Canopic clan: Difference between revisions

The '''canopic clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[canopic comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.  

== Canopus ==

[[Subgroup]]: 3.5.7

[[Comma list]]: 16875/16807

{{Mapping|legend=2| 1 -2 -1 | 0 5 4 }}

: mapping generators: ~3, ~15/7

[[Optimal tuning]]s:

: [[error map]]: {{val| +1.785 -0.771 -2.248 }}

* [[CWE]]: ~3 = 1901.9550{{c}}, ~15/7 = 1317.9686{{c}}

: error map: {{val| 0.000 -0.381 +1.093 }}

[[Optimal ET sequence]]: [[13edt|b13]], [[62edt|b62]], [[75edt|b75]], [[88edt|b88]], [[101edt|b101]], [[114edt|b114]], [[355edt|b355]], [[469edt|b469]], [[583edt|b583]], [[697edt|b697]]

[[Badness]] (Sintel): 0.0996

* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]

The others are weak extensions. Mirkat tempers out [[19683/19600]], splitting the generator in two with a semitwelfth period. Sqrtphi tempers out [[15625/15552]], splitting the period in six. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Kwai tempers out [[5120/5103]], splitting the generator in ten. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.

* ''[[Grendel]]'' (+6144/6125) → [[Porwell temperaments #Grendel|Porwell temperaments]]

* ''[[Quinmage]]'' (+3125/3072) → [[Magic family #Quinmage|Magic family]]

* ''[[Familia]]'' (+1600000/1594323) → [[Amity family #Familia|Amity family]]

* [[Sqrtphi]] (+15625/15552) → [[Kleismic family #Sqrtphi|Kleismic family]]

* ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]

For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].

Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, browser, and grazer, in the order of increasing [[badness]].

== Mirkat ==

Mirkat tempers out 19683/19600, the [[cataharry comma]], as well as 250047/250000, the [[landscape comma]], and may be described as the {{nowrap| 72 & 111 }} temperament with a [[ploidacot]] signature of triploid alpha-hexacot.

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 16875/16807, 19683/19600

{{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}

: mapping generators: ~63/50, ~10/9

[[Optimal tuning]]s:

: [[error map]]: {{val| +0.083 -0.591 -0.117 +0.950 }}

* [[CWE]]: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5470{{c}}

: error map: {{val| 0.000 -0.673 -0.203 +0.831 }}

{{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}

[[Badness]] (Sintel): 1.50

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 8019/8000

Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}

Optimal tunings:  

* CWE: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5391{{c}}

{{Optimal ET sequence|legend=0| 39d, 72, 111, 183, 255 }}

Badness (Sintel): 0.731

Subgroup: 2.3.5.7.11.13

Comma list: 351/350, 540/539, 676/675, 1375/1372

Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}

Optimal tunings:  

* CWE: ~63/50 = 400.0000{{c}}, ~10/9 = 183.5825{{c}}

{{Optimal ET sequence|legend=0| 39df, 72, 111, 183 }}

Badness (Sintel): 0.770

Subgroup: 2.3.5.7.11.13.17

Comma list: 351/350, 442/441, 540/539, 561/560, 715/714

Mapping: {{mapping| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}

Optimal tunings:  

* CWE: ~34/27 = 400.0000{{c}}, ~10/9 = 183.5843{{c}}

{{Optimal ET sequence|legend=0| 39dfg, 72, 111, 183 }}

Badness (Sintel): 0.600

Eris tempers out 65625/65536, the [[horwell comma]], and may be described as the {{nowrap| 31 & 224 }} temperament. The [[2.5.7-subgroup|2.5.7 subgroup]] restriction of this temperament is [[exodia]].

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 16875/16807, 65625/65536

{{Mapping|legend=1| 1 -19 8 -5 | 0 29 -8 11 }}

: mapping generators: ~2, ~49/30

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1200.0256{{c}}, ~49/30 = 851.8023{{c}}

: [[error map]]: {{val| +0.026 -0.173 -0.528 +0.872 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/30 = 851.7845{{c}}

: error map: {{val| 0.000 -0.204 -0.590 +0.804 }}

{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224 }}

[[Badness]] (Sintel): 1.89

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 65625/65536

Mapping: {{mapping| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}

Optimal tunings:  

* WE: ~2 = 1200.0218{{c}}, ~18/11 = 851.7963{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~18/11 = 851.7812{{c}}

{{Optimal ET sequence|legend=0| 31, …, 193, 224, 703, 927d }}

Badness (Sintel): 0.913

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 625/624, 1375/1372, 4096/4095

Mapping: {{mapping| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}

Optimal tuning:  

* WE ~2 = 1199.9623{{c}}, ~18/11 = 851.7598{{c}}

* CWE ~2 = 1200.0000{{c}}, ~18/11 = 851.7865{{c}}

{{Optimal ET sequence|legend=0| 31, 193, 224 }}

Badness (Sintel): 1.04

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 16875/16807, 26873856/26796875

: mapping generators: ~2, ~144/125

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1199.9182{{c}}, ~144/125 = 244.7020{{c}}

: [[error map]]: {{val| -0.082 -0.305 -0.223 +1.037 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~144/125 = 244.7172{{c}}

: error map: {{val| 0.000 -0.248 -0.082 +1.184 }}

{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407 }}

[[Badness]] (Sintel): 3.42

=== 11-limit ===

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 234375/234256

Mapping: {{mapping| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}

Optimal tunings:  

* WE: ~2 = 1199.9229{{c}}, ~121/105 = 244.7033{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~121/105 = 244.7175{{c}}

{{Optimal ET sequence|legend=0| 49, 103, 152, 255, 407 }}

Badness (Sintel): 1.13

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 847/845, 1375/1372, 1575/1573

Mapping: {{mapping| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}

Optimal tunings:  

* WE: ~2 = 1199.9003{{c}}, ~15/13 = 244.6932{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~15/13 = 244.7116{{c}}

{{Optimal ET sequence|legend=0| 49f, 103, 152f, 255, 407f }}

Badness (Sintel): 1.17

Septendesemi tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit, and may be described as the {{nowrap| 80 & 103 }} temperament. [[183edo]] provides an excellent tuning for 7-, 11-, 13-, and 17-limit septendesemi. Septendesemi was named by [[Xenllium]] in 2021; the name ''septendesemi'' refers to a septendecimal semitone ([[17/16]]).  

[[Subgroup]]: 2.3.5.7

[[Comma list]]: 16875/16807, 1959552/1953125

{{Mapping|legend=1| 1 -2 -1 -2 | 0 41 38 55 }}

: mapping generators: ~2, ~343/324

* [[WE]]: ~2 = 1199.8649{{c}}, ~343/324 = 104.9046{{c}}

: [[error map]]: {{val| -0.135 -0.597 +0.195 +1.196 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~343/324 = 104.9134{{c}}

: error map: {{val| 0.000 -0.506 +0.395 +1.410 }}

{{Optimal ET sequence|legend=0| 80, 103, 183 }}

[[Badness]] (Sintel): 3.71

 

Subgroup: 2.3.5.7.11

 

Comma list: 540/539, 1375/1372, 43923/43750

 

Mapping: {{mapping| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}

 

* WE: ~2 = 1199.9327{{c}}, ~35/33 = 104.9100{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 104.9144{{c}}

 

 

Badness (Sintel): 1.37

 

=== 13-limit ===

 

Comma list: 351/350, 540/539, 1375/1372, 4225/4224

 

Mapping: {{mapping| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}

 

Optimal tunings:  

* WE: ~2 = 1200.1082{{c}}, ~35/33 = 104.9170{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 104.9094{{c}}

 

{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}

 

 

=== 17-limit ===

 

Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224

 

Mapping: {{mapping| 1 -2 -1 -2 -1 3 4 | 0 41 38 55 51 8 1 }}

 

Optimal tunings:  

* WE: ~2 = 1200.0758{{c}}, ~17/16 = 104.9158{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/16 = 104.9101{{c}}

 

Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/16 = 104.909{{c}}

 

 

Badness (Sintel): 1.03

 

: ''For the 5-limit version, see [[Very high accuracy temperaments #Gaster]].''

 

Gaster tempers out {{monzo| -70 72 -19 }} in the 5-limit, mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit, and may be described as the {{nowrap| 111 & 113 }} temperament.

 

It was named by [[Xenllium]] in 2022; the word "[[Wiktionary: gaster|gaster]]" means [[Wiktionary: abdomen|abdomen]] or [[Wiktionary: stomach|stomach]], but also a restructuring of the words "gassormic tritone", which is a generator of this temperament. This temperament is sufficient to obtain high prime limit harmonics like a stomach, so that patent vals [[111edo|111]], [[113edo|113]] and [[224edo|224]] support it even in the 41-limit.

 

[[Subgroup]]: 2.3.5.7

 

[[Comma list]]: 16875/16807, 14348907/14336000

 

{{Mapping|legend=1| 1 -8 -34 -32 | 0 19 72 69 }}

: mapping generators: ~2, ~567/400

 

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1199.9920{{c}}, ~567/400 = 605.3546{{c}}

: [[error map]]: {{val| -0.008 -0.152 -0.506 +0.902 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~567/400 = 605.3586{{c}}

: error map: {{val| 0.000 -0.142 -0.497 +0.915 }}

 

 

[[Badness]] (Sintel): 3.91

 

=== 11-limit ===

Subgroup: 2.3.5.7.11

 

 

Mapping: {{mapping| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}

 

Optimal tunings:  

* WE: ~2 = 1199.9387{{c}}, ~363/256 = 605.3300{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~363/256 = 605.3603{{c}}

 

 

 

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

 

Comma list: 540/539, 729/728, 1375/1372, 2200/2197

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}

 

Optimal tunings:  

* WE: ~2 = 1199.9154{{c}}, ~78/55 = 605.3183{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~78/55 = 605.3601{{c}}

 

 

Badness (Sintel): 1.03

 

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

 

Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}

 

Optimal tunings:  

* WE: ~2 = 1199.8076{{c}}, ~17/12 = 605.2674{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3626{{c}}

 

 

Badness (Sintel): 1.09

 

=== 19-limit ===

Subgroup: 2.3.5.7.11.13.17.19

 

Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}

 

Optimal tunings:  

* WE: ~2 = 1199.7542{{c}}, ~17/12 = 605.2674{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3613{{c}}

 

 

 

=== 23-limit ===

Subgroup: 2.3.5.7.11.13.17.19.23

 

Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}

 

Optimal tunings:  

* WE: ~2 = 1199.8733{{c}}, ~17/12 = 605.2946{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3575{{c}}

 

 

Badness (Sintel): 1.26

 

=== 29-limit ===

Subgroup: 2.3.5.7.11.13.17.19.23.29

 

Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}

 

Optimal tunings:  

* WE: ~2 = 1199.9442{{c}}, ~17/12 = 605.3263{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3541{{c}}

 

 

Badness (Sintel): 1.41

 

=== 31-limit ===

Subgroup: 2.3.5.7.11.13.17.19.23.29.31

 

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}

 

* WE: ~2 = 1199.9100{{c}}, ~17/12 = 605.3107{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3556{{c}}

 

 

Badness (Sintel): 1.42

 

=== 37-limit ===

 

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 667/666, 715/714

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}

 

* WE: ~2 = 1199.9087{{c}}, ~17/12 = 605.3101{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3559{{c}}

 

 

Badness (Sintel): 1.56

 

=== 41-limit ===

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37.41

 

Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 533/532, 540/539, 575/574, 667/666

 

Mapping: {{mapping| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 -35 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 80 }}

 

Optimal tunings:  

* WE: ~2 = 1199.9179{{c}}, ~17/12 = 605.3156{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3567{{c}}

 

{{Optimal ET sequence|legend=0| 111, 113, 224 }}

 

 

Hemiseptisix tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit, and may be described as the {{nowrap| 103 & 121 }} temperament. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix. Hemiseptisix was named by [[Xenllium]] in 2021; the name ''hemiseptisix'' refers to a half of septimal major sixth ([[12/7]]).

 

 

 

{{Mapping|legend=1| 1 -19 -7 -17 | 0 53 24 51 }}

: mapping generators: ~2, ~98/75

 

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1199.2693{{c}}, ~98/75 = 466.0801{{c}}

: [[error map]]: {{val| +0.023 -0.149 -0.553 +0.866 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~98/75 = 466.0715{{c}}

: error map: {{val| 0.000 -0.167 -0.598 +0.819 }}

 

 

 

=== 11-limit ===

 

Comma list: 540/539, 1375/1372, 2734375/2725888

 

Mapping: {{mapping| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}

 

* WE: ~2 = 1200.0183{{c}}, ~55/42 = 466.0767{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~55/42 = 466.0699{{c}}

 

 

 

=== 13-limit ===

 

Comma list: 540/539, 625/624, 1375/1372, 2200/2197

 

Mapping: {{mapping| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}

 

Optimal tunings:  

* WE: ~2 = 1199.9784{{c}}, ~55/42 = 466.0622{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~55/42 = 466.0703{{c}}

 

{{Optimal ET sequence|legend=0| 103, 121, 224 }}

 

Badness (Sintel): 0.873

 

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

 

Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197

 

Mapping: {{mapping| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}

 

* WE: ~2 = 1199.8544{{c}}, ~17/13 = 466.0174{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~17/13 = 466.0718{{c}}

 

{{Optimal ET sequence|legend=0| 103, 121, 224 }}

 

Badness (Sintel): 0.948

 

{{See also| Sensipent family }}

 

Named by [[Xenllium]] in 2022, browser may be described as the {{nowrap| 103 & 111 }} temperament.

 

This can also be considered a [[non-over-1 temperament]], with considerable scope for harmony in the 2.5/3.7/3.11/3.13/3.17/3 subgroup with mos scales of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8d-et, with a generator very slightly flat of 7\8.

 

[[Subgroup]]: 2.3.5.7

 

[[Comma list]]: 16875/16807, 78732/78125

 

{{Mapping|legend=1| 1 -29 -37 -47 | 0 35 45 57 }}

: mapping generators: ~2, ~90/49

 

* [[WE]]: ~2 = 1199.9313{{c}}, ~90/49 = 1048.5414{{c}}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~90/49 = 1048.5998{{c}}

: error map: {{val| 0.000 -0.962 +0.677 +1.362 }}

 

{{Optimal ET sequence|legend=1| 103, 111, 214 }}

 

[[Badness]] (Sintel): 4.57

 

Subgroup: 2.3.5.7.11

 

Comma list: 540/539, 1375/1372, 78732/78125

 

Mapping: {{mapping| 1 -29 -37 -47 -28 | 0 35 45 57 36 }}

 

Optimal tunings:  

* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5981{{c}}

 

{{Optimal ET sequence|legend=0| 103, 214 }}

 

 

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

 

Comma list: 351/350, 540/539, 847/845, 1375/1372

 

Mapping: {{mapping| 1 -29 -37 -47 -28 -33 | 0 35 45 57 36 42 }}

 

* WE: ~2 = 1200.1344{{c}}, ~11/6 = 1048.7124{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.5984{{c}}

 

 

 

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

 

Comma list: 351/350, 540/539, 561/560, 715/714, 847/845

 

Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 | 0 35 45 57 36 42 31 }}

 

* WE: ~2 = 1199.9191{{c}}, ~11/6 = 1048.5324{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6014{{c}}

 

 

Badness (Sintel): 1.04

 

=== 19-limit ===

Subgroup: 2.3.5.7.11.13.17.19

 

Comma list: 324/323, 351/350, 456/455, 495/494, 540/539, 715/714

 

Mapping: {{mapping| 1 -29 -37 -47 -28 -33 -23 -91 | 0 35 45 57 36 42 31 109 }}

 

* WE: ~2 = 1199.9145{{c}}, ~11/6 = 1048.5290{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~11/6 = 1048.6021{{c}}

 

{{Optimal ET sequence|legend=0| 103h, 111, 214 }}

 

Badness (Sintel): 1.07

 

== Grazer ==

Named by [[Xenllium]] in 2022, grazer may be described as the {{nowrap| 113 & 121 }} temperament.  

 

[[Subgroup]]: 2.3.5.7

 

 

{{Mapping|legend=1| 1 -3 -4 -5 | 0 37 51 63 }}

: mapping generators: ~2, ~49/45

 

[[Optimal tuning]]s:  

* [[WE]]: ~2 = 1200.0310{{c}}, ~49/45 = 148.7229{{c}}

: [[error map]]: {{val| +0.031 +0.700 -1.561 +0.563 }}

* [[CWE]]: ~2 = 1200.0000{{c}}, ~49/45 = 148.7198{{c}}

: error map: {{val| 0.000 +0.676 -1.606 +0.519 }}

 

 

 

=== 11-limit ===

Subgroup: 2.3.5.7.11

 

Comma list: 540/539, 1375/1372, 218750/216513

 

 

Optimal tunings:  

* WE: ~2 = 1199.7242{{c}}, ~12/11 = 148.6946{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7230{{c}}

 

{{Optimal ET sequence|legend=0| 113, 121, 234 }}

 

 

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

 

Comma list: 325/324, 364/363, 540/539, 2200/2197

 

Mapping: {{mapping| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}

 

* WE: ~2 = 1199.7257{{c}}, ~12/11 = 148.6947{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7230{{c}}

 

{{Optimal ET sequence|legend=0| 113, 121, 234 }}

 

Badness (Sintel): 1.50

 

 

Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989

 

Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}

 

* WE: ~2 = 1199.5690{{c}}, ~12/11 = 148.6815{{c}}

* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7267{{c}}

 

{{Optimal ET sequence|legend=0| 113, 121, 234g }}

 

 

=== 19-limit ===

Subgroup: 2.3.5.7.11.13.17.19

 

Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663

 

Mapping: {{mapping| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}

 

* WE: ~2 = 1199.7269{{c}}, ~12/11 = 148.6928{{c}}

 

 

Badness (Sintel): 1.37

 

[[Category:Temperament clans]]

[[Category:Mirkwai clan| ]] <!-- main article -->

[[Category:Rank 2]]