Canopic clan: Difference between revisions

Latest revision as of 18:05, 20 October 2026

This is a list showing technical temperament data. For an explanation of what information is shown here, you may look at the technical data guide for regular temperaments.

The canopic clan of temperaments tempers out the canopic comma (monzo: [0 3 4 -5⟩, ratio: 16875/16807), a no-twos comma.

Canopus

Main article: Canopus

Subgroup: 3.5.7

Comma list: 16875/16807

Subgroup-val mapping: [⟨1 -2 -1], ⟨0 5 4]]

mapping generators: ~3, ~15/7

Optimal tunings:

WE: ~3 = 1901.7826 ¢, ~15/7 = 1317.8771 ¢

error map: ⟨+1.785 -0.771 -2.248]

CWE: ~3 = 1901.9550 ¢, ~15/7 = 1317.9686 ¢

error map: ⟨0.000 -0.381 +1.093]

Optimal ET sequence: b13, b62, b75, b88, b101, b114, b355, b469, b583, 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 clan and collection pages.

Nusecond (+126/125) → Starling temperaments
Octoid (+4375/4374) → Stearnsmic clan

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) → Aberschismic temperaments
Octokaidecal (+28/27 or 50/49) → Trienstonic clan
Meantritone (+81/80) → Meantone family
Quanharuk (+32805/32768) → Schismatic family
Miracle (+225/224) → Gamelismic clan
Pluto (+4000/3969) → Octagar temperaments
Bohpier (+245/243) → Sensamagic clan
Subsedia (+65536/64827) → Buzzardsmic clan
Semisept (+1728/1715 or 3136/3125) → Hemimean clan
Grendel (+6144/6125) → Porwell temperaments
Quinmage (+3125/3072) → Magic family
Familia (+1600000/1594323) → Amity family
Sqrtphi (+15625/15552) → Kleismic family
Rainwell (+2100875/2097152) → Semicomma family
Browser (+78732/78125) → Sensipent family
Quintiquart (+390625000/387420489) → Quartonic family

For no-2's extensions, see No-twos subgroup temperaments #Canopus.

Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, 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 72 & 111 temperament with a ploidacot signature of triploid alpha-hexacot.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 19683/19600

Mapping: [⟨3 2 1 2], ⟨0 6 13 14]]

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

Optimal tunings:

WE: ~63/50 = 400.0277 ¢, ~10/9 = 183.5515 ¢

error map: ⟨+0.083 -0.591 -0.117 +0.950]

CWE: ~63/50 = 400.0000 ¢, ~10/9 = 183.5470 ¢

error map: ⟨0.000 -0.673 -0.203 +0.831]

Optimal ET sequence: 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: [⟨3 2 1 2 9], ⟨0 6 13 14 3]]

Optimal tunings:

WE: ~63/50 = 400.0463 ¢, ~10/9 = 183.5496 ¢
CWE: ~63/50 = 400.0000 ¢, ~10/9 = 183.5391 ¢

Optimal ET sequence: 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: [⟨3 2 1 2 9 1], ⟨0 6 13 14 3 22]]

Optimal tunings:

WE: ~63/50 = 400.0245 ¢, ~10/9 = 183.5885 ¢
CWE: ~63/50 = 400.0000 ¢, ~10/9 = 183.5825 ¢

Optimal ET sequence: 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: [⟨3 2 1 2 9 1 4], ⟨0 6 13 14 3 22 18]]

Optimal tunings:

WE: ~34/27 = 400.0257 ¢, ~10/9 = 183.5906 ¢
CWE: ~34/27 = 400.0000 ¢, ~10/9 = 183.5843 ¢

Optimal ET sequence: 39dfg, 72, 111, 183

Badness (Sintel): 0.600

Eris

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

Subgroup: 2.3.5.7

Comma list: 16875/16807, 65625/65536

Mapping: [⟨1 -19 8 -5], ⟨0 29 -8 11]]

mapping generators: ~2, ~49/30

Optimal tunings:

WE: ~2 = 1200.0256 ¢, ~49/30 = 851.8023 ¢

error map: ⟨+0.026 -0.173 -0.528 +0.872]

CWE: ~2 = 1200.0000 ¢, ~49/30 = 851.7845 ¢

error map: ⟨0.000 -0.204 -0.590 +0.804]

Optimal ET sequence: 31, 131, 162, 193, 224

Badness (Sintel): 1.89

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -19 8 -5 -37], ⟨0 29 -8 11 57]]

Optimal tunings:

WE: ~2 = 1200.0218 ¢, ~18/11 = 851.7963 ¢
CWE: ~2 = 1200.0000 ¢, ~18/11 = 851.7812 ¢

Optimal ET sequence: 31, …, 193, 224, 703, 927d

Badness (Sintel): 0.913

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -19 8 -5 -37 47], ⟨0 29 -8 11 57 -61]]

Optimal tuning:

WE ~2 = 1199.9623 ¢, ~18/11 = 851.7598 ¢
CWE ~2 = 1200.0000 ¢, ~18/11 = 851.7865 ¢

Optimal ET sequence: 31, 193, 224

Badness (Sintel): 1.04

Subsemifourth

Subgroup: 2.3.5.7

Comma list: 16875/16807, 26873856/26796875

Mapping: [⟨1 -8 -4 -8], ⟨0 47 31 53]]

mapping generators: ~2, ~144/125

Optimal tunings:

WE: ~2 = 1199.9182 ¢, ~144/125 = 244.7020 ¢

error map: ⟨-0.082 -0.305 -0.223 +1.037]

CWE: ~2 = 1200.0000 ¢, ~144/125 = 244.7172 ¢

error map: ⟨0.000 -0.248 -0.082 +1.184]

Optimal ET sequence: 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: [⟨1 -8 -4 -8 -10], ⟨0 47 31 53 66]]

Optimal tunings:

WE: ~2 = 1199.9229 ¢, ~121/105 = 244.7033 ¢
CWE: ~2 = 1200.0000 ¢, ~121/105 = 244.7175 ¢

Optimal ET sequence: 49, 103, 152, 255, 407

Badness (Sintel): 1.13

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -8 -4 -8 -10 -12], ⟨0 0 47 31 53 66 77]]

Optimal tunings:

WE: ~2 = 1199.9003 ¢, ~15/13 = 244.6932 ¢
CWE: ~2 = 1200.0000 ¢, ~15/13 = 244.7116 ¢

Optimal ET sequence: 49f, 103, 152f, 255, 407f

Badness (Sintel): 1.17

Septendesemi

Septendesemi tempers out the mirkwai comma and 1959552/1953125 (parkleiness comma) in the 7-limit, and may be described as the 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: [⟨1 -2 -1 -2], ⟨0 41 38 55]]

mapping generators: ~2, ~343/324

Optimal tunings:

WE: ~2 = 1199.8649 ¢, ~343/324 = 104.9046 ¢

error map: ⟨-0.135 -0.597 +0.195 +1.196]

CWE: ~2 = 1200.0000 ¢, ~343/324 = 104.9134 ¢

error map: ⟨0.000 -0.506 +0.395 +1.410]

Optimal ET sequence: 80, 103, 183

Badness (Sintel): 3.71

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -2 -1 -2 -1], ⟨0 41 38 55 51]]

Optimal tunings:

WE: ~2 = 1199.9327 ¢, ~35/33 = 104.9100 ¢
CWE: ~2 = 1200.0000 ¢, ~35/33 = 104.9144 ¢

Optimal ET sequence: 80, 103, 183

Badness (Sintel): 1.37

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -2 -1 -2 -1 3], ⟨0 41 38 55 51 8]]

Optimal tunings:

WE: ~2 = 1200.1082 ¢, ~35/33 = 104.9170 ¢
CWE: ~2 = 1200.0000 ¢, ~35/33 = 104.9094 ¢

Optimal ET sequence: 80, 103, 183, 469f

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: [⟨1 -2 -1 -2 -1 3 4], ⟨0 41 38 55 51 8 1]]

Optimal tunings:

WE: ~2 = 1200.0758 ¢, ~17/16 = 104.9158 ¢
CWE: ~2 = 1200.0000 ¢, ~17/16 = 104.9101 ¢

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~17/16 = 104.909 ¢

Optimal ET sequence: 80, 103, 183, 469f

Badness (Sintel): 1.03

Gaster

For the 5-limit version, see Very high accuracy temperaments #Gaster.

Main article: Gaster temperament

Gaster tempers out [-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 111 & 113 temperament.

It was named by Xenllium in 2022; the word "gaster" means abdomen or 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 111, 113 and 224 support it even in the 41-limit.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 14348907/14336000

Mapping: [⟨1 -8 -34 -32], ⟨0 19 72 69]]

mapping generators: ~2, ~567/400

Optimal tunings:

WE: ~2 = 1199.9920 ¢, ~567/400 = 605.3546 ¢

error map: ⟨-0.008 -0.152 -0.506 +0.902]

CWE: ~2 = 1200.0000 ¢, ~567/400 = 605.3586 ¢

error map: ⟨0.000 -0.142 -0.497 +0.915]

Optimal ET sequence: 111, 224

Badness (Sintel): 3.91

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 14348907/14336000

Mapping: [⟨1 -8 -34 -32 8], ⟨0 19 72 69 -9]]

Optimal tunings:

WE: ~2 = 1199.9387 ¢, ~363/256 = 605.3300 ¢
CWE: ~2 = 1200.0000 ¢, ~363/256 = 605.3603 ¢

Optimal ET sequence: 111, 224, 783d

Badness (Sintel): 1.79

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -8 -34 -32 8 -19], ⟨0 19 72 69 -9 45]]

Optimal tunings:

WE: ~2 = 1199.9154 ¢, ~78/55 = 605.3183 ¢
CWE: ~2 = 1200.0000 ¢, ~78/55 = 605.3601 ¢

Optimal ET sequence: 111, 224, 783df

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: [⟨1 -8 -34 -32 8 -19 -6], ⟨0 19 72 69 -9 45 20]]

Optimal tunings:

WE: ~2 = 1199.8076 ¢, ~17/12 = 605.2674 ¢
CWE: ~2 = 1200.0000 ¢, ~17/12 = 605.3626 ¢

Optimal ET sequence: 111, 224, 559dgg

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: [⟨1 -8 -34 -32 8 -19 -6 -24], ⟨0 19 72 69 -9 45 20 56]]

Optimal tunings:

WE: ~2 = 1199.7542 ¢, ~17/12 = 605.2674 ¢
CWE: ~2 = 1200.0000 ¢, ~17/12 = 605.3613 ¢

Optimal ET sequence: 111, 224

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: [⟨1 -8 -34 -32 8 -19 -6 -24 2], ⟨0 19 72 69 -9 45 20 56 5]]

Optimal tunings:

WE: ~2 = 1199.8733 ¢, ~17/12 = 605.2946 ¢
CWE: ~2 = 1200.0000 ¢, ~17/12 = 605.3575 ¢

Optimal ET sequence: 111, 224

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: [⟨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 ¢, ~17/12 = 605.3263 ¢
CWE: ~2 = 1200.0000 ¢, ~17/12 = 605.3541 ¢

Optimal ET sequence: 111, 113, 224

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: [⟨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 ¢, ~17/12 = 605.3107 ¢
CWE: ~2 = 1200.0000 ¢, ~17/12 = 605.3556 ¢

Optimal ET sequence: 111, 113, 224

Badness (Sintel): 1.42

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: [⟨1 -8 -34 -32 8 -19 -6 -24 2 21 10 38], ⟨0 19 72 69 -9 45 20 56 5 -32 -10 -65]]

Optimal tunings:

WE: ~2 = 1199.9087 ¢, ~17/12 = 605.3101 ¢
CWE: ~2 = 1200.0000 ¢, ~17/12 = 605.3559 ¢

Optimal ET sequence: 111, 113, 224

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: [⟨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 ¢, ~17/12 = 605.3156 ¢
CWE: ~2 = 1200.0000 ¢, ~17/12 = 605.3567 ¢

Optimal ET sequence: 111, 113, 224

Badness (Sintel): 1.57

Hemiseptisix

Hemiseptisix tempers out the mirkwai comma and 95703125/95551488 (pontiqak comma) in the 7-limit, and may be described as the 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: [⟨1 -19 -7 -17], ⟨0 53 24 51]]

mapping generators: ~2, ~98/75

Optimal tunings:

WE: ~2 = 1199.2693 ¢, ~98/75 = 466.0801 ¢

error map: ⟨+0.023 -0.149 -0.553 +0.866]

CWE: ~2 = 1200.0000 ¢, ~98/75 = 466.0715 ¢

error map: ⟨0.000 -0.167 -0.598 +0.819]

Optimal ET sequence: 103, 121, 224

Badness (Sintel): 4.12

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -19 -7 -17 -28], ⟨0 53 24 51 81]]

Optimal tunings:

WE: ~2 = 1200.0183 ¢, ~55/42 = 466.0767 ¢
CWE: ~2 = 1200.0000 ¢, ~55/42 = 466.0699 ¢

Optimal ET sequence: 103, 121, 224

Badness (Sintel): 1.43

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -19 -7 -17 -28 -13], ⟨0 53 24 51 81 43]]

Optimal tunings:

WE: ~2 = 1199.9784 ¢, ~55/42 = 466.0622 ¢
CWE: ~2 = 1200.0000 ¢, ~55/42 = 466.0703 ¢

Optimal ET sequence: 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: [⟨1 -19 -7 -17 -28 -13 -13], ⟨0 53 24 51 81 43 44]]

Optimal tunings:

WE: ~2 = 1199.8544 ¢, ~17/13 = 466.0174 ¢
CWE: ~2 = 1200.0000 ¢, ~17/13 = 466.0718 ¢

Optimal ET sequence: 103, 121, 224

Badness (Sintel): 0.948

Grazer

Named by Xenllium in 2022, grazer may be described as the 113 & 121 temperament.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 1071875/1062882

Mapping: [⟨1 -3 -4 -5], ⟨0 37 51 63]]

mapping generators: ~2, ~49/45

Optimal tunings:

WE: ~2 = 1200.0310 ¢, ~49/45 = 148.7229 ¢

error map: ⟨+0.031 +0.700 -1.561 +0.563]

CWE: ~2 = 1200.0000 ¢, ~49/45 = 148.7198 ¢

error map: ⟨0.000 +0.676 -1.606 +0.519]

Optimal ET sequence: 113, 121, 234

Badness (Sintel): 5.50

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -3 -4 -5 -1], ⟨0 37 51 63 36]]

Optimal tunings:

WE: ~2 = 1199.7242 ¢, ~12/11 = 148.6946 ¢
CWE: ~2 = 1200.0000 ¢, ~12/11 = 148.7230 ¢

Optimal ET sequence: 113, 121, 234

Badness (Sintel): 2.51

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 -3 -4 -5 -1 -2], ⟨0 37 51 63 36 46]]

Optimal tunings:

WE: ~2 = 1199.7257 ¢, ~12/11 = 148.6947 ¢
CWE: ~2 = 1200.0000 ¢, ~12/11 = 148.7230 ¢

Optimal ET sequence: 113, 121, 234

Badness (Sintel): 1.50

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 -3 -4 -5 -1 -2 0], ⟨0 37 51 63 36 46 33]]

Optimal tunings:

WE: ~2 = 1199.5690 ¢, ~12/11 = 148.6815 ¢
CWE: ~2 = 1200.0000 ¢, ~12/11 = 148.7267 ¢

Optimal ET sequence: 113, 121, 234g

Badness (Sintel): 1.29

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: [⟨1 -3 -4 -5 -1 -2 0 4], ⟨0 37 51 63 36 46 33 2]]

Optimal tunings:

WE: ~2 = 1199.7269 ¢, ~12/11 = 148.6928 ¢
CWE: ~2 = 1200.0000 ¢, ~12/11 = 148.7227 ¢

Optimal ET sequence: 113, 121, 234g

Badness (Sintel): 1.37

Canopic clan: Difference between revisions

FloraC (talk | contribs)

Latest revision as of 18:05, 20 October 2026

Contents

Canopus

Overview to extensions

Mirkat

11-limit

13-limit

17-limit

Eris

11-limit

13-limit

Subsemifourth

11-limit

13-limit

Septendesemi

11-limit

13-limit

17-limit

Gaster

11-limit

13-limit

17-limit

19-limit

23-limit

29-limit

31-limit

37-limit

41-limit

Hemiseptisix

11-limit

13-limit

17-limit

Grazer

11-limit

13-limit

17-limit

19-limit

Navigation menu

@@ Line 1: / Line 1: @@
 {{Technical data page}}
-The '''mirkwai clan''' of [[regular temperament|temperaments]] [[tempering out|tempers out]] the [[mirkwai comma]] ({{monzo|legend=1| 0 3 4 -5 }}, [[ratio]]: 16875/16807), a no-twos comma.
+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 ==
@@ Line 9: / Line 9: @@
 [[Comma list]]: 16875/16807
-{{Mapping|legend=2| 1 3 3 | 0 -5 -4 }}
+{{Mapping|legend=3| 1 -2 -1 | 0 5 4 }}
-: mapping generators: ~3, ~7/5
+: mapping generators: ~3, ~15/7
-[[Optimal tuning]] ([[POTE]]): ~3 = 1901.9550{{c}}, ~7/5 = 583.9584{{c}}
+[[Optimal tuning]]s:
+* [[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.
+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 clan and collection pages.
 * ''[[Nusecond]]'' (+126/125) → [[Starling temperaments #Nusecond|Starling temperaments]]
-* ''[[Octoid]]'' (+4375/4374) → [[Ragismic microtemperaments #Octoid|Ragismic microtemperaments]]
+* [[Octoid]] (+4375/4374) → [[Stearnsmic clan #Octoid|Stearnsmic clan]]
-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. Miracle tempers out [[225/224]]. Pluto tempers out [[4000/3969]]. These split the generator in five. Quanharuk tempers out [[32805/32768]], splitting the generator in three with a 1/5-twelfth period. Semisept tempers out [[1728/1715]] and [[3136/3125]], splitting the generator in six. Kwai tempers out [[5120/5103]], splitting the generator in ten. Grendel tempers out [[6144/6125]], splitting the generator in eleven. Finally, eris tempers out [[65625/65536]], splitting the generator in sixteen.
+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) → [[Aberschismic temperaments #Kwai|Aberschismic temperaments]]
 * ''[[Octokaidecal]]'' (+28/27 or 50/49) → [[Trienstonic clan #Octokaidecal|Trienstonic clan]]
 * ''[[Meantritone]]'' (+81/80) → [[Meantone family #Meantritone|Meantone family]]
+* ''[[Quanharuk]]'' (+32805/32768) → [[Schismatic family #Quanharuk|Schismatic family]]
 * [[Miracle]] (+225/224) → [[Gamelismic clan #Miracle|Gamelismic clan]]
+* ''[[Pluto]]'' (+4000/3969) → [[Octagar temperaments #Pluto|Octagar temperaments]]
 * ''[[Bohpier]]'' (+245/243) → [[Sensamagic clan #Bohpier|Sensamagic clan]]
+* ''[[Subsedia]]'' (+65536/64827) → [[Buzzardsmic clan #Subsedia|Buzzardsmic clan]]
 * ''[[Semisept]]'' (+1728/1715 or 3136/3125) → [[Hemimean clan #Semisept|Hemimean clan]]
+* ''[[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]]
-* ''[[Quanharuk]]'' (+32805/32768) → [[Schismatic family #Quanharuk|Schismatic family]]
-* ''[[Familia]]'' (+1600000/1594323) → [[Amity family #Familia|Amity family]]
 * ''[[Rainwell]]'' (+2100875/2097152) → [[Semicomma family #Rainwell|Semicomma family]]
+* ''[[Browser]]'' (+78732/78125) → [[Sensipent family #Browser|Sensipent family]]
 * ''[[Quintiquart]]'' (+390625000/387420489) → [[Quartonic family #Quintiquart|Quartonic family]]
-For ''no-twos'' extensions, see [[No-twos subgroup temperaments #Canopus]].
+For ''no-2's'' extensions, see [[No-twos subgroup temperaments #Canopus]].
-Considered below are grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer.
+Considered below are mirkat, eris, subsemifourth, septendesemi, gaster, hemiseptisix, and grazer, in the order of increasing [[badness]].
-== Grendel ==
+== Mirkat ==
-: ''For the 5-limit version of this temperament, see [[Syntonic–31 equivalence continuum #Counterwürschmidt]].''
+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]]: 6144/6125, 16875/16807
-{{Mapping|legend=1| 1 9 2 7 | 0 -23 1 -13 }}
-: mapping generators: ~2, ~5/4
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~5/4 = 386.863
-{{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d }}
-[[Badness]]: 0.051834
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 5632/5625
-Mapping: {{mapping| 1 9 2 7 17 | 0 -23 1 -13 -42 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.856
-{{Optimal ET sequence|legend=1| 31, 90e, 121, 152, 335d, 487d }}
-Badness: 0.019845
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 540/539, 625/624, 1375/1372
-Mapping: {{mapping| 1 9 2 7 17 -5 | 0 -23 1 -13 -42 27 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.826
-{{Optimal ET sequence|legend=1| 31, 121, 152f, 425deff }}
-Badness: 0.024839
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 352/351, 625/624, 715/714, 1275/1274
-Mapping: {{mapping| 1 9 2 7 17 -5 -3 | 0 -23 1 -13 -42 27 22 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.812
-{{Optimal ET sequence|legend=1| 31, 121, 273defgg }}
-Badness: 0.021400
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 256/255, 352/351, 375/374, 400/399, 456/455, 715/714
-Mapping: {{mapping| 1 9 2 7 17 -5 -3 -8 | 0 -23 1 -13 -42 27 22 38 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.819
-{{Optimal ET sequence|legend=1| 31, 121, 152fg, 273defgg }}
-Badness: 0.018413
-== Kwai ==
-: ''For the 5-limit version of this temperament, see [[High badness temperaments #Kwai]].''
-Named by [[Gene Ward Smith]] in 2004 for its "bridgeability"<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_10766.html Yahoo! Tuning Group | ''Kwai'']</ref>, kwai is generated by a fifth, and can be described as 41 & 70.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 5120/5103, 16875/16807
-{{Mapping|legend=1| 1 0 -50 -40 | 0 1 33 27 }}
-: mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~3/2 = 702.616
-{{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }}
-[[Badness]]: 0.054476
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.623
-{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152 }}
-Badness: 0.026219
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 540/539, 729/728, 1375/1372
-Mapping: {{mapping| 1 0 -50 -40 32 27 | 0 1 33 27 -18 -21 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.644
-{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152f }}
-Badness: 0.024555
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 352/351, 540/539, 715/714, 1089/1088
-Mapping: {{mapping| 1 0 -50 -40 32 27 58 | 0 1 33 27 -18 -21 -34 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.660
-{{Optimal ET sequence|legend=1| 29cdg, 41, 111, 152fg, 263dfg }}
-Badness: 0.021950
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 256/255, 352/351, 400/399, 456/455, 715/714, 847/845
-Mapping: {{mapping| 1 0 -50 -40 32 27 58 -56 | 0 1 33 27 -18 -21 -34 38 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.657
-{{Optimal ET sequence|legend=1| 29cdgh, 41, 111, 152fg, 263dfgh }}
-Badness: 0.016957
-==== Hemikwai ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 540/539, 676/675, 1375/1372, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 -51 | 0 2 66 54 -36 69 }}
-: mapping generators: ~2, ~26/15
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.314
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
-Badness: 0.044108
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 442/441, 540/539, 676/675, 715/714, 5120/5103
-Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 | 0 2 66 54 -36 69 43 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.314
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
-Badness: 0.025806
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 400/399, 442/441, 540/539, 676/675, 715/714, 1445/1444
-Mapping: {{mapping| 1 0 -50 -40 32 -51 -30 -56 | 0 2 66 54 -36 69 43 76 }}
-Optimal tuning (POTE): ~2 = 1\1, ~26/15 = 951.313
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304dh }}
-Badness: 0.019146
-== Pluto ==
-{{Distinguish| plutus }}
-Pluto, named by [[Gene Ward Smith]] in 2010<ref>[https://yahootuninggroupsultimatebackup.github.io/tuning-math/topicId_18465.html Yahoo! Tuning Group | ''19-limit Pluto temperament'']</ref>, can be described as the 41 & 80 temperament. It is generated by a sharpened [[7/5]], and [[121edo|59\121]] is about perfect as a tuning.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 4000/3969, 10976/10935
-{{Mapping|legend=1| 1 5 15 15 | 0 -7 -26 -25 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 585.147
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121, 404bd }}
-[[Badness]]: 0.057514
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 896/891, 1375/1372
-Mapping: {{mapping| 1 5 15 15 2 | 0 -7 -26 -25 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.114
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.029844
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 325/324, 352/351, 364/363, 540/539
-Mapping: {{mapping| 1 5 15 15 2 -8 | 0 -7 -26 -25 3 24 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.123
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.025717
-===== 17-limit =====
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 325/324, 352/351, 364/363, 540/539
-Mapping: {{mapping| 1 5 15 15 2 -8 -12 | 0 -7 -26 -25 3 24 33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.116
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.021463
-===== 19-limit =====
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 190/189, 256/255, 325/324, 352/351, 361/360, 595/594
-Mapping: {{mapping| 1 5 15 15 2 -8 -12 14 | 0 -7 -26 -25 3 24 33 -20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.109
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
-Badness: 0.017650
-==== Orcus ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 144/143, 196/195, 275/273, 896/891
-Mapping: {{mapping| 1 5 15 15 2 12 | 0 -7 -26 -25 3 -17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.111
-{{Optimal ET sequence|legend=1| 39df, 41, 80f, 121ff }}
-Badness: 0.033441
-=== Plutino ===
-Subgroup: 2.3.5.7.11
-Comma list: 100/99, 245/242, 10976/10935
-Mapping: {{mapping| 1 5 15 15 22 | 0 -7 -26 -25 -38 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.283
-{{Optimal ET sequence|legend=1| 39dee, 41 }}
-Badness: 0.057966
-==== 13-limit ====
-Subgroup: 2.3.5.7.11.13
-Comma list: 100/99, 196/195, 245/242, 729/728
-Mapping: {{mapping| 1 5 15 15 22 12 | 0 -7 -26 -25 -38 -17 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.232
-{{Optimal ET sequence|legend=1| 39deef, 41 }}
-Badness: 0.040182
-== Mirkat ==
 [[Subgroup]]: 2.3.5.7
@@ Line 335: / Line 59: @@
 {{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}
+: mapping generators: ~63/50, ~10/9
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 183.539
+[[Optimal tuning]]s:
+* [[WE]]: ~63/50 = 400.0277{{c}}, ~10/9 = 183.5515{{c}}
+: [[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]]: 0.059376
+[[Badness]] (Sintel): 1.50
 === 11-limit ===
@@ Line 347: / Line 76: @@
 Comma list: 540/539, 1375/1372, 8019/8000
-Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}
+{{Mapping|legend=0| 3 2 1 2 9 | 0 6 13 14 3 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~10/9 = 183.528
+Optimal tunings:
+* 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=1| 39d, 72, 111, 183, 255 }}
+{{Optimal ET sequence|legend=0| 39d, 72, 111, 183, 255 }}
-Badness: 0.022126
+Badness (Sintel): 0.731
 === 13-limit ===
@@ Line 360: / Line 91: @@
 Comma list: 351/350, 540/539, 676/675, 1375/1372
-Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
+{{Mapping|legend=0| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~10/9 = 183.577
+Optimal tunings:
+* 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=1| 39df, 72, 111, 183 }}
+{{Optimal ET sequence|legend=0| 39df, 72, 111, 183 }}
-Badness: 0.018632
+Badness (Sintel): 0.770
 === 17-limit ===
@@ Line 373: / Line 106: @@
 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 }}
+{{Mapping|legend=0| 3 2 1 2 9 1 4 | 0 6 13 14 3 22 18 }}
-Optimal tuning (POTE): ~34/27 = 1\3, ~10/9 = 183.579
+Optimal tunings:
+* 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=1| 39dfg, 72, 111, 183 }}
+{{Optimal ET sequence|legend=0| 39dfg, 72, 111, 183 }}
-Badness: 0.011775
+Badness (Sintel): 0.600
 == Eris ==
-The [[2.5.7 subgroup]] restriction of this temperament is [[exodia]].
+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
@@ Line 388: / Line 123: @@
 [[Comma list]]: 16875/16807, 65625/65536
-{{Mapping|legend=1| 1 10 0 6 | 0 -29 8 -11 }}
+{{Mapping|legend=1| 1 -19 8 -5 | 0 29 -8 11 }}
+: mapping generators: ~2, ~49/30
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~60/49 = 348.216
+[[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, 1823cd, 2271cd }}
+{{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224 }}
-[[Badness]]: 0.074719
+[[Badness]] (Sintel): 1.89
 === 11-limit ===
@@ Line 401: / Line 141: @@
 Comma list: 540/539, 1375/1372, 65625/65536
-Mapping: {{mapping| 1 10 0 6 20 | 0 -29 8 -11 -57 }}
+{{Mapping|legend=0| 1 -19 8 -5 -37 | 0 29 -8 11 57 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.219
+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=1| 31, 193, 224, 703, 927d, 1151cd }}
+{{Optimal ET sequence|legend=0| 31, …, 193, 224, 703, 927d }}
-Badness: 0.027621
+Badness (Sintel): 0.913
 === 13-limit ===
@@ Line 414: / Line 156: @@
 Comma list: 540/539, 625/624, 1375/1372, 4096/4095
-Mapping: {{mapping| 1 10 0 6 20 -14 | 0 -29 8 -11 -57 61 }}
+{{Mapping|legend=0| 1 -19 8 -5 -37 47 | 0 29 -8 11 57 -61 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.213
+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=1| 31, 193, 224 }}
+{{Optimal ET sequence|legend=0| 31, 193, 224 }}
-Badness: 0.025137
+Badness (Sintel): 1.04
 == Subsemifourth ==
@@ Line 427: / Line 171: @@
 [[Comma list]]: 16875/16807, 26873856/26796875
-{{Mapping|legend=1| 1 39 27 45 | 0 -47 -31 -53 }}
+{{Mapping|legend=1| 1 -8 -4 -8 | 0 47 31 53 }}
+: mapping generators: ~2, ~144/125
-: mapping generators: ~2, ~125/72
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~144/125 = 244.719
+[[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]]: 0.135173
+[[Badness]] (Sintel): 3.42
 === 11-limit ===
@@ Line 442: / Line 189: @@
 Comma list: 540/539, 1375/1372, 234375/234256
-Mapping: {{mapping| 1 39 27 45 56 | 0 -47 -31 -53 -66 }}
+{{Mapping|legend=0| 1 -8 -4 -8 -10 | 0 47 31 53 66 }}
-Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 244.719
+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=1| 49, 103, 152, 255, 407, 966d }}
+{{Optimal ET sequence|legend=0| 49, 103, 152, 255, 407 }}
-Badness: 0.034276
+Badness (Sintel): 1.13
 === 13-limit ===
@@ Line 455: / Line 204: @@
 Comma list: 540/539, 847/845, 1375/1372, 1575/1573
-Mapping: {{mapping| 1 39 27 45 56 65 | 0 -47 -31 -53 -66 -77 }}
+{{Mapping|legend=0| 1 -8 -4 -8 -10 -12 | 0 0 47 31 53 66 77 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/13 = 244.714
+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=1| 49f, 103, 152f, 255, 407f, 662df }}
+{{Optimal ET sequence|legend=0| 49f, 103, 152f, 255, 407f }}
-Badness: 0.028387
+Badness (Sintel): 1.17
 == Septendesemi ==
-The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 &amp; 103) tempers out the mirkwai comma and 1959552/1953125 (''parkleiness'' comma, zotritrigu) in the 7-limit. [[183edo]] provides an excellent tuning for 7, 11, 13, and 17-limit septendesemi.
+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
@@ Line 470: / Line 221: @@
 [[Comma list]]: 16875/16807, 1959552/1953125
-{{Mapping|legend=1| 1 39 37 53 | 0 -41 -38 -55 }}
+{{Mapping|legend=1| 1 -2 -1 -2 | 0 41 38 55 }}
+: mapping generators: ~2, ~343/324
-: mapping generators: ~2, ~648/343
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/324 = 104.916
+[[Optimal tuning]]s:
+* [[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=1| 80, 103, 183 }}
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-[[Badness]]: 0.146795
+[[Badness]] (Sintel): 3.71
 === 11-limit ===
@@ Line 485: / Line 239: @@
 Comma list: 540/539, 1375/1372, 43923/43750
-Mapping: {{mapping| 1 39 37 53 50 | 0 -41 -38 -55 -51 }}
+{{Mapping|legend=0| 1 -2 -1 -2 -1 | 0 41 38 55 51 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.916
+Optimal tunings:
+* WE: ~2 = 1199.9327{{c}}, ~35/33 = 104.9100{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~35/33 = 104.9144{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183 }}
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-Badness: 0.041554
+Badness (Sintel): 1.37
 === 13-limit ===
@@ Line 498: / Line 254: @@
 Comma list: 351/350, 540/539, 1375/1372, 4225/4224
-Mapping: {{mapping| 1 39 37 53 50 11 | 0 -41 -38 -55 -51 -8 }}
+{{Mapping|legend=0| 1 -2 -1 -2 -1 3 | 0 41 38 55 51 8 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.908
+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=1| 80, 103, 183, 469f, 652def }}
+{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}
-Badness: 0.027908
+Badness (Sintel): 1.15
 === 17-limit ===
@@ Line 511: / Line 269: @@
 Comma list: 351/350, 540/539, 561/560, 715/714, 4225/4224
-Mapping: {{mapping| 1 39 37 53 50 11 5 | 0 -41 -38 -55 -51 -8 -1 }}
+{{Mapping|legend=0| 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 = 1\1, ~17/16 = 104.909
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/16 = 104.909{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183, 469f, 652def }}
+{{Optimal ET sequence|legend=0| 80, 103, 183, 469f }}
-Badness: 0.020128
+Badness (Sintel): 1.03
 == Gaster ==
-: ''For the 5-limit version of this temperament, see [[Very high accuracy temperaments #Gaster]].''
+: ''For the 5-limit version, see [[Very high accuracy temperaments #Gaster]].''
 {{Main| Gaster temperament }}
-The ''gaster'' temperament (111 &amp; 113) tempers out {{monzo| -70 72 -19 }} (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and [[scheme comma]] (14348907/14336000) in the 7-limit. 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.
+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
@@ Line 529: / Line 293: @@
 [[Comma list]]: 16875/16807, 14348907/14336000
-{{Mapping|legend=1| 1 11 38 37 | 0 -19 -72 -69 }}
+{{Mapping|legend=1| 1 -8 -34 -32 | 0 19 72 69 }}
+: mapping generators: ~2, ~567/400
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~800/567 = 594.641
+[[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 }}
 {{Optimal ET sequence|legend=1| 111, 224 }}
-[[Badness]]: 0.154521
+[[Badness]] (Sintel): 3.91
 === 11-limit ===
@@ Line 542: / Line 311: @@
 Comma list: 540/539, 1375/1372, 14348907/14336000
-Mapping: {{mapping| 1 11 38 37 -1 | 0 -19 -72 -69 9 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 | 0 19 72 69 -9 }}
-Optimal tuning (POTE): ~2 = 1\1, ~512/363 = 594.639
+Optimal tunings:
+* WE: ~2 = 1199.9387{{c}}, ~363/256 = 605.3300{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~363/256 = 605.3603{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 783d, 1007d, 1231dd }}
+{{Optimal ET sequence|legend=0| 111, 224, 783d }}
-Badness: 0.054060
+Badness (Sintel): 1.79
 === 13-limit ===
@@ Line 555: / Line 326: @@
 Comma list: 540/539, 729/728, 1375/1372, 2200/2197
-Mapping: {{mapping| 1 11 38 37 -1 26 | 0 -19 -72 -69 9 -45 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 | 0 19 72 69 -9 45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/39 = 594.639
+Optimal tunings:
+* WE: ~2 = 1199.9154{{c}}, ~78/55 = 605.3183{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~78/55 = 605.3601{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 783df, 1007df, 1231ddf }}
+{{Optimal ET sequence|legend=0| 111, 224, 783df }}
-Badness: 0.024882
+Badness (Sintel): 1.03
 === 17-limit ===
@@ Line 568: / Line 341: @@
 Comma list: 540/539, 715/714, 729/728, 936/935, 2200/2197
-Mapping: {{mapping| 1 11 38 37 -1 26 14 | 0 -19 -72 -69 9 -45 -20 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 | 0 19 72 69 -9 45 20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
+Optimal tunings:
+* WE: ~2 = 1199.8076{{c}}, ~17/12 = 605.2674{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3626{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 559dgg }}
+{{Optimal ET sequence|legend=0| 111, 224, 559dgg }}
-Badness: 0.021436
+Badness (Sintel): 1.09
 === 19-limit ===
@@ Line 581: / Line 356: @@
 Comma list: 324/323, 400/399, 495/494, 540/539, 715/714, 1445/1444
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 | 0 -19 -72 -69 9 -45 -20 -56 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 | 0 19 72 69 -9 45 20 56 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
+Optimal tunings:
+* WE: ~2 = 1199.7542{{c}}, ~17/12 = 605.2674{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3613{{c}}
-{{Optimal ET sequence|legend=1| 111, 224 }}
+{{Optimal ET sequence|legend=0| 111, 224 }}
-Badness: 0.018370
+Badness (Sintel): 1.12
 === 23-limit ===
@@ Line 594: / Line 371: @@
 Comma list: 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 | 0 -19 -72 -69 9 -45 -20 -56 -5 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 | 0 19 72 69 -9 45 20 56 5 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.641
+Optimal tunings:
+* WE: ~2 = 1199.8733{{c}}, ~17/12 = 605.2946{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3575{{c}}
-{{Optimal ET sequence|legend=1| 111, 224 }}
+{{Optimal ET sequence|legend=0| 111, 224 }}
-Badness: 0.017619
+Badness (Sintel): 1.26
 === 29-limit ===
@@ Line 607: / Line 386: @@
 Comma list: 290/289, 324/323, 400/399, 460/459, 495/494, 529/528, 540/539, 715/714
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 | 0 19 72 69 -9 45 20 56 5 -32 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.646
+Optimal tunings:
+* WE: ~2 = 1199.9442{{c}}, ~17/12 = 605.3263{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3541{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.016815
+Badness (Sintel): 1.41
 === 31-limit ===
@@ Line 620: / Line 401: @@
 Comma list: 290/289, 324/323, 400/399, 435/434, 460/459, 495/494, 528/527, 540/539, 715/714
-Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 | 0 19 72 69 -9 45 20 56 5 -32 -10 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
+Optimal tunings:
+* WE: ~2 = 1199.9100{{c}}, ~17/12 = 605.3107{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3556{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.014790
+Badness (Sintel): 1.42
 === 37-limit ===
@@ Line 633: / Line 416: @@
 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 11 38 37 -1 26 14 32 7 -11 0 -27 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 }}
+{{Mapping|legend=0| 1 -8 -34 -32 8 -19 -6 -24 2 21 10 38 | 0 19 72 69 -9 45 20 56 5 -32 -10 -65 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
+Optimal tunings:
+* WE: ~2 = 1199.9087{{c}}, ~17/12 = 605.3101{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3559{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.014377
+Badness (Sintel): 1.56
 === 41-limit ===
@@ Line 646: / Line 431: @@
 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 11 38 37 -1 26 14 32 7 -11 0 -27 45 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65 -80 }}
+{{Mapping|legend=0| 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 tuning (POTE): ~2 = 1\1, ~24/17 = 594.643
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
-Badness: 0.012858
-== Subsedia ==
-The generator for ''subsedia'' (10 &amp; 111) is 0.5 cents flat of [[15/14]]-wide semitone and tempers out the mirkwai comma and 65536/64827 (''buzzardisma'', saquadru comma). In this temperament, three generators makes ~[[16/13]], five of them equals ~[[24/17]], twelve of them equals ~[[16/7]], sixteen of them equals ~[[3/1]], and 45 of them equals ~22/1.
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 16875/16807, 65536/64827
-{{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 118.965
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
-[[Badness]]: 0.157658
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 65536/64827
-Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
-Badness: 0.066838
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 352/351, 540/539, 676/675, 1375/1372
-Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
+Optimal tunings:
+* WE: ~2 = 1199.9179{{c}}, ~17/12 = 605.3156{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/12 = 605.3567{{c}}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
+Badness (Sintel): 1.57
-Badness: 0.031635
-=== 17-limit ===
-Subgroup: 2.3.5.7.11.13.17
-Comma list: 256/255, 352/351, 442/441, 540/539, 715/714
-Mapping: {{mapping| 1 0 5 4 -1 4 3 | 0 16 -27 -12 45 -3 11 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232dg }}
-Badness: 0.019707
-=== 19-limit ===
-Subgroup: 2.3.5.7.11.13.17.19
-Comma list: 256/255, 352/351, 400/399, 442/441, 456/455, 715/714
-Mapping: {{mapping| 1 0 5 4 -1 4 3 10 | 0 16 -27 -12 45 -3 11 -58 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.964
-{{Optimal ET sequence|legend=1| 10, 101h, 111, 121, 232dg }}
-Badness: 0.017935
 == Hemiseptisix ==
-The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 &amp; 121) tempers out the mirkwai comma and 95703125/95551488 (''pontiqak'' comma, lazozotritriyo) in the 7-limit. [[224edo]] provides an excellent tuning for 7-, 11-, and 13-limit hemiseptisix.
+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
@@ Line 728: / Line 448: @@
 [[Comma list]]: 16875/16807, 95703125/95551488
-{{Mapping|legend=1| 1 34 17 34 | 0 -53 -24 -51 }}
+{{Mapping|legend=1| 1 -19 -7 -17 | 0 53 24 51 }}
+: mapping generators: ~2, ~98/75
-: mapping generators: ~2, ~75/49
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 466.071
+[[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 }}
 {{Optimal ET sequence|legend=1| 103, 121, 224 }}
-[[Badness]]: 0.162826
+[[Badness]] (Sintel): 4.12
 === 11-limit ===
@@ Line 743: / Line 466: @@
 Comma list: 540/539, 1375/1372, 2734375/2725888
-Mapping: {{mapping| 1 34 17 34 53 | 0 -53 -24 -51 -81 }}
+{{Mapping|legend=0| 1 -19 -7 -17 -28 | 0 53 24 51 81 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.070
+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=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.043381
+Badness (Sintel): 1.43
 === 13-limit ===
@@ Line 756: / Line 481: @@
 Comma list: 540/539, 625/624, 1375/1372, 2200/2197
-Mapping: {{mapping| 1 34 17 34 53 30 | 0 -53 -24 -51 -81 -43 }}
+{{Mapping|legend=0| 1 -19 -7 -17 -28 -13 | 0 53 24 51 81 43 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.071
+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=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.021127
+Badness (Sintel): 0.873
 === 17-limit ===
@@ Line 769: / Line 496: @@
 Comma list: 375/374, 540/539, 625/624, 715/714, 2200/2197
-Mapping: {{mapping| 1 34 17 34 53 30 31 | 0 -53 -24 -51 -81 -43 -44 }}
+{{Mapping|legend=0| 1 -19 -7 -17 -28 -13 -13 | 0 53 24 51 81 43 44 }}
-Optimal tuning (POTE): ~2 = 1\1, ~17/13 = 466.074
+Optimal tunings:
+* WE: ~2 = 1199.8544{{c}}, ~17/13 = 466.0174{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~17/13 = 466.0718{{c}}
-{{Optimal ET sequence|legend=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.018611
+Badness (Sintel): 0.948
-== Browser ==
+== Grazer ==
-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 MOSes of 8, 15, 23, and 31 notes despite no harmonics from the root. It can be considered a detemperament of 8et, with a generator very slightly sharp of 1\8.
+Named by [[Xenllium]] in 2022, grazer may be described as the {{nowrap| 113 & 121 }} temperament.
-{{See also| Sensipent family }}
-[[Subgroup]]: 2.3.5.7
-[[Comma list]]: 16875/16807, 78732/78125
-{{Mapping|legend=1| 1 6 8 10 | 0 -35 -45 -57 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 151.399
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
-[[Badness]]: 0.180645
-=== 11-limit ===
-Subgroup: 2.3.5.7.11
-Comma list: 540/539, 1375/1372, 78732/78125
-Mapping: {{mapping| 1 6 8 10 8 | 0 -35 -45 -57 -36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.405
-{{Optimal ET sequence|legend=1| 103, 214 }}
-Badness: 0.057634
-=== 13-limit ===
-Subgroup: 2.3.5.7.11.13
-Comma list: 351/350, 540/539, 847/845, 1375/1372
-Mapping: {{mapping| 1 6 8 10 8 9 | 0 -35 -45 -57 -36 -42 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.403
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
-Badness: 0.028822
-=== 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 6 8 10 8 9 8 | 0 -35 -45 -57 -36 -42 -31 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.397
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
-Badness: 0.020384
-=== 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 6 8 10 8 9 8 18 | 0 -35 -45 -57 -36 -42 -31 -109 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.396
-{{Optimal ET sequence|legend=1| 103h, 111, 214 }}
-Badness: 0.017570
-== Grazer ==
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: 16875/16807, 1071875/1062882
-{{Mapping|legend=1| 1 34 47 58 | 0 -37 -51 -63 }}
+{{Mapping|legend=1| 1 -3 -4 -5 | 0 37 51 63 }}
+: mapping generators: ~2, ~49/45
-: mapping generators: ~2, ~90/49
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 148.719
+[[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 }}
-[[Badness]]: 0.217166
+[[Badness]] (Sintel): 5.50
 === 11-limit ===
@@ Line 865: / Line 531: @@
 Comma list: 540/539, 1375/1372, 218750/216513
-Mapping: {{mapping| 1 34 47 58 35 | 0 -37 -51 -63 -36 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 | 0 37 51 63 36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
+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=1| 113, 121, 234, 355e, 589cee }}
+{{Optimal ET sequence|legend=0| 113, 121, 234 }}
-Badness: 0.076062
+Badness (Sintel): 2.51
 === 13-limit ===
@@ Line 878: / Line 546: @@
 Comma list: 325/324, 364/363, 540/539, 2200/2197
-Mapping: {{mapping| 1 34 47 58 35 44 | 0 -37 -51 -63 -36 -46 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 -2 | 0 37 51 63 36 46 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
+Optimal tunings:
+* WE: ~2 = 1199.7257{{c}}, ~12/11 = 148.6947{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7230{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234, 355e, 589cee }}
+{{Optimal ET sequence|legend=0| 113, 121, 234 }}
-Badness: 0.036248
+Badness (Sintel): 1.50
 === 17-limit ===
@@ Line 891: / Line 561: @@
 Comma list: 325/324, 364/363, 540/539, 595/594, 2000/1989
-Mapping: {{mapping| 1 34 47 58 35 44 33 | 0 -37 -51 -63 -36 -46 -33 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 -2 0 | 0 37 51 63 36 46 33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.735
+Optimal tunings:
+* WE: ~2 = 1199.5690{{c}}, ~12/11 = 148.6815{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7267{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg }}
+{{Optimal ET sequence|legend=0| 113, 121, 234g }}
-Badness: 0.025410
+Badness (Sintel): 1.29
 === 19-limit ===
@@ Line 904: / Line 576: @@
 Comma list: 325/324, 364/363, 400/399, 540/539, 595/594, 665/663
-Mapping: {{mapping| 1 34 47 58 35 44 33 6 | 0 -37 -51 -63 -36 -46 -33 -2 }}
+{{Mapping|legend=0| 1 -3 -4 -5 -1 -2 0 4 | 0 37 51 63 36 46 33 2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.727
-{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg, 589ceegg }}
+Optimal tunings:
+* WE: ~2 = 1199.7269{{c}}, ~12/11 = 148.6928{{c}}
+* CWE: ~2 = 1200.0000{{c}}, ~12/11 = 148.7227{{c}}
-Badness: 0.022574
+{{Optimal ET sequence|legend=0| 113, 121, 234g }}
-== Notes ==
+Badness (Sintel): 1.37
+[[Category:Canopic clan| ]] <!-- main article -->
+[[Category:Canopic| ]] <!-- key article -->
 [[Category:Temperament clans]]
-[[Category:Mirkwai clan| ]] <!-- main article -->
+[[Category:Catalogs of rank-2 temperaments]]
-[[Category:Mirkwai| ]] <!-- key article -->
-[[Category:Rank 2]]

Canopic clan: Difference between revisions

FloraC (talk | contribs)

Latest revision as of 18:05, 20 October 2026

Canopus

Overview to extensions

Mirkat

11-limit

13-limit

17-limit

Eris

11-limit

13-limit

Subsemifourth

11-limit

13-limit

Septendesemi

11-limit

13-limit

17-limit

Gaster

11-limit

13-limit

17-limit

19-limit

23-limit

29-limit

31-limit

37-limit

41-limit

Hemiseptisix

11-limit

13-limit

17-limit

Grazer

11-limit

13-limit

17-limit

19-limit

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