POTE generator: ~10/9 = 186.348
Badness: 0.022926


Map: [&lt;1 5 9 7 12 11 3|, &lt;0 -22 -43 -27 -55 -47 7|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 58, 103, 161, 264
Comma list: 625/624, 1575/1573, 2080/2079, 2401/2400


=Catafourth=
Mapping: {{mapping| 1 29 33 25 25 99 | 0 -42 -47 -34 -33 -146 }}
Commas: 2401/2400, 78732/78125


POTE generator: ~250/189 = 489.235
Optimal tuning (POTE): ~2 = 1\1, ~14/11 = 416.716


Map: [&lt;1 13 17 13|, &lt;0 -28 -36 -25|]
Optimal ET sequence: {{Optimal ET sequence| 72, 239f, 311, 694, 1005c }}


Wedgie: &lt;&lt;28 36 25 -8 -39 -43||
Badness: 0.020888


EDOs: 27, 76, 103, 130
== 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.


Badness: 0.0796
[[Subgroup]]: 2.3.5.7


==11-limit==
[[Comma list]]: 2401/2400, 33554432/33480783
Commas: 243/242, 441/440, 78408/78125


POTE generator: ~250/189 = 489.252
{{Mapping|legend=1| 1 1 19 11 | 0 2 -57 -28 }}


Map: [&lt;1 13 17 13 32|, &lt;0 -28 -36 -25 -70|]
: mapping generators: ~2, ~49/40


EDOs: 103, 130, 233, 363, 493e, 856be
[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/40 = 351.113


Badness: 0.0368
{{Optimal ET sequence|legend=1| 41, 147c, 188, 229, 270, 1121, 1391, 1661, 1931, 2201 }}


==13-limit==
[[Badness]]: 0.041878
Commas: 243/242, 351/350, 441/440, 10985/10976


POTE generator: ~65/49 = 489.256
=== 11-limit ===
Subgroup: 2.3.5.7.11


Map: [&lt;1 13 17 13 32 9|, &lt;0 -28 -36 -25 -70 -13|]
Comma list: 2401/2400, 3025/3024, 19712/19683


EDOs: 103, 130, 233, 363
Mapping: {{mapping| 1 1 19 11 -10 | 0 2 -57 -28 46 }}


Badness: 0.0217
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.115


=Cotritone=
Optimal ET sequence: {{Optimal ET sequence| 41, 147ce, 188, 229, 270, 581, 851, 1121, 1972 }}
Commas: 2401/2400, 390625/387072


POTE generator: ~7/5 = 583.3848
Badness: 0.019461


Map: [&lt;1 -13 -4 -4|, &lt;0 30 13 14|]
=== 13-limit ===
Subgroup: 2.3.5.7.11.13


EDOs: 35, 37, 72, 109, 181, 253
Comma list: 2080/2079, 2401/2400, 3025/3024, 4096/4095


==11-limit==
Mapping: {{mapping| 1 1 19 11 -10 -20 | 0 2 -57 -28 46 81 }}
Commas: 385/384, 1375/1372, 4000/3993


POTE generator: ~7/5 = 583.3872
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.117


Map: [&lt;1 -13 -4 -4 2|, &lt;0 30 13 14 3|]
Optimal ET sequence: {{Optimal ET sequence| 41, 147cef, 188f, 229, 270, 581, 851, 2283b, 3134b }}


EDOs: 35, 37, 72, 109, 181, 253
Badness: 0.013830


==13-limit==
=== 2.3.5.7.11.13.19 subgroup (neonewt) ===
Commas: 169/168, 364/363, 385/384, 625/624
Subgroup: 2.3.5.7.11.13.19


POTE generator: ~7/5 = 583.3866
Comma list: 1216/1215, 1540/1539, 1729/1728, 2080/2079, 2401/2400


Map: [&lt;1 -13 -4 -4 2 -7|, &lt;0 30 13 14 3 22|]
Mapping: {{mapping| 1 1 19 11 -10 -20 18 | 0 2 -57 -28 46 81 -47 }}


EDOs: 37, 72, 109, 181f
Optimal tuning (POTE): ~2 = 1\1, ~49/40 = 351.117


[[Category:breed]]
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]]
Retrieved from "https://en.xen.wiki/w/Breedsmic_temperaments"