Canopic clan: Difference between revisions

Revision as of 10:18, 2 April 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 mirkwai clan of temperaments tempers out the mirkwai 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 3 3], ⟨0 -5 -4]]

mapping generators: ~3, ~7/5

Optimal tuning (POTE): ~3 = 1901.9550 ¢, ~7/5 = 583.9584 ¢

Optimal ET sequence: b13, b62, b75, b88, b101, b114, b355, b469, b583, b697

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
Octoid (+4375/4374) → 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. 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.

Members of the clan discussed elsewhere are:

Octokaidecal (+28/27 or 50/49) → Trienstonic clan
Meantritone (+81/80) → Meantone family
Miracle (+225/224) → Gamelismic clan
Bohpier (+245/243) → Sensamagic clan
Semisept (+1728/1715 or 3136/3125) → Hemimean clan
Quinmage (+3125/3072) → Magic family
Sqrtphi (+15625/15552) → Kleismic family
Quanharuk (+32805/32768) → Schismatic family
Familia (+1600000/1594323) → Amity family
Rainwell (+2100875/2097152) → Semicomma family
Quintiquart (+390625000/387420489) → Quartonic family

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

Considered below are grendel, kwai, pluto, mirkat, eris, subsemifourth, septendesemi, gaster, subsedia, hemiseptisix, browser, and grazer.

Grendel

For the 5-limit version of this temperament, see Syntonic–31 equivalence continuum #Counterwürschmidt.

Subgroup: 2.3.5.7

Comma list: 6144/6125, 16875/16807

Mapping: [⟨1 9 2 7], ⟨0 -23 1 -13]]

mapping generators: ~2, ~5/4

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~5/4 = 386.863 ¢

Optimal ET sequence: 31, 90, 121, 152, 335d

Badness (Smith): 0.051834

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 5632/5625

Mapping: [⟨1 9 2 7 17], ⟨0 -23 1 -13 -42]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~5/4 = 386.856 ¢

Optimal ET sequence: 31, 90e, 121, 152, 335d, 487d

Badness (Smith): 0.019845

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 625/624, 1375/1372

Mapping: [⟨1 9 2 7 17 -5], ⟨0 -23 1 -13 -42 27]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~5/4 = 386.826 ¢

Optimal ET sequence: 31, 121, 152f, 425deff

Badness (Smith): 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: [⟨1 9 2 7 17 -5 -3], ⟨0 -23 1 -13 -42 27 22]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~5/4 = 386.812 ¢

Optimal ET sequence: 31, 121, 273defgg

Badness (Smith): 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: [⟨1 9 2 7 17 -5 -3 -8], ⟨0 -23 1 -13 -42 27 22 38]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~5/4 = 386.819 ¢

Optimal ET sequence: 31, 121, 152fg, 273defgg

Badness (Smith): 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"^[1], 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: [⟨1 0 -50 -40], ⟨0 1 33 27]]

mapping generators: ~2, ~3

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 702.616 ¢

Optimal ET sequence: 41, 111, 152, 345, 497d

Badness (Smith): 0.054476

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 5120/5103

Mapping: [⟨1 0 -50 -40 32], ⟨0 1 33 27 -18]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 702.623 ¢

Optimal ET sequence: 29cd, 41, 111, 152

Badness (Smith): 0.026219

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 729/728, 1375/1372

Mapping: [⟨1 0 -50 -40 32 27], ⟨0 1 33 27 -18 -21]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 702.644 ¢

Optimal ET sequence: 29cd, 41, 111, 152f

Badness (Smith): 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: [⟨1 0 -50 -40 32 27 58], ⟨0 1 33 27 -18 -21 -34]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 702.660 ¢

Optimal ET sequence: 29cdg, 41, 111, 152fg, 263dfg

Badness (Smith): 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: [⟨1 0 -50 -40 32 27 58 -56], ⟨0 1 33 27 -18 -21 -34 38]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~3/2 = 702.657 ¢

Optimal ET sequence: 29cdgh, 41, 111, 152fg, 263dfgh

Badness (Smith): 0.016957

Hemikwai

Subgroup: 2.3.5.7.11.13

Comma list: 540/539, 676/675, 1375/1372, 5120/5103

Mapping: [⟨1 0 -50 -40 32 -51], ⟨0 2 66 54 -36 69]]

mapping generators: ~2, ~26/15

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~26/15 = 951.314 ¢

Optimal ET sequence: 82, 111, 193, 304d

Badness (Smith): 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: [⟨1 0 -50 -40 32 -51 -30], ⟨0 2 66 54 -36 69 43]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~26/15 = 951.314 ¢

Optimal ET sequence: 82, 111, 193, 304d

Badness (Smith): 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: [⟨1 0 -50 -40 32 -51 -30 -56], ⟨0 2 66 54 -36 69 43 76]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~26/15 = 951.313 ¢

Optimal ET sequence: 82, 111, 193, 304dh

Badness (Smith): 0.019146

Pluto

Not to be confused with Plutus.

Pluto, named by Gene Ward Smith in 2010^[2], can be described as the 41 & 80 temperament. It is generated by a sharpened 7/5, and 59\121 is about perfect as a tuning.

Subgroup: 2.3.5.7

Comma list: 4000/3969, 10976/10935

Mapping: [⟨1 5 15 15], ⟨0 -7 -26 -25]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.147 ¢

Optimal ET sequence: 39d, 41, 80, 121, 404bd

Badness (Smith): 0.057514

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 896/891, 1375/1372

Mapping: [⟨1 5 15 15 2], ⟨0 -7 -26 -25 3]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.114 ¢

Optimal ET sequence: 39d, 41, 80, 121

Badness (Smith): 0.029844

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 325/324, 352/351, 364/363, 540/539

Mapping: [⟨1 5 15 15 2 -8], ⟨0 -7 -26 -25 3 24]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.123 ¢

Optimal ET sequence: 39d, 41, 80, 121

Badness (Smith): 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: [⟨1 5 15 15 2 -8 -12], ⟨0 -7 -26 -25 3 24 33]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.116 ¢

Optimal ET sequence: 39d, 41, 80, 121

Badness (Smith): 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: [⟨1 5 15 15 2 -8 -12 14], ⟨0 -7 -26 -25 3 24 33 -20]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.109 ¢

Optimal ET sequence: 39d, 41, 80, 121

Badness (Smith): 0.017650

Orcus

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 196/195, 275/273, 896/891

Mapping: [⟨1 5 15 15 2 12], ⟨0 -7 -26 -25 3 -17]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.111 ¢

Optimal ET sequence: 39df, 41, 80f, 121ff

Badness (Smith): 0.033441

Plutino

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 10976/10935

Mapping: [⟨1 5 15 15 22], ⟨0 -7 -26 -25 -38]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.283 ¢

Optimal ET sequence: 39dee, 41

Badness (Smith): 0.057966

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 100/99, 196/195, 245/242, 729/728

Mapping: [⟨1 5 15 15 22 12], ⟨0 -7 -26 -25 -38 -17]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~7/5 = 585.232 ¢

Optimal ET sequence: 39deef, 41

Badness (Smith): 0.040182

Mirkat

Subgroup: 2.3.5.7

Comma list: 16875/16807, 19683/19600

Mapping: [⟨3 2 1 2], ⟨0 6 13 14]]

Optimal tuning (POTE): ~63/50 = 400.000 ¢, ~10/9 = 183.539 ¢

Optimal ET sequence: 39d, 72, 111, 183, 255

Badness (Smith): 0.059376

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 tuning (POTE): ~63/50 = 400.000 ¢, ~10/9 = 183.528 ¢

Optimal ET sequence: 39d, 72, 111, 183, 255

Badness (Smith): 0.022126

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 tuning (POTE): ~63/50 = 400.000 ¢, ~10/9 = 183.577 ¢

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

Badness (Smith): 0.018632

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 tuning (POTE): ~34/27 = 400.000 ¢, ~10/9 = 183.579 ¢

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

Badness (Smith): 0.011775

Eris

The 2.5.7 subgroup restriction of this temperament is exodia.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 65625/65536

Mapping: [⟨1 10 0 6], ⟨0 -29 8 -11]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~60/49 = 348.216 ¢

Optimal ET sequence: 31, 131, 162, 193, 224, 1823cd, 2271cd

Badness (Smith): 0.074719

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 10 0 6 20], ⟨0 -29 8 -11 -57]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~11/9 = 348.219 ¢

Optimal ET sequence: 31, 193, 224, 703, 927d, 1151cd

Badness (Smith): 0.027621

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 10 0 6 20 -14], ⟨0 -29 8 -11 -57 61]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~11/9 = 348.213 ¢

Optimal ET sequence: 31, 193, 224

Badness (Smith): 0.025137

Subsemifourth

Subgroup: 2.3.5.7

Comma list: 16875/16807, 26873856/26796875

Mapping: [⟨1 39 27 45], ⟨0 -47 -31 -53]]

mapping generators: ~2, ~125/72

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~144/125 = 244.719 ¢

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

Badness (Smith): 0.135173

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 39 27 45 56], ⟨0 -47 -31 -53 -66]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~121/105 = 244.719 ¢

Optimal ET sequence: 49, 103, 152, 255, 407, 966d

Badness (Smith): 0.034276

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 39 27 45 56 65], ⟨0 -47 -31 -53 -66 -77]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~15/13 = 244.714 ¢

Optimal ET sequence: 49f, 103, 152f, 255, 407f, 662df

Badness (Smith): 0.028387

Septendesemi

The name septendesemi means a septendecimal semitone (17/16). The septendesemi temperament (80 & 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.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 1959552/1953125

Mapping: [⟨1 39 37 53], ⟨0 -41 -38 -55]]

mapping generators: ~2, ~648/343

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~343/324 = 104.916 ¢

Optimal ET sequence: 80, 103, 183

Badness (Smith): 0.146795

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 39 37 53 50], ⟨0 -41 -38 -55 -51]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~35/33 = 104.916 ¢

Optimal ET sequence: 80, 103, 183

Badness (Smith): 0.041554

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 39 37 53 50 11], ⟨0 -41 -38 -55 -51 -8]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~35/33 = 104.908 ¢

Optimal ET sequence: 80, 103, 183, 469f, 652def

Badness (Smith): 0.027908

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 39 37 53 50 11 5], ⟨0 -41 -38 -55 -51 -8 -1]]

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

Optimal ET sequence: 80, 103, 183, 469f, 652def

Badness (Smith): 0.020128

Gaster

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

Main article: Gaster temperament

The gaster temperament (111 & 113) tempers out [-70 72 -19⟩ (quadbila-negu) in the 5-limit; mirkwai comma (16875/16807) and scheme comma (14348907/14336000) in the 7-limit. 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 11 38 37], ⟨0 -19 -72 -69]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~800/567 = 594.641 ¢

Optimal ET sequence: 111, 224

Badness (Smith): 0.154521

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 11 38 37 -1], ⟨0 -19 -72 -69 9]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~512/363 = 594.639 ¢

Optimal ET sequence: 111, 224, 783d, 1007d, 1231dd

Badness (Smith): 0.054060

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 11 38 37 -1 26], ⟨0 -19 -72 -69 9 -45]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~55/39 = 594.639 ¢

Optimal ET sequence: 111, 224, 783df, 1007df, 1231ddf

Badness (Smith): 0.024882

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 11 38 37 -1 26 14], ⟨0 -19 -72 -69 9 -45 -20]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~24/17 = 594.636 ¢

Optimal ET sequence: 111, 224, 559dgg

Badness (Smith): 0.021436

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 11 38 37 -1 26 14 32], ⟨0 -19 -72 -69 9 -45 -20 -56]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~24/17 = 594.636 ¢

Optimal ET sequence: 111, 224

Badness (Smith): 0.018370

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 11 38 37 -1 26 14 32 7], ⟨0 -19 -72 -69 9 -45 -20 -56 -5]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~24/17 = 594.641 ¢

Optimal ET sequence: 111, 224

Badness (Smith): 0.017619

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 11 38 37 -1 26 14 32 7 -11], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~24/17 = 594.646 ¢

Optimal ET sequence: 111, 113, 224

Badness (Smith): 0.016815

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 11 38 37 -1 26 14 32 7 -11 0], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~24/17 = 594.644 ¢

Optimal ET sequence: 111, 113, 224

Badness (Smith): 0.014790

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 11 38 37 -1 26 14 32 7 -11 0 -27], ⟨0 -19 -72 -69 9 -45 -20 -56 -5 32 10 65]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~24/17 = 594.644 ¢

Optimal ET sequence: 111, 113, 224

Badness (Smith): 0.014377

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 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]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~24/17 = 594.643 ¢

Optimal ET sequence: 111, 113, 224

Badness (Smith): 0.012858

Subsedia

The generator for subsedia (10 & 111) is 0.5 cents flat of 15/14-wide semitone and tempers out the mirkwai comma and buzzardsma. 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: [⟨1 0 5 4], ⟨0 16 -27 -12]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~15/14 = 118.965 ¢

Optimal ET sequence: 10, 101, 111, 121, 232d

Badness (Smith): 0.157658

11-limit

Subgroup: 2.3.5.7.11

Comma list: 540/539, 1375/1372, 65536/64827

Mapping: [⟨1 0 5 4 -1], ⟨0 16 -27 -12 45]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~15/14 = 118.968 ¢

Optimal ET sequence: 10, 101, 111, 121, 232d

Badness (Smith): 0.066838

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 352/351, 540/539, 676/675, 1375/1372

Mapping: [⟨1 0 5 4 -1 4], ⟨0 16 -27 -12 45 -3]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~15/14 = 118.968 ¢

Optimal ET sequence: 10, 101, 111, 121, 232d

Badness (Smith): 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: [⟨1 0 5 4 -1 4 3], ⟨0 16 -27 -12 45 -3 11]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~15/14 = 118.968 ¢

Optimal ET sequence: 10, 101, 111, 121, 232dg

Badness (Smith): 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: [⟨1 0 5 4 -1 4 3 10], ⟨0 16 -27 -12 45 -3 11 -58]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~15/14 = 118.964 ¢

Optimal ET sequence: 10, 101h, 111, 121, 232dg

Badness (Smith): 0.017935

Hemiseptisix

The name hemiseptisix means a half of septimal major sixth (12/7). The hemiseptisix temperament (103 & 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.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 95703125/95551488

Mapping: [⟨1 34 17 34], ⟨0 -53 -24 -51]]

mapping generators: ~2, ~75/49

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~98/75 = 466.071 ¢

Optimal ET sequence: 103, 121, 224

Badness (Smith): 0.162826

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 34 17 34 53], ⟨0 -53 -24 -51 -81]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~55/42 = 466.070 ¢

Optimal ET sequence: 103, 121, 224

Badness (Smith): 0.043381

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 34 17 34 53 30], ⟨0 -53 -24 -51 -81 -43]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~55/42 = 466.071 ¢

Optimal ET sequence: 103, 121, 224

Badness (Smith): 0.021127

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 34 17 34 53 30 31], ⟨0 -53 -24 -51 -81 -43 -44]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~17/13 = 466.074 ¢

Optimal ET sequence: 103, 121, 224

Badness (Smith): 0.018611

Browser

See also: Sensipent family

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.

Subgroup: 2.3.5.7

Comma list: 16875/16807, 78732/78125

Mapping: [⟨1 6 8 10], ⟨0 -35 -45 -57]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~49/45 = 151.399 ¢

Optimal ET sequence: 103, 111, 214

Badness (Smith): 0.180645

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 6 8 10 8], ⟨0 -35 -45 -57 -36]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 151.405 ¢

Optimal ET sequence: 103, 214

Badness (Smith): 0.057634

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 6 8 10 8 9], ⟨0 -35 -45 -57 -36 -42]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 151.403 ¢

Optimal ET sequence: 103, 111, 214

Badness (Smith): 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: [⟨1 6 8 10 8 9 8], ⟨0 -35 -45 -57 -36 -42 -31]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 151.397 ¢

Optimal ET sequence: 103, 111, 214

Badness (Smith): 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: [⟨1 6 8 10 8 9 8 18], ⟨0 -35 -45 -57 -36 -42 -31 -109]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 151.396 ¢

Optimal ET sequence: 103h, 111, 214

Badness (Smith): 0.017570

Grazer

Subgroup: 2.3.5.7

Comma list: 16875/16807, 1071875/1062882

Mapping: [⟨1 34 47 58], ⟨0 -37 -51 -63]]

mapping generators: ~2, ~90/49

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~49/45 = 148.719 ¢

Optimal ET sequence: 113, 121, 234

Badness (Smith): 0.217166

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 34 47 58 35], ⟨0 -37 -51 -63 -36]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 148.729 ¢

Optimal ET sequence: 113, 121, 234, 355e, 589cee

Badness (Smith): 0.076062

13-limit

Subgroup: 2.3.5.7.11.13

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

Mapping: [⟨1 34 47 58 35 44], ⟨0 -37 -51 -63 -36 -46]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 148.729 ¢

Optimal ET sequence: 113, 121, 234, 355e, 589cee

Badness (Smith): 0.036248

17-limit

Subgroup: 2.3.5.7.11.13.17

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

Mapping: [⟨1 34 47 58 35 44 33], ⟨0 -37 -51 -63 -36 -46 -33]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 148.735 ¢

Optimal ET sequence: 113, 121, 234g, 355eg

Badness (Smith): 0.025410

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 34 47 58 35 44 33 6], ⟨0 -37 -51 -63 -36 -46 -33 -2]]

Optimal tuning (POTE): ~2 = 1200.000 ¢, ~12/11 = 148.727 ¢

Optimal ET sequence: 113, 121, 234g, 355eg, 589ceegg

Badness (Smith): 0.022574

References

[1] Yahoo! Tuning Group | Kwai

[2] Yahoo! Tuning Group | 19-limit Pluto temperament

[1]

[2]

@@ Line 48: / Line 48: @@
 {{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 tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~5/4 = 386.863{{c}}
 {{Optimal ET sequence|legend=1| 31, 90, 121, 152, 335d }}
-[[Badness]]: 0.051834
+[[Badness]] (Smith): 0.051834
 === 11-limit ===
@@ Line 64: / Line 63: @@
 Mapping: {{mapping| 1 9 2 7 17 | 0 -23 1 -13 -42 }}
-Optimal tuning (POTE): ~2 = 1\1, ~5/4 = 386.856
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.856{{c}}
-{{Optimal ET sequence|legend=1| 31, 90e, 121, 152, 335d, 487d }}
+{{Optimal ET sequence|legend=0| 31, 90e, 121, 152, 335d, 487d }}
-Badness: 0.019845
+Badness (Smith): 0.019845
 === 13-limit ===
@@ Line 77: / Line 76: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.826{{c}}
-{{Optimal ET sequence|legend=1| 31, 121, 152f, 425deff }}
+{{Optimal ET sequence|legend=0| 31, 121, 152f, 425deff }}
-Badness: 0.024839
+Badness (Smith): 0.024839
 === 17-limit ===
@@ Line 90: / Line 89: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.812{{c}}
-{{Optimal ET sequence|legend=1| 31, 121, 273defgg }}
+{{Optimal ET sequence|legend=0| 31, 121, 273defgg }}
-Badness: 0.021400
+Badness (Smith): 0.021400
 === 19-limit ===
@@ Line 103: / Line 102: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~5/4 = 386.819{{c}}
-{{Optimal ET sequence|legend=1| 31, 121, 152fg, 273defgg }}
+{{Optimal ET sequence|legend=0| 31, 121, 152fg, 273defgg }}
-Badness: 0.018413
+Badness (Smith): 0.018413
 == Kwai ==
@@ Line 119: / Line 118: @@
 {{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 tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~3/2 = 702.616{{c}}
 {{Optimal ET sequence|legend=1| 41, 111, 152, 345, 497d }}
-[[Badness]]: 0.054476
+[[Badness]] (Smith): 0.054476
 === 11-limit ===
@@ Line 135: / Line 133: @@
 Mapping: {{mapping| 1 0 -50 -40 32 | 0 1 33 27 -18 }}
-Optimal tuning (POTE): ~2 = 1\1, ~3/2 = 702.623
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.623{{c}}
-{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152 }}
+{{Optimal ET sequence|legend=0| 29cd, 41, 111, 152 }}
-Badness: 0.026219
+Badness (Smith): 0.026219
 ==== 13-limit ====
@@ Line 148: / Line 146: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.644{{c}}
-{{Optimal ET sequence|legend=1| 29cd, 41, 111, 152f }}
+{{Optimal ET sequence|legend=0| 29cd, 41, 111, 152f }}
-Badness: 0.024555
+Badness (Smith): 0.024555
 ===== 17-limit =====
@@ Line 161: / Line 159: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.660{{c}}
-{{Optimal ET sequence|legend=1| 29cdg, 41, 111, 152fg, 263dfg }}
+{{Optimal ET sequence|legend=0| 29cdg, 41, 111, 152fg, 263dfg }}
-Badness: 0.021950
+Badness (Smith): 0.021950
 ===== 19-limit =====
@@ Line 174: / Line 172: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~3/2 = 702.657{{c}}
-{{Optimal ET sequence|legend=1| 29cdgh, 41, 111, 152fg, 263dfgh }}
+{{Optimal ET sequence|legend=0| 29cdgh, 41, 111, 152fg, 263dfgh }}
-Badness: 0.016957
+Badness (Smith): 0.016957
 ==== Hemikwai ====
@@ Line 186: / Line 184: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.314{{c}}
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
+{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}
-Badness: 0.044108
+Badness (Smith): 0.044108
 ===== 17-limit =====
@@ Line 202: / Line 199: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.314{{c}}
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304d }}
+{{Optimal ET sequence|legend=0| 82, 111, 193, 304d }}
-Badness: 0.025806
+Badness (Smith): 0.025806
 ===== 19-limit =====
@@ Line 215: / Line 212: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~26/15 = 951.313{{c}}
-{{Optimal ET sequence|legend=1| 82, 111, 193, 304dh }}
+{{Optimal ET sequence|legend=0| 82, 111, 193, 304dh }}
-Badness: 0.019146
+Badness (Smith): 0.019146
 == Pluto ==
-{{Distinguish| plutus }}
+{{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.
+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 {{nowrap| 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
@@ Line 232: / Line 229: @@
 {{Mapping|legend=1| 1 5 15 15 | 0 -7 -26 -25 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~7/5 = 585.147
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~7/5 = 585.147{{c}}
 {{Optimal ET sequence|legend=1| 39d, 41, 80, 121, 404bd }}
-[[Badness]]: 0.057514
+[[Badness]] (Smith): 0.057514
 === 11-limit ===
@@ Line 245: / Line 242: @@
 Mapping: {{mapping| 1 5 15 15 2 | 0 -7 -26 -25 3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.114
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.114{{c}}
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
-Badness: 0.029844
+Badness (Smith): 0.029844
 ==== 13-limit ====
@@ Line 258: / Line 255: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.123{{c}}
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
-Badness: 0.025717
+Badness (Smith): 0.025717
 ===== 17-limit =====
@@ Line 271: / Line 268: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.116{{c}}
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
-Badness: 0.021463
+Badness (Smith): 0.021463
 ===== 19-limit =====
@@ Line 284: / Line 281: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.109{{c}}
-{{Optimal ET sequence|legend=1| 39d, 41, 80, 121 }}
+{{Optimal ET sequence|legend=0| 39d, 41, 80, 121 }}
-Badness: 0.017650
+Badness (Smith): 0.017650
 ==== Orcus ====
@@ Line 297: / Line 294: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.111{{c}}
-{{Optimal ET sequence|legend=1| 39df, 41, 80f, 121ff }}
+{{Optimal ET sequence|legend=0| 39df, 41, 80f, 121ff }}
-Badness: 0.033441
+Badness (Smith): 0.033441
 === Plutino ===
@@ Line 310: / Line 307: @@
 Mapping: {{mapping| 1 5 15 15 22 | 0 -7 -26 -25 -38 }}
-Optimal tuning (POTE): ~2 = 1\1, ~7/5 = 585.283
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.283{{c}}
-{{Optimal ET sequence|legend=1| 39dee, 41 }}
+{{Optimal ET sequence|legend=0| 39dee, 41 }}
-Badness: 0.057966
+Badness (Smith): 0.057966
 ==== 13-limit ====
@@ Line 323: / Line 320: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~7/5 = 585.232{{c}}
-{{Optimal ET sequence|legend=1| 39deef, 41 }}
+{{Optimal ET sequence|legend=0| 39deef, 41 }}
-Badness: 0.040182
+Badness (Smith): 0.040182
 == Mirkat ==
@@ Line 336: / Line 333: @@
 {{Mapping|legend=1| 3 2 1 2 | 0 6 13 14 }}
-[[Optimal tuning]] ([[POTE]]): ~63/50 = 1\3, ~10/9 = 183.539
+[[Optimal tuning]] ([[POTE]]): ~63/50 = 400.000{{c}}, ~10/9 = 183.539{{c}}
 {{Optimal ET sequence|legend=1| 39d, 72, 111, 183, 255 }}
-[[Badness]]: 0.059376
+[[Badness]] (Smith): 0.059376
 === 11-limit ===
@@ Line 349: / Line 346: @@
 Mapping: {{mapping| 3 2 1 2 9 | 0 6 13 14 3 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~10/9 = 183.528
+Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~10/9 = 183.528{{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 (Smith): 0.022126
 === 13-limit ===
@@ Line 362: / Line 359: @@
 Mapping: {{mapping| 3 2 1 2 9 1 | 0 6 13 14 3 22 }}
-Optimal tuning (POTE): ~63/50 = 1\3, ~10/9 = 183.577
+Optimal tuning (POTE): ~63/50 = 400.000{{c}}, ~10/9 = 183.577{{c}}
-{{Optimal ET sequence|legend=1| 39df, 72, 111, 183 }}
+{{Optimal ET sequence|legend=0| 39df, 72, 111, 183 }}
-Badness: 0.018632
+Badness (Smith): 0.018632
 === 17-limit ===
@@ Line 375: / Line 372: @@
 Mapping: {{mapping| 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 tuning (POTE): ~34/27 = 400.000{{c}}, ~10/9 = 183.579{{c}}
-{{Optimal ET sequence|legend=1| 39dfg, 72, 111, 183 }}
+{{Optimal ET sequence|legend=0| 39dfg, 72, 111, 183 }}
-Badness: 0.011775
+Badness (Smith): 0.011775
 == Eris ==
@@ Line 390: / Line 387: @@
 {{Mapping|legend=1| 1 10 0 6 | 0 -29 8 -11 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~60/49 = 348.216
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~60/49 = 348.216{{c}}
 {{Optimal ET sequence|legend=1| 31, 131, 162, 193, 224, 1823cd, 2271cd }}
-[[Badness]]: 0.074719
+[[Badness]] (Smith): 0.074719
 === 11-limit ===
@@ Line 403: / Line 400: @@
 Mapping: {{mapping| 1 10 0 6 20 | 0 -29 8 -11 -57 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.219
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.219{{c}}
-{{Optimal ET sequence|legend=1| 31, 193, 224, 703, 927d, 1151cd }}
+{{Optimal ET sequence|legend=0| 31, 193, 224, 703, 927d, 1151cd }}
-Badness: 0.027621
+Badness (Smith): 0.027621
 === 13-limit ===
@@ Line 416: / Line 413: @@
 Mapping: {{mapping| 1 10 0 6 20 -14 | 0 -29 8 -11 -57 61 }}
-Optimal tuning (POTE): ~2 = 1\1, ~11/9 = 348.213
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~11/9 = 348.213{{c}}
-{{Optimal ET sequence|legend=1| 31, 193, 224 }}
+{{Optimal ET sequence|legend=0| 31, 193, 224 }}
-Badness: 0.025137
+Badness (Smith): 0.025137
 == Subsemifourth ==
@@ Line 428: / Line 425: @@
 {{Mapping|legend=1| 1 39 27 45 | 0 -47 -31 -53 }}
 : mapping generators: ~2, ~125/72
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~144/125 = 244.719
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~144/125 = 244.719{{c}}
 {{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407 }}
-[[Badness]]: 0.135173
+[[Badness]] (Smith): 0.135173
 === 11-limit ===
@@ Line 444: / Line 440: @@
 Mapping: {{mapping| 1 39 27 45 56 | 0 -47 -31 -53 -66 }}
-Optimal tuning (POTE): ~2 = 1\1, ~121/105 = 244.719
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~121/105 = 244.719{{c}}
-{{Optimal ET sequence|legend=1| 49, 103, 152, 255, 407, 966d }}
+{{Optimal ET sequence|legend=0| 49, 103, 152, 255, 407, 966d }}
-Badness: 0.034276
+Badness (Smith): 0.034276
 === 13-limit ===
@@ Line 457: / Line 453: @@
 Mapping: {{mapping| 1 39 27 45 56 65 | 0 -47 -31 -53 -66 -77 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/13 = 244.714
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/13 = 244.714{{c}}
-{{Optimal ET sequence|legend=1| 49f, 103, 152f, 255, 407f, 662df }}
+{{Optimal ET sequence|legend=0| 49f, 103, 152f, 255, 407f, 662df }}
-Badness: 0.028387
+Badness (Smith): 0.028387
 == 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.
+The name ''septendesemi'' means a septendecimal semitone ([[17/16]]). The septendesemi temperament (80 & 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.
 [[Subgroup]]: 2.3.5.7
@@ Line 471: / Line 467: @@
 {{Mapping|legend=1| 1 39 37 53 | 0 -41 -38 -55 }}
 : mapping generators: ~2, ~648/343
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~343/324 = 104.916
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~343/324 = 104.916{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183 }}
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-[[Badness]]: 0.146795
+[[Badness]] (Smith): 0.146795
 === 11-limit ===
@@ Line 487: / Line 482: @@
 Mapping: {{mapping| 1 39 37 53 50 | 0 -41 -38 -55 -51 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.916
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 104.916{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183 }}
+{{Optimal ET sequence|legend=0| 80, 103, 183 }}
-Badness: 0.041554
+Badness (Smith): 0.041554
 === 13-limit ===
@@ Line 500: / Line 495: @@
 Mapping: {{mapping| 1 39 37 53 50 11 | 0 -41 -38 -55 -51 -8 }}
-Optimal tuning (POTE): ~2 = 1\1, ~35/33 = 104.908
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~35/33 = 104.908{{c}}
-{{Optimal ET sequence|legend=1| 80, 103, 183, 469f, 652def }}
+{{Optimal ET sequence|legend=0| 80, 103, 183, 469f, 652def }}
-Badness: 0.027908
+Badness (Smith): 0.027908
 === 17-limit ===
@@ Line 513: / Line 508: @@
 Mapping: {{mapping| 1 39 37 53 50 11 5 | 0 -41 -38 -55 -51 -8 -1 }}
-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, 652def }}
-Badness: 0.020128
+Badness (Smith): 0.020128
 == Gaster ==
@@ Line 523: / Line 518: @@
 {{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.
+The gaster temperament (111 & 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.
 [[Subgroup]]: 2.3.5.7
@@ Line 531: / Line 526: @@
 {{Mapping|legend=1| 1 11 38 37 | 0 -19 -72 -69 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~800/567 = 594.641
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~800/567 = 594.641{{c}}
 {{Optimal ET sequence|legend=1| 111, 224 }}
-[[Badness]]: 0.154521
+[[Badness]] (Smith): 0.154521
 === 11-limit ===
@@ Line 544: / Line 539: @@
 Mapping: {{mapping| 1 11 38 37 -1 | 0 -19 -72 -69 9 }}
-Optimal tuning (POTE): ~2 = 1\1, ~512/363 = 594.639
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~512/363 = 594.639{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 783d, 1007d, 1231dd }}
+{{Optimal ET sequence|legend=0| 111, 224, 783d, 1007d, 1231dd }}
-Badness: 0.054060
+Badness (Smith): 0.054060
 === 13-limit ===
@@ Line 557: / Line 552: @@
 Mapping: {{mapping| 1 11 38 37 -1 26 | 0 -19 -72 -69 9 -45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/39 = 594.639
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/39 = 594.639{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 783df, 1007df, 1231ddf }}
+{{Optimal ET sequence|legend=0| 111, 224, 783df, 1007df, 1231ddf }}
-Badness: 0.024882
+Badness (Smith): 0.024882
 === 17-limit ===
@@ Line 570: / Line 565: @@
 Mapping: {{mapping| 1 11 38 37 -1 26 14 | 0 -19 -72 -69 9 -45 -20 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.636{{c}}
-{{Optimal ET sequence|legend=1| 111, 224, 559dgg }}
+{{Optimal ET sequence|legend=0| 111, 224, 559dgg }}
-Badness: 0.021436
+Badness (Smith): 0.021436
 === 19-limit ===
@@ Line 583: / Line 578: @@
 Mapping: {{mapping| 1 11 38 37 -1 26 14 32 | 0 -19 -72 -69 9 -45 -20 -56 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.636
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.636{{c}}
-{{Optimal ET sequence|legend=1| 111, 224 }}
+{{Optimal ET sequence|legend=0| 111, 224 }}
-Badness: 0.018370
+Badness (Smith): 0.018370
 === 23-limit ===
@@ Line 596: / Line 591: @@
 Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 | 0 -19 -72 -69 9 -45 -20 -56 -5 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.641
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.641{{c}}
-{{Optimal ET sequence|legend=1| 111, 224 }}
+{{Optimal ET sequence|legend=0| 111, 224 }}
-Badness: 0.017619
+Badness (Smith): 0.017619
 === 29-limit ===
@@ Line 609: / Line 604: @@
 Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.646
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.646{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.016815
+Badness (Smith): 0.016815
 === 31-limit ===
@@ Line 622: / Line 617: @@
 Mapping: {{mapping| 1 11 38 37 -1 26 14 32 7 -11 0 | 0 -19 -72 -69 9 -45 -20 -56 -5 32 10 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.644{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.014790
+Badness (Smith): 0.014790
 === 37-limit ===
@@ Line 635: / Line 630: @@
 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 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.644
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.644{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.014377
+Badness (Smith): 0.014377
 === 41-limit ===
@@ Line 648: / Line 643: @@
 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 }}
-Optimal tuning (POTE): ~2 = 1\1, ~24/17 = 594.643
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~24/17 = 594.643{{c}}
-{{Optimal ET sequence|legend=1| 111, 113, 224 }}
+{{Optimal ET sequence|legend=0| 111, 113, 224 }}
-Badness: 0.012858
+Badness (Smith): 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.
+The generator for subsedia (10 & 111) is 0.5 cents flat of [[15/14]]-wide semitone and tempers out the mirkwai comma and [[buzzardsma]]. 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
@@ Line 663: / Line 658: @@
 {{Mapping|legend=1| 1 0 5 4 | 0 16 -27 -12 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~15/14 = 118.965
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~15/14 = 118.965{{c}}
 {{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
-[[Badness]]: 0.157658
+[[Badness]] (Smith): 0.157658
 === 11-limit ===
@@ Line 676: / Line 671: @@
 Mapping: {{mapping| 1 0 5 4 -1 | 0 16 -27 -12 45 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
+{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
-Badness: 0.066838
+Badness (Smith): 0.066838
 === 13-limit ===
@@ Line 689: / Line 684: @@
 Mapping: {{mapping| 1 0 5 4 -1 4 | 0 16 -27 -12 45 -3 }}
-Optimal tuning (POTE): ~2 = 1\1, ~15/14 = 118.968
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232d }}
+{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232d }}
-Badness: 0.031635
+Badness (Smith): 0.031635
 === 17-limit ===
@@ Line 702: / Line 697: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.968{{c}}
-{{Optimal ET sequence|legend=1| 10, 101, 111, 121, 232dg }}
+{{Optimal ET sequence|legend=0| 10, 101, 111, 121, 232dg }}
-Badness: 0.019707
+Badness (Smith): 0.019707
 === 19-limit ===
@@ Line 715: / Line 710: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~15/14 = 118.964{{c}}
-{{Optimal ET sequence|legend=1| 10, 101h, 111, 121, 232dg }}
+{{Optimal ET sequence|legend=0| 10, 101h, 111, 121, 232dg }}
-Badness: 0.017935
+Badness (Smith): 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.
+The name ''hemiseptisix'' means a half of septimal major sixth ([[12/7]]). The hemiseptisix temperament (103 & 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.
 [[Subgroup]]: 2.3.5.7
@@ Line 729: / Line 724: @@
 {{Mapping|legend=1| 1 34 17 34 | 0 -53 -24 -51 }}
 : mapping generators: ~2, ~75/49
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~98/75 = 466.071
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~98/75 = 466.071{{c}}
 {{Optimal ET sequence|legend=1| 103, 121, 224 }}
-[[Badness]]: 0.162826
+[[Badness]] (Smith): 0.162826
 === 11-limit ===
@@ Line 745: / Line 739: @@
 Mapping: {{mapping| 1 34 17 34 53 | 0 -53 -24 -51 -81 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.070
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/42 = 466.070{{c}}
-{{Optimal ET sequence|legend=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.043381
+Badness (Smith): 0.043381
 === 13-limit ===
@@ Line 758: / Line 752: @@
 Mapping: {{mapping| 1 34 17 34 53 30 | 0 -53 -24 -51 -81 -43 }}
-Optimal tuning (POTE): ~2 = 1\1, ~55/42 = 466.071
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~55/42 = 466.071{{c}}
-{{Optimal ET sequence|legend=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.021127
+Badness (Smith): 0.021127
 === 17-limit ===
@@ Line 771: / Line 765: @@
 Mapping: {{mapping| 1 34 17 34 53 30 31 | 0 -53 -24 -51 -81 -43 -44 }}
-Optimal tuning (POTE): ~2 = 1\1, ~17/13 = 466.074
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~17/13 = 466.074{{c}}
-{{Optimal ET sequence|legend=1| 103, 121, 224 }}
+{{Optimal ET sequence|legend=0| 103, 121, 224 }}
-Badness: 0.018611
+Badness (Smith): 0.018611
 == Browser ==
+{{See also| Sensipent family }}
 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.
-{{See also| Sensipent family }}
 [[Subgroup]]: 2.3.5.7
@@ Line 787: / Line 782: @@
 {{Mapping|legend=1| 1 6 8 10 | 0 -35 -45 -57 }}
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 151.399
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 151.399{{c}}
 {{Optimal ET sequence|legend=1| 103, 111, 214 }}
-[[Badness]]: 0.180645
+[[Badness]] (Smith): 0.180645
 === 11-limit ===
@@ Line 800: / Line 795: @@
 Mapping: {{mapping| 1 6 8 10 8 | 0 -35 -45 -57 -36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 151.405
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.405{{c}}
-{{Optimal ET sequence|legend=1| 103, 214 }}
+{{Optimal ET sequence|legend=0| 103, 214 }}
-Badness: 0.057634
+Badness (Smith): 0.057634
 === 13-limit ===
@@ Line 813: / Line 808: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.403{{c}}
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
+{{Optimal ET sequence|legend=0| 103, 111, 214 }}
-Badness: 0.028822
+Badness (Smith): 0.028822
 === 17-limit ===
@@ Line 826: / Line 821: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.397{{c}}
-{{Optimal ET sequence|legend=1| 103, 111, 214 }}
+{{Optimal ET sequence|legend=0| 103, 111, 214 }}
-Badness: 0.020384
+Badness (Smith): 0.020384
 === 19-limit ===
@@ Line 839: / Line 834: @@
 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 tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 151.396{{c}}
-{{Optimal ET sequence|legend=1| 103h, 111, 214 }}
+{{Optimal ET sequence|legend=0| 103h, 111, 214 }}
-Badness: 0.017570
+Badness (Smith): 0.017570
 == Grazer ==
@@ Line 851: / Line 846: @@
 {{Mapping|legend=1| 1 34 47 58 | 0 -37 -51 -63 }}
 : mapping generators: ~2, ~90/49
-[[Optimal tuning]] ([[POTE]]): ~2 = 1\1, ~49/45 = 148.719
+[[Optimal tuning]] ([[POTE]]): ~2 = 1200.000{{c}}, ~49/45 = 148.719{{c}}
 {{Optimal ET sequence|legend=1| 113, 121, 234 }}
-[[Badness]]: 0.217166
+[[Badness]] (Smith): 0.217166
 === 11-limit ===
@@ Line 867: / Line 861: @@
 Mapping: {{mapping| 1 34 47 58 35 | 0 -37 -51 -63 -36 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.729{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234, 355e, 589cee }}
+{{Optimal ET sequence|legend=0| 113, 121, 234, 355e, 589cee }}
-Badness: 0.076062
+Badness (Smith): 0.076062
 === 13-limit ===
@@ Line 880: / Line 874: @@
 Mapping: {{mapping| 1 34 47 58 35 44 | 0 -37 -51 -63 -36 -46 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.729
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.729{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234, 355e, 589cee }}
+{{Optimal ET sequence|legend=0| 113, 121, 234, 355e, 589cee }}
-Badness: 0.036248
+Badness (Smith): 0.036248
 === 17-limit ===
@@ Line 893: / Line 887: @@
 Mapping: {{mapping| 1 34 47 58 35 44 33 | 0 -37 -51 -63 -36 -46 -33 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.735
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.735{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg }}
+{{Optimal ET sequence|legend=0| 113, 121, 234g, 355eg }}
-Badness: 0.025410
+Badness (Smith): 0.025410
 === 19-limit ===
@@ Line 906: / Line 900: @@
 Mapping: {{mapping| 1 34 47 58 35 44 33 6 | 0 -37 -51 -63 -36 -46 -33 -2 }}
-Optimal tuning (POTE): ~2 = 1\1, ~12/11 = 148.727
+Optimal tuning (POTE): ~2 = 1200.000{{c}}, ~12/11 = 148.727{{c}}
-{{Optimal ET sequence|legend=1| 113, 121, 234g, 355eg, 589ceegg }}
+{{Optimal ET sequence|legend=0| 113, 121, 234g, 355eg, 589ceegg }}
-Badness: 0.022574
+Badness (Smith): 0.022574
-== Notes ==
+== References ==
 [[Category:Temperament clans]]
 [[Category:Mirkwai clan| ]] <!-- main article -->
-[[Category:Mirkwai| ]] <!-- key article -->
 [[Category:Rank 2]]

Canopic clan: Difference between revisions

Revision as of 10:18, 2 April 2026

Canopus

Overview to extensions

Grendel

11-limit

13-limit

17-limit

19-limit

Kwai

11-limit

13-limit

17-limit

19-limit

Hemikwai

17-limit

19-limit

Pluto

11-limit

13-limit

17-limit

19-limit

Orcus

Plutino

13-limit

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

Subsedia

11-limit

13-limit

17-limit

19-limit

Hemiseptisix

11-limit

13-limit

17-limit

Browser

11-limit

13-limit

17-limit

19-limit

Grazer

11-limit

13-limit

17-limit

19-limit

References

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