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The [[2.3.7 subgroup|2.3.7-subgroup]] [[comma]] for the '''gamelismic clan''' is the gamelisma, [[1029/1024]], with [[monzo]] {{monzo| -10 1 0 3 }}. For any member of the clan, for the rank-3 [[gamelismic family #Gamelismic|gamelismic temperament]] itself, and for the rank-2 2.3.7 temperament [[slendric]] (a.k.a. gamelic), this means three [[~]][[8/7]] intervals give a fifth, [[3/2]]. In fact, we find that 3/2 = (8/7)<sup>3</sup> × 1029/1024. From this it follows that gamelismic temperaments tend to flatten both the fifth and the harmonic seventh, or if they do not, the other of the pair must be flattened even more. [[36edo]] is a good tuning for slendric, though if the full 7-limit is desired, [[72edo]], [[77edo]] or [[118edo]] might be preferred.

To the gamelisma itself we need to add the comma which appears next on the modified [[Normal lists #Normal interval list|normal comma list]] for the full 7-limit. The second comma on the list for mothra is [[81/80]], for rodan [[245/243]], for guiron [[32805/32768]], for gorgo [[36/35]], and for gidorah [[256/245]]. These all use ~8/7 as a generator, though in the case of gidorah that is the same as ~6/5. 

Miracle adds [[33075/32768]] and uses the [[secor]], half an ~8/7, as generator. Lemba adds [[525/512]] to the list, and has a half-octave [[period]]. Valentine adds [[6144/6125]] with a generator of ~21/20 and superkleismic adds [[875/864]] with a generator of ~6/5. Unidec adds [[4375/4374]], and has a generator of ~10/9 with a half-octave period. Hemithirds adds [[65625/65536]] with a generator half of a classical major third. Finally, tritikleismic adds [[15625/15552]] and has a generator of 6/5 with a 1/3-octave period.

Full 7-limit temperaments discussed elsewhere are:
* [[Lemba]] (+50/49) → [[Jubilismic clan #Lemba|Jubilismic clan]]
* ''[[Echidnic]]'' (+686/675} → [[Diaschismic family #Echidnic|Diaschismic family]]
* [[Valentine]] (+126/125) → [[Starling temperaments #Valentine|Starling temperaments]]
* [[Superkleismic]] (+875/864) → [[Shibboleth family #Superkleismic|Shibboleth family]]
* ''[[Blacksmith]]'' (+28/27) → [[Limmic temperaments #Blacksmith|Limmic temperaments]]
* ''[[Trismegistus]]'' (+3125/3072) → [[Magic family #Trismegistus|Magic family]]
* [[Hemithirds]] (+3136/3125) → [[Hemimean clan #Hemithirds|Hemimean clan]]
* ''[[Gamity]]'' (+1071875/1062882) → [[Amity family #Gamity|Amity family]]
* ''[[Tritikleismic]]'' (+15625/15552) → [[Kleismic family #Tritikleismic|Kleismic family]]
* ''[[Heinz]]'' (+78732/78125) → [[Sensipent family #Heinz|Sensipent family]]
* ''[[Triwell]]'' (+235298/234375) → [[Semicomma family #Triwell|Semicomma family]]
* ''[[Decades]]'' (+118098/117649) → [[Compton family #Decades|Compton family]]

The rest are considered below.

No-five subgroup extensions of slendric include radon, a 2.3.7.11 extension that may be viewed as no-five rodan, and baladic, a 2.3.7.13.17 extension, considered below. Dicussed elsewhere is [[No-fives subgroup temperaments #Gigapyth|gigapyth]] in the 2.3.7.85 subgroup. 

== Slendric ==
{{Main| Slendric }}

[[Subgroup]]: 2.3.7

[[Comma list]]: 1029/1024

{{Mapping|legend=2| 1 1 3 | 0 3 -1 }}

: sval mapping generators: ~2, ~8/7

{{Mapping|legend=3| 1 1 0 3 | 0 3 0 -1 }}

: [[gencom]]: [2 8/7; 1029/1024] 

[[Optimal tuning]]s: 
* [[CTE]]: ~2 = 1200.000, ~8/7 = 233.889
* [[POTE]]: ~2 = 1200.000, ~8/7 = 233.688

{{Optimal ET sequence|legend=1| 36, 77, 113, 190 }}

=== Radon ===
[[Subgroup]]: 2.3.7.11

[[Comma list]]: 896/891, 1029/1024

{{Mapping|legend=2| 1 1 3 6 | 0 3 -1 -13 }}

{{Mapping|legend=3| 1 1 0 3 6 | 0 3 0 -1 -13 }}

: [[gencom]]: [2 8/7; 896/891 1029/1024]

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 234.381

{{Optimal ET sequence|legend=1| 36, 41, 87, 128 }}

=== Baladic ===
Baladic is a 2.3.7.13.17 subgroup temperament that attempts to approximate the Maqam Sikah Baladi scale. 36edo is an excellent baladic tuning.

[[Subgroup]]: 2.3.7.13.17

[[Comma list]]: 169/168, 273/272, 289/288

{{Mapping|legend=2| 2 2 6 7 7 | 0 3 -1 1 3 }}

: sval mapping generators: ~17/12, ~8/7

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 233.616

{{Optimal ET sequence|legend=1| 10, 26, 36, 154f, 190ffg, 226ffg }}

== Rodan ==
{{Main| Rodan }}
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #Rodan (5-limit)]].''

Rodan tempers out 245/243 and can be described as the 41 & 46 temperament. This temperament extends neatly to the 13-limit, though the perfect fifth is sharper than ideal for slendric. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 245/243, 1029/1024

{{Mapping|legend=1| 1 1 -1 3 | 0 3 17 -1 }}

{{Multival|legend=1| 3 17 -1 20 -10 -50 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 234.417

[[Minimax tuning]]: 
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 2/9 0 1/18 -1/18 }}
: {{monzo list| 1 0 0 0 | 5/3 0 1/6 -1/6 | 25/9 0 17/18 -17/18 | 25/9 0 -1/18 1/18 }}
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5

[[Algebraic generator]]: larger root of 20''x''<sup>2</sup> - 36''x'' + 15, or (9 + √6)/10.

{{Optimal ET sequence|legend=1| 41, 87, 128, 215d }}

[[Badness]] (Smith): 0.037112

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 245/243, 385/384, 441/440

Mapping: {{mapping| 1 1 -1 3 6 | 0 3 17 -1 -13 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.459

Minimax tuning: 
* 11-odd-limit: ~8/7 = {{monzo| 4/19 2/19 0 0 -1/19 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 31/19 6/19 0 0 -3/19 }}, {{monzo| 49/19 34/19 0 0 -17/19 }}, {{monzo| 53/19 -2/19 0 0 1/19 }}, {{monzo| 62/19 -26/19 0 0 13/19 }}]
: eigenmonzo (unchanged-interval) basis: 2.11/9

Algebraic generator: positive root of ''x''<sup>2</sup> + 16''x'' - 31, or √95 - 8.

{{Optimal ET sequence|legend=0| 41, 46, 87 }}

Badness (Smith): 0.023093

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 245/243, 352/351, 364/363

Mapping: {{mapping| 1 1 -1 3 6 8 | 0 3 17 -1 -13 -22 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.482

Minimax tuning: 
* 13- and 15-odd-limit: ~8/7 = {{monzo| 3/14 1/14 0 0 0 -1/28 }}
: eigenmonzo (unchanged-interval) basis: 2.13/9

Algebraic generator: Gatetone, positive root of 4''x''<sup>6</sup> - 7''x'' - 1. Recurrence converges slowly.

{{Optimal ET sequence|legend=0| 41, 46, 87 }}

Badness (Smith): 0.018448

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 154/153, 196/195, 245/243, 256/255, 273/272

Mapping: {{mapping| 1 1 -1 3 6 8 8 | 0 3 17 -1 -13 -22 -20 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.524

Minimax tuning:
* 17-odd-limit: ~8/7 = {{monzo| 3/13 1/13 0 0 0 0 -1/26 }}
: eigenmonzo (unchanged-interval) basis: 2.17/9

{{Optimal ET sequence|legend=0| 41, 46, 87, 220dg, 307dgg }}

Badness (Smith): 0.016743

==== Aerodactyl ====
Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 245/243, 385/384, 441/440

Mapping: {{mapping| 1 1 -1 3 6 -1 | 0 3 17 -1 -13 24 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.639

{{Optimal ET sequence|legend=0| 5, 41f, 46, 133ff }}

Badness (Smith): 0.033986

=== Aerodino ===
Subgroup: 2.3.5.7.11

Comma list: 176/175, 245/243, 1029/1024

Mapping: {{mapping| 1 1 -1 3 -3 | 0 3 17 -1 33 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.728

{{Optimal ET sequence|legend=0| 41e, 46 }}

Badness (Smith): 0.054294

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 91/90, 176/175, 245/243, 847/845

Mapping: {{mapping| 1 1 -1 3 -3 -1 | 0 3 17 -1 33 24 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.782

{{Optimal ET sequence|legend=0| 41ef, 46 }}

Badness (Smith): 0.035836

=== Varan ===
Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/243, 1029/1024

Mapping: {{mapping| 1 1 -1 3 -2 | 0 3 17 -1 28 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.145

{{Optimal ET sequence|legend=0| 36ce, 41 }}

Badness (Smith): 0.044937

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 105/104, 245/243, 352/351

Mapping: {{mapping| 1 1 -1 3 -2 0 | 0 3 17 -1 28 19 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 234.089

{{Optimal ET sequence|legend=0| 36ce, 41 }}

Badness (Smith): 0.032284

== Guiron ==
Guiron tempers out the [[schisma]], and finds the prime 5 at the diminished fourth as does any temperament in the [[schismatic family]]. It can be described as 36 & 41. It is more complex than rodan, but the optimal tuning is closer to optimal slendric. 

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 10976/10935

{{Mapping|legend=1| 1 1 7 3 | 0 3 -24 -1 }}

: mapping generators: ~2, ~8/7

{{Multival|legend=1| 3 -24 -1 -45 -10 65 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 233.930

[[Minimax tuning]]:
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 7/24 0 -1/24 }}
: {{monzo list| 1 0 0 0 | 15/8 0 -1/8 0 | 0 0 1 0 | 65/24 0 1/24 0 }}
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5

{{Optimal ET sequence|legend=1| 36, 41, 77, 118, 277d }}

[[Badness]] (Smith): 0.047544

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 10976/10935

Mapping: {{mapping| 1 1 7 3 -2 | 0 3 -24 -1 28 }}

: mapping generators: ~2, ~8/7

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 233.931

Minimax tuning:
* 11-odd-limit: ~8/7 = {{monzo| 7/24 0 -1/24 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 15/8 0 -1/8 0 0 }}, {{monzo| 0 0 1 0 0 }}, {{monzo| 65/24 0 1/24 0 0 }}, {{monzo| 37/6 0 -7/6 0 0 }}]
: eigenmonzo (unchanged-interval) basis: 2.5

{{Optimal ET sequence|legend=0| 36e, 41, 77, 118, 159, 277d }}

Badness (Smith): 0.026648

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 729/728

Mapping: {{mapping| 1 1 7 3 -2 0 | 0 3 -24 -1 28 19 }}

: mapping generators: ~2, ~8/7

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 233.890

{{Optimal ET sequence|legend=0| 36e, 41, 77, 118 }}

Badness (Smith): 0.028444

== Mothra ==
Mothra tempers out [[81/80]] and finds the prime 5 at a stack of four fifths as does any temperament in the [[meantone family]]. It also tempers out [[1728/1715]], the orwellisma. It can be described as 26 & 31. Using [[31edo]] with a generator of 6/31 is an excellent tuning choice. However, a pure mos mothra scale is often described as directionless and has limited chord-building potential<ref>https://www.youtube.com/watch?v=uH3ahBzDSrs</ref>, so something other than a mos may be used as a scale to get the most out of mothra. There are examples of non-mos mothra scales in 31edo [[Strictly proper 7-tone 31edo scales|in the article on strictly proper 7-tone 31edo scales]]. 

Note that mothra is also called '''cynder''' in the 7-limit, which can be a little confusing sometimes. 

Its [[S-expression]]-based comma list is {[[1728/1715|S6/S7]], [[1029/1024|S7/S8]](, [[81/80|S6/S8 = S9]])}, taking advantage of the fact that [[81/80]] is a [[semiparticular]].

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 81/80, 1029/1024

{{Mapping|legend=1| 1 1 0 3 | 0 3 12 -1 }}

: mapping generators: ~2, ~8/7

{{Multival|legend=1| 3 12 -1 12 -10 -36 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 232.193

[[Algebraic generator]]: Rabrindanath, largest real root of ''x''<sup>8</sup> - 3''x''<sup>2</sup> + 1, or 232.0774 cents.

[[Minimax tuning]]: 
* [[7-odd-limit|7-]] and [[9-odd-limit]]: ~8/7 = {{monzo| 0 0 1/12 }}
: [{{monzo| 1 0 0 0 }}, {{monzo| 1 0 1/4 0 }}, {{monzo| 0 0 1 0 }}, {{monzo| 3 0 -1/12 0 }}]
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5

{{Optimal ET sequence|legend=1| 5, 26, 31 }}

[[Badness]] (Smith): 0.037146

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 81/80, 99/98, 385/384

Mapping: {{mapping| 1 1 0 3 5 | 0 3 12 -1 -8 }}

{{Multival|legend=1| 3 12 -1 -8 12 -10 -23 -36 -60 -19 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 232.031

{{Optimal ET sequence|legend=0| 5, 26, 31, 88, 150be, 181bee }}

Badness (Smith): 0.025642

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 81/80, 99/98, 105/104, 144/143

Mapping: {{mapping| 1 1 0 3 5 1 | 0 3 12 -1 -8 14 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 231.811

{{Optimal ET sequence|legend=0| 5, 26, 31, 57, 88 }}

Badness (Smith): 0.023954

; Music
* ''Prelude for solo piano'' (2014) by [[Chris Vaisvil]] – [https://web.archive.org/web/20201127013310/http://micro.soonlabel.com/16-ET/mothra/20141028_mothra16br4.mp3 play] | [https://www.chrisvaisvil.com/prelude-for-solo-piano-in-mothra16-brat-4-tuning/ blog] – in Mothra[16], brat 4 tuning

=== Cynder ===
Subgroup: 2.3.5.7.11

Comma list: 45/44, 81/80, 1029/1024

Mapping: {{mapping| 1 1 0 3 0 | 0 3 12 -1 18 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 231.317

{{Optimal ET sequence|legend=0| 5e, 26, 57e, 83bce }}

Badness (Smith): 0.055706

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 45/44, 78/77, 81/80, 640/637

Mapping: {{mapping| 1 1 0 3 0 1 | 0 3 12 -1 18 14 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 231.293

{{Optimal ET sequence|legend=0| 5e, 26, 57e, 83bce }}

Badness (Smith): 0.034124

=== Mosura ===
The S-expression-based comma list of mosura suggests it might be the most natural extension of 7-limit cynder to the 11-limit: {[[1728/1715|S6/S7]], [[1029/1024|S7/S8]], ([[81/80|S6/S8 = S9]],) [[176/175|S8/S10]]}.

Subgroup: 2.3.5.7.11

Comma list: 81/80, 176/175, 540/539

Mapping: {{mapping| 1 1 0 3 -1 | 0 3 12 -1 23 }}

Wedgie: {{Multival| 3 12 -1 23 12 -10 26 -36 12 68 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 232.419

{{Optimal ET sequence|legend=0| 31, 129, 160be, 191bce, 222bce, 253bcee }}

Badness (Smith): 0.031334

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 81/80, 144/143, 176/175, 196/195

Mapping: {{mapping| 1 1 0 3 -1 7 | 0 3 12 -1 23 -17 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 232.640

{{Optimal ET sequence|legend=0| 31, 36, 67, 98 }}

Badness (Smith): 0.036857

== Gorgo ==
In the 5-limit, gorgo tempers out the laconic comma, [[2187/2000]], which is the difference between three [[10/9]]'s and a [[3/2]]. Although a higher-error temperament, it does pop up enough in the low-numbered edos to be useful, most notably in [[16edo]] and [[21edo]]. The only 7-limit extension that makes any sense to use is to add the gamelisma to the comma list.

=== 5-limit (laconic) ===
[[Subgroup]]: 2.3.5

[[Comma list]]: 2187/2000

{{Mapping|legend=1| 1 1 1 | 0 3 7 }}

{{Multival|legend=1| 3 7 4 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~10/9 = 227.426

{{Optimal ET sequence|legend=1| 5, 16, 21, 37b }}

[[Badness]] (Smith): 0.161799

=== 7-limit ===
[[Subgroup]]: 2.3.5.7

[[Comma list]]: 36/35, 1029/1024

{{Mapping|legend=1| 1 1 1 3 | 0 3 7 -1 }}

{{Multival|legend=1| 3 7 -1 4 -10 -22 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 228.334

{{Optimal ET sequence|legend=1| 5, 11c, 16, 21 }}

[[Badness]] (Smith): 0.060663

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 36/35, 45/44, 1029/1024

Mapping: {{mapping| 1 1 1 3 1 | 0 3 7 -1 13 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 227.373

{{Optimal ET sequence|legend=0| 16, 21, 37b }}

Badness (Smith): 0.049500

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 45/44, 507/500

Mapping: {{mapping| 1 1 1 3 1 2 | 0 3 7 -1 13 9 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 227.230

{{Optimal ET sequence|legend=0| 16, 21, 37b }}

Badness (Smith): 0.032664

=== Spartan ===
Subgroup: 2.3.5.7.11

Comma list: 36/35, 56/55, 1029/1024

Mapping: {{mapping| 1 1 1 3 5 | 0 3 7 -1 -8 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 229.535

{{Optimal ET sequence|legend=0| 5, 16e, 21, 47c, 68bcce }}

Badness (Smith): 0.062683

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 27/26, 36/35, 56/55, 507/500

Mapping: {{mapping| 1 1 1 3 5 2 | 0 3 7 -1 -8 9 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 229.059

{{Optimal ET sequence|legend=0| 5, 16e, 21, 68bccef }}

Badness (Smith): 0.047071

; Music
* [https://web.archive.org/web/20201127012514/http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Herman/gorgo-example.mp3 ''Gorgo Example''] by [[Herman Miller]]

== Gidorah ==
: ''For the 5-limit version, see [[Syntonic–diatonic equivalence continuum #University]].''

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 21/20, 144/125

{{Mapping|legend=1| 1 1 2 3 | 0 3 2 -1 }}

{{Multival|legend=1| 3 2 -1 -4 -10 -8 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 230.762

{{Optimal ET sequence|legend=1| 5, 16c, 21cc, 26ccc }}

[[Badness]] (Smith): 0.062262

== Oncle ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Oncle]].''

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 2430/2401

{{Mapping|legend=1| 1 1 6 3 | 0 3 -19 -1 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 232.498

{{Optimal ET sequence|legend=1| 31, 98c, 129c, 160bc }}

[[Badness]] (Smith): 0.088384

== Archaeotherium ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Archaeotherium]].''

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 405/392, 1029/1024

{{Mapping|legend=1| 1 1 5 3 | 0 3 -14 -1 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 230.258

{{Optimal ET sequence|legend=1| 21, 26, 47, 73bc, 99bc }}

[[Badness]] (Smith): 0.146306

== Clyndro ==
{{See also| Mavila family }}

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 135/128, 360/343

{{Mapping|legend=1| 1 1 4 3 | 0 3 -9 -1 }}

{{Multival|legend=1| 3 -9 -1 -21 -10 23 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~8/7 = 226.469

{{Optimal ET sequence|legend=1| 5c, 11, 16 }}

[[Badness]] (Smith): 0.159179

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 33/32, 45/44, 352/343

Mapping: {{mapping| 1 1 4 3 4 | 0 3 -9 -1 -3 }}

Optimal tuning (POTE): ~2 = 1200.000, ~8/7 = 226.428

{{Optimal ET sequence|legend=0| 5c, 11, 16 }}

Badness (Smith): 0.069703

== Miracle ==
{{Main| Miracle }}
: ''For the 5-limit version, see [[Syntonic–31 equivalence continuum #Ampersand]].''

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 225/224, 1029/1024

{{Mapping|legend=1| 1 1 3 3 | 0 6 -7 -2 }}

: mapping generator: ~2, ~15/14

{{Multival|legend=1| 6 -7 -2 -25 -20 15 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~15/14 = 116.675

[[Minimax tuning]]:
* [[7-odd-limit]]: ~15/14 = {{monzo| 2/13 1/13 -1/13 }}
: {{monzo list| 1 0 0 0 | 25/13 6/13 -6/13 0 | 25/13 -7/13 7/13 0 | 35/13 -2/13 2/13 0 }}
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.5/3
* [[9-odd-limit]]: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: {{monzo list| 1 0 0 0 | 25/19 12/19 -6/19 0 | 50/19 -14/19 7/19 0 | 55/19 -4/19 2/19 0 }}
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/5

[[Tuning ranges]]:
* 7-odd-limit [[diamond monotone]]: ~15/14 = [114.286, 120.000] (2\21 to 1\10)
* 9-odd-limit diamond monotone: ~15/14 = [116.129, 120.000] (3\31 to 1\10)
* 7- and 9-odd-limit [[diamond tradeoff]]: ~15/14 = [115.587, 116.993]

[[Algebraic generator]]: Secor59, positive root of 15''x''<sup>6</sup> - 8''x''<sup>4</sup> - 12

{{Optimal ET sequence|legend=1| 10, 21, 31, 41, 72 }}

[[Badness]] (Smith): 0.016742

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 225/224, 243/242, 385/384

Mapping: {{mapping| 1 1 3 3 2 | 0 6 -7 -2 15 }}

{{Multival|legend=1| 6 -7 -2 15 -25 -20 3 15 59 49 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.633

Minimax tuning:
* 11-odd-limit: ~15/14 = {{monzo| 1/19 2/19 -1/19 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 25/19 12/19 -6/19 0 0 }}, {{monzo| 50/19 -14/19 7/19 0 0 }}, {{monzo| 55/19 -4/19 2/19 0 0 }}, {{monzo| 53/19 30/19 -15/19 0 0 }}]
: eigenmonzo (unchanged-interval) basis: 2.9/5

Tuning ranges:
* 11-odd-limit diamond monotone: ~15/14 = [116.129, 117.073] (3\31 to 4\41)
* 11-odd-limit diamond tradeoff: ~15/14 = [115.587, 116.993]

Algebraic generator: Secor59

{{Optimal ET sequence|legend=0| 10, 21e, 31, 41, 72, 247c, 319bcde, 391bcde, 463bccde }}

Badness (Smith): 0.010684

==== Miraculous ====
Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 144/143, 196/195, 243/242

Mapping: {{mapping| 1 1 3 3 2 4 | 0 6 -7 -2 15 -3 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.747

{{Optimal ET sequence|legend=0| 10, 21e, 31, 41, 72f, 113f, 185cff }}

Badness (Smith): 0.018669

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 105/104, 120/119, 144/143, 154/153, 170/169

Mapping: {{mapping| 1 1 3 3 2 4 4 | 0 6 -7 -2 15 -3 1 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.769

{{Optimal ET sequence|legend=0| 10, 21e, 31, 41, 72fg, 113fgg }}

Badness (Smith): 0.017084

==== Benediction ====
Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 351/350, 385/384

Mapping: {{mapping| 1 1 3 3 2 7 | 0 6 -7 -2 15 -34 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.574

{{Optimal ET sequence|legend=0| 31, 72, 103, 175f }}

Badness (Smith): 0.015715

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 351/350, 375/374

Mapping: {{mapping| 1 1 3 3 2 7 7 | 0 6 -7 -2 15 -34 -30 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.585

{{Optimal ET sequence|legend=0| 31, 72, 103, 175f }}

Badness (Smith): 0.012537

==== Manna ====
Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 325/324, 385/384

Mapping: {{mapping| 1 1 3 3 2 0 | 0 6 -7 -2 15 38 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.739

{{Optimal ET sequence|legend=0| 31f, 41, 72, 185cf, 257cff }}

Badness (Smith): 0.017012

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 325/324, 385/384

Mapping: {{mapping| 1 1 3 3 2 0 0 | 0 6 -7 -2 15 38 42 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.727

{{Optimal ET sequence|legend=0| 31fg, 41, 72, 185cf, 257cff }}

Badness (Smith): 0.014680

==== Semimiracle ====
Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 225/224, 243/242, 385/384

Mapping: {{mapping| 2 2 6 6 4 7 | 0 6 -7 -2 15 2 }}

Optimal tuning (POTE): ~99/70 = 600.000, ~15/14 = 116.624

{{Optimal ET sequence|legend=0| 10, 62, 72 }}

Badness (Smith): 0.024622

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 225/224, 243/242, 273/272

Mapping: {{mapping| 2 2 6 6 4 7 7 | 0 6 -7 -2 15 2 6 }}

Optimal tuning (POTE): ~17\12 = 600.000, ~15/14 = 116.628

{{Optimal ET sequence|legend=0| 10, 62, 72 }}

Badness (Smith): 0.016130

==== Hemisecordite ====
Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 847/845

Mapping: {{mapping| 1 1 3 3 2 2 | 0 12 -14 -4 30 35 }}

Optimal tuning (POTE): ~2 = 1200.000, ~27/26 = 58.288

{{Optimal ET sequence|legend=0| 41, 62, 103, 247c, 350bcde }}

Badness (Smith): 0.025589

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 385/384, 847/845

Mapping: {{mapping| 1 1 3 3 2 2 2 | 0 12 -14 -4 30 35 43 }}

Optimal tuning (POTE): ~2 = 1200.000, ~27/26 = 58.261

{{Optimal ET sequence|legend=0| 41, 62, 103 }}

Badness (Smith): 0.022535

===== Semihemisecordite =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 289/288, 385/384, 847/845

Mapping: {{mapping| 2 2 6 6 4 4 7 | 0 12 -14 -4 30 35 12 }}

Optimal tuning (POTE): ~17/12 = 600.000, ~27/26 = 58.288

{{Optimal ET sequence|legend=0| 62, 144g, 206begg, 350bcdeggg }}

Badness (Smith): 0.046958

====== 19-limit ======
Subgroup: 2.3.5.7.11.13.17.19

Comma list: 209/208, 225/224, 243/242, 289/288, 361/360, 385/384

Mapping: {{mapping| 2 2 6 6 4 4 7 8 | 0 12 -14 -4 30 35 12 5 }}

Optimal tuning (POTE): ~17/12 = 600.000, ~27/26 = 58.283

{{Optimal ET sequence|legend=0| 62, 144gh, 206begghh }}

Badness (Smith): 0.035057

====== 23-limit ======
Subgroup: 2.3.5.7.11.13.17.19.23

Comma list: 209/208, 225/224, 243/242, 289/288, 323/322, 361/360, 385/384

Mapping: {{mapping| 2 2 6 6 4 4 7 8 7 | 0 12 -14 -4 30 35 12 5 21 }}

Optimal tuning (POTE): ~17/12 = 600.000, ~27/26 = 58.283

{{Optimal ET sequence|legend=0| 62, 144gh, 206begghhi }}

Badness (Smith): 0.026421

==== Phicordial ====
Subgroup: 2.3.5.7.11.13

Comma list: 225/224, 243/242, 385/384, 2200/2197

Mapping: {{mapping| 1 7 -4 1 17 4 | 0 -18 21 6 -45 -1 }}

Optimal tuning (POTE): ~2 = 1200.000, ~16/13 = 361.121

{{Optimal ET sequence|legend=0| 103, 113, 216c }}

Badness (Smith): 0.033198

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 225/224, 243/242, 273/272, 441/440, 2200/2197

Mapping: {{mapping| 1 7 -4 1 17 4 8 | 0 -18 21 6 -45 -1 -13 }}

Optimal tuning (POTE): ~2 = 1200.000, ~16/13 = 361.123

{{Optimal ET sequence|legend=0| 103, 113, 216c }}

Badness (Smith): 0.024705

=== Revelation ===
Subgroup: 2.3.5.7.11

Comma list: 99/98, 176/175, 1029/1024

Mapping: {{mapping| 1 1 3 3 5 | 0 6 -7 -2 -16 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.277

{{Optimal ET sequence|legend=0| 10e, 21, 31 }}

Badness (Smith): 0.032946

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 99/98, 105/104, 512/507

Mapping: {{mapping| 1 1 3 3 5 4 | 0 6 -7 -2 -16 -3 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/14 = 116.268

{{Optimal ET sequence|legend=0| 10e, 21, 31 }}

Badness (Smith): 0.029452

=== Hemimiracle ===
Subgroup: 2.3.5.7.11

Comma list: 225/224, 245/242, 1029/1024

Mapping: {{mapping| 1 1 3 3 4 | 0 12 -14 -4 -11 }}

Optimal tuning (POTE): ~2 = 1200.000, ~33/32 = 58.408

{{Optimal ET sequence|legend=0| 20, 21, 41, 144e, 185cee, 226cee }}

Badness (Smith): 0.059232

==== 13-limit ====
Subgroup: 2.3.5.7.11.13

Comma list: 105/104, 196/195, 245/242, 512/507

Mapping: {{mapping| 1 1 3 3 4 4 | 0 12 -14 -4 -11 -6 }}

Optimal tuning (POTE): ~2 = 1200.000, ~33/32 = 58.430

{{Optimal ET sequence|legend=0| 20, 21, 41, 144eff, 185ceeff }}

Badness (Smith): 0.043151

=== Oracle ===
Subgroup: 2.3.5.7.11

Comma list: 121/120, 225/224, 1029/1024

Mapping: {{mapping| 1 7 -4 1 3 | 0 -12 14 4 1 }}

Optimal tuning (POTE): ~2 = 1200.000, ~11/8 = 541.668

{{Optimal ET sequence|legend=0| 11, 20, 31, 82e, 113e, 144ee }}

Badness (Smith): 0.042687

== Hemiseven ==
[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 19683/19600

{{Mapping|legend=1| 1 4 14 2 | 0 -6 -29 2 }}

{{Multival|legend=1| 6 29 -2 32 -20 -86 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~320/243 = 483.267

{{Optimal ET sequence|legend=1| 72, 77, 149, 221, 514bd, 735bcdd }}

[[Badness]] (Smith): 0.056557

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 19683/19600

Mapping: {{mapping| 1 4 14 2 -5 | 0 -6 -29 2 21 }}

Optimal tuning (POTE): ~2 = 1200.000, ~320/243 = 483.276

{{Optimal ET sequence|legend=0| 72, 77, 149, 221e, 293de }}

Badness (Smith): 0.028467

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 385/384, 441/440, 676/675

Mapping: {{mapping| 1 4 14 2 -5 19 | 0 -6 -29 2 21 -38 }}

Optimal tuning (POTE): ~2 = 1200.000, ~120/91 = 483.256

{{Optimal ET sequence|legend=0| 72, 77, 149, 221ef }}

Badness (Smith): 0.021900

=== 17-limit ===
Subgroup: 2.3.5.7.11.13.17

Comma list: 273/272, 351/350, 385/384, 441/440, 676/675

Mapping: {{mapping| 1 4 14 2 -5 19 21 | 0 -6 -29 2 21 -38 -42 }}

Optimal tuning (POTE): ~2 = 1200.000, ~45/34 = 483.261

{{Optimal ET sequence|legend=0| 72, 77, 149, 221ef }}

Badness (Smith): 0.015701

== Unidec ==
{{Main| Unidec }}

=== 5-limit (unidecmic) ===
[[Subgroup]]: 2.3.5

[[Comma list]]: 31381059609/31250000000

{{Mapping|legend=1| 2 5 8 | 0 -6 -11 }}

: mapping generators: ~177147/125000, ~10/9

[[Optimal tuning]] ([[POTE]]): ~177147/125000 = 600.000, ~10/9 = 183.047

{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 2524, 2642, 2760, 2878b, …, 5002bc }}

[[Badness]] (Smith): 0.082423

=== 7-limit ===
[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 4375/4374

{{Mapping|legend=1| 2 5 8 5 | 0 -6 -11 2 }}

{{Multival|legend=1| 12 22 -4 7 -40 -71 }}

[[Optimal tuning]] ([[POTE]]): ~1225/864 = 600.000, ~10/9 = 183.161

[[Minimax tuning]]:
* [[7-odd-limit]]: ~10/9 = {{monzo| 3/26 0 -1/13 1/13 }}
: {{monzo list| 1 0 0 0 | 47/26 0 6/13 -6/13 | 71/26 0 11/13 -11/13 | 71/26 0 -2/13 2/13 }}
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.7/5
* [[9-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: {{Monzo list| 1 0 0 0 | 10/7 6/7 0 -3/7 | 57/28 11/7 0 -11/14 | 20/7 -2/7 0 1/7 }}
: [[eigenmonzo basis|eigenmonzo (unchanged-interval) basis]]: 2.9/7

{{Optimal ET sequence|legend=1| 26, 46, 72, 118, 190 }}

[[Badness]] (Smith): 0.038393

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 4375/4374

Mapping: {{mapping| 2 5 8 5 6 | 0 -6 -11 2 3 }}

Minimax tuning:
* [[11-odd-limit]]: ~10/9 = {{monzo| 5/28 -1/7 0 1/14 }}
: [{{monzo| 1 0 0 0 0 }}, {{monzo| 10/7 6/7 0 -3/7 0 }}, {{monzo| 57/28 11/7 0 -11/14 0 }}, {{monzo| 20/7 -2/7 0 1/7 0 }}, {{monzo| 99/28 -3/7 0 3/14 0 }}]
: eigenmonzo (unchanged-interval) basis: 2.9/7

{{Optimal ET sequence|legend=0| 26, 46, 72, 118, 190 }}

Badness (Smith): 0.015479

==== Ekadash ====
Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624, 729/728

Mapping: {{mapping| 2 5 8 5 6 19 | 0 -6 -11 2 3 -38 }}

Optimal tuning (POTE): ~99/70 = 600.000, ~10/9 = 183.187

{{Optimal ET sequence|legend=0| 26f, 46f, 72, 118, 190, 262df, 452cdef }}

Badness (Smith): 0.020381

==== Hendec ====
Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 325/324, 364/363, 385/384

Mapping: {{mapping| 2 5 8 5 6 8 | 0 -6 -11 2 3 -2 }}

Optimal tuning (POTE): ~91/64 = 600.000, ~10/9 = 183.198

{{Optimal ET sequence|legend=0| 26, 46, 72, 190ff }}

Badness (Smith): 0.017707

===== 17-limit =====
Subgroup: 2.3.5.7.11.13.17

Comma list: 169/168, 221/220, 273/272, 325/324, 364/363

Mapping: {{mapping| 2 5 8 5 6 8 10 | 0 -6 -11 2 3 -2 -6 }}

Optimal tuning (POTE): ~17/12 = 600.000, ~10/9 = 183.196

{{Optimal ET sequence|legend=0| 26, 46, 72, 190ffg }}

Badness (Smith): 0.011676

== Lagaca ==
[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 11529602/11390625

{{Mapping|legend=1| 2 5 2 5 | 0 -9 13 3 }}

{{Multival|legend=1| 18 -26 -6 -83 -60 59 }}

[[Optimal tuning]] ([[POTE]]): ~3375/2401 = 600.000, ~15/14 = 122.027

{{Optimal ET sequence|legend=1| 10, 98, 108, 118 }}

[[Badness]] (Smith): 0.144345

== Necromanteion ==
[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 5103/5000

{{Mapping|legend=1| 1 7 10 1 | 0 -12 -17 4 }}

{{Multival|legend=1| 12 17 -4 -1 -40 -57 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~48/35 = 541.779

{{Optimal ET sequence|legend=1| 11c, 20c, 31, 144c, 175c, 206bc, 237bc, 505bbccd }}

[[Badness]] (Smith): 0.117680

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 176/175, 243/242, 1029/1024

Mapping: {{mapping| 1 7 10 1 17 | 0 -12 -17 4 -30 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/11 = 541.729

{{Optimal ET sequence|legend=0| 20ce, 31, 113c, 144c, 175c, 381bccdee }}

Badness (Smith): 0.053459

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 243/242, 343/338

Mapping: {{mapping| 1 7 10 1 17 1 | 0 -12 -17 4 -30 6 }}

Optimal tuning (POTE): ~2 = 1200.000, ~15/11 = 541.606

{{Optimal ET sequence|legend=0| 20ce, 31, 51ce, 82cf, 113cf, 144cf }}

Badness (Smith): 0.047015

== Restles ==
{{See also| Lesser tendoneutralic }}

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 153664/151875

{{Mapping|legend=1| 1 -2 8 4 | 0 12 -19 -4 }}

{{Multival|legend=1| 12 -19 -4 -58 -40 44 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~315/256 = 358.548

{{Optimal ET sequence|legend=1| 10, 77, 87, 164 }}

[[Badness]] (Smith): 0.108011

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 153664/151875

Mapping: {{mapping| 1 -2 8 4 -7 | 0 12 -19 -4 35 }}

Optimal tuning (POTE): ~2 = 1200.000, ~27/22 = 358.571

{{Optimal ET sequence|legend=0| 10, 77, 87, 164 }}

Badness (Smith): 0.054655

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 196/195, 352/351, 385/384, 676/675

Mapping: {{mapping| 1 -2 8 4 -7 4 | 0 12 -19 -4 35 -1 }}

Optimal tuning (POTE): ~2 = 1200.000, ~16/13 = 358.574

{{Optimal ET sequence|legend=0| 10, 77, 87, 164 }}

Badness (Smith): 0.028187

== Quartemka ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Quartemka]].''

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 1250000/1240029

{{Mapping|legend=1| 1 4 6 2 | 0 -21 -32 7 }}

{{Multival|legend=1| 21 32 -7 2 -70 -106 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~27/25 = 138.006

{{Optimal ET sequence|legend=1| 26, 61, 87, 113, 200 }}

[[Badness]] (Smith): 0.152287

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 800000/793881

Mapping: {{mapping| 1 4 6 2 3 | 0 -21 -32 7 4 }}

Optimal tuning (POTE): ~2 = 1200.000, ~27/25 = 137.990

{{Optimal ET sequence|legend=0| 26, 61, 87, 200, 287d, 487cdd }}

Badness (Smith): 0.057307

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 364/363, 385/384, 2200/2197

Mapping: {{mapping| 1 4 6 2 3 6 | 0 -21 -32 7 4 -20 }}

Optimal tuning (POTE): ~2 = 1200.000, ~13/12 = 137.990

{{Optimal ET sequence|legend=0| 26, 61, 87, 200, 487cdd }}

Badness (Smith): 0.028393

== Tritriple ==
: ''For the 5-limit version, see [[Miscellaneous 5-limit temperaments #Tritriple]].''

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 1959552/1953125

{{Mapping|legend=1| 1 -11 -7 7 | 0 27 20 -9 }}

{{Multival|legend=1| 27 20 -9 -31 -90 -77 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~864/625 = 559.295

{{Optimal ET sequence|legend=1| 15, 88, 103, 118, 339d }}

[[Badness]] (Smith): 0.118640

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 43923/43750

Mapping: {{mapping| 1 -11 -7 7 -4 | 0 27 20 -9 16 }}

Optimal tuning (POTE): ~2 = 1200.000, ~242/175 = 559.293

{{Optimal ET sequence|legend=0| 15, 88, 103, 118, 339de }}

Badness (Smith): 0.035350

== Widefourth ==
[[Subgroup]]: 2.3.5.7

[[Comma list]]: 1029/1024, 48828125/48771072

{{Mapping|legend=1| 1 16 8 -2 | 0 -33 -13 11 }}

{{Multival|legend=1| 33 13 -11 -56 -110 -62 }}

[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000, ~3125/2304 = 524.210

{{Optimal ET sequence|legend=1| 16, 55b, 71, 87, 103, 190 }}

[[Badness]] (Smith): 0.154117

=== 11-limit ===
Subgroup: 2.3.5.7.11

Comma list: 385/384, 441/440, 234375/234256

Mapping: {{mapping| 1 16 8 -2 17 | 0 -33 -13 11 -31 }}

Optimal tuning (POTE): ~2 = 1200.000, ~847/625 = 524.210

{{Optimal ET sequence|legend=0| 16, 55be, 71, 87, 103, 190 }}

Badness (Smith): 0.040785

=== 13-limit ===
Subgroup: 2.3.5.7.11.13

Comma list: 385/384, 441/440, 625/624, 847/845

Mapping: {{mapping| 1 16 8 -2 17 12 | 0 -33 -13 11 -31 -19 }}

Optimal tuning (POTE): ~2 = 1200.000, ~65/48 = 524.209

{{Optimal ET sequence|legend=0| 16, 55be, 71, 87, 103, 190 }}

Badness (Smith): 0.021636

[[Category:Temperament clans]]
[[Category:Gamelismic clan| ]] <!-- main article -->
[[Category:Rank 2]]
[[Category:Listen]]
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