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.

{{Main| Canopus }}

[[Subgroup]]: 3.5.7

[[Comma list]]: 16875/16807

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

: mapping generators: ~3, ~15/7

* [[WE]]: ~3 = 1901.7826{{c}}, ~15/7 = 1317.8771{{c}}

: [[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

=== Overview to extensions ===

The full 7-limit extensions' relation to canopus is clearer if the mapping is normalized in terms of 3.5.7.2. In fact, the strong extensions are nusecond and octoid. These temperaments are distributed into different temperament collection pages.

* ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]

* ''[[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.  

Members of the clan discussed elsewhere are:  

* ''[[Kwai]]'' (+5120/5103) → [[Hemifamity temperaments #Kwai|Hemifamity temperaments]]

* ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]

* ''[[Subsedia]]'' (+65536/64827) → [[Buzzardsmic clan #Subsedia|Buzzardsmic clan]]

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 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

* [[WE]]: ~63/50 = 400.0277{{c}}, ~10/9 = 183.5515{{c}}

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

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

[[Badness]] (Sintel): 1.50

=== 11-limit ===

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 }}

* WE: ~63/50 = 400.0463{{c}}, ~10/9 = 183.5496{{c}}

* 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

=== 13-limit ===

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 }}

* WE: ~63/50 = 400.0245{{c}}, ~10/9 = 183.5885{{c}}

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

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

Badness (Sintel): 0.770

=== 17-limit ===

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 }}

* WE: ~34/27 = 400.0257{{c}}, ~10/9 = 183.5906{{c}}

* 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 ==

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:

: [[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:  

* 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|legend=1| 1 -8 -4 -8 | 0 47 31 53 }}

: mapping generators: ~2, ~144/125

[[Optimal tuning]]s:  

* [[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

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:  

* 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:  

* 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 }}

 

 

=== 11-limit ===

 

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}}

 

 

 

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

 

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}}

 

 

Badness (Sintel): 1.15

 

=== 17-limit ===

Subgroup: 2.3.5.7.11.13.17

 

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}}

 

 

 

== Gaster ==

: ''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 }}

 

* 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 }}

 

* 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

 

 

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}}

 

 

Badness (Sintel): 1.12

 

=== 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 }}

 

* 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 ===

 

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 }}

 

Optimal tunings:  

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

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

 

 

 

=== 37-limit ===

Subgroup: 2.3.5.7.11.13.17.19.23.29.31.37

 

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}}

 

 

 

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]]).

 

[[Subgroup]]: 2.3.5.7

 

[[Comma list]]: 16875/16807, 95703125/95551488

 

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

: mapping generators: ~2, ~98/75

 

* [[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 }}

 

{{Optimal ET sequence|legend=1| 103, 121, 224 }}

 

 

=== 11-limit ===

Subgroup: 2.3.5.7.11

 

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

 

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

 

Optimal tunings:  

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

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

 

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

 

 

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

 

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

 

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

 

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

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

 

 

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 }}

 

Optimal tunings:  

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

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

 

 

Badness (Sintel): 0.948

 

== Browser ==

 

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

 

[[Optimal tuning]]s:  

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

: [[error map]]: {{val| -0.069 -1.013 +0.592 +1.264 }}

* [[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 }}

 

 

 

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

 

 

* 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 }}

 

Badness (Sintel): 1.91

 

=== 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 }}

 

Optimal tunings:  

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

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

 

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

 

Badness (Sintel): 1.19

 

=== 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 }}

 

Optimal tunings:  

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

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

 

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

 

 

=== 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 }}

 

Optimal tunings:  

* 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

 

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

 

 

 

{{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 }}

 

{{Optimal ET sequence|legend=1| 113, 121, 234 }}

 

 

 

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

 

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

 

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

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

 

 

Badness (Sintel): 2.51

 

=== 13-limit ===

Subgroup: 2.3.5.7.11.13

 

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

 

 

* 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

 

=== 17-limit ===

 

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 }}

 

Optimal tunings:  

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

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

 

 

 

=== 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 }}

 

Optimal tunings:  

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

* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7227{{c}}

 

 

Badness (Sintel): 1.37

 

[[Category:Temperament clans]]

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

[[Category:Rank 2]]