Latest revision as of 15:37, 14 July 2025

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.

Below are listed some very high accuracy temperaments (Breed's TE error < 0.005 cents/octave).

Rank-2 temperaments

Kwazy

Kwazy (118 & 612) tempers out the kwazy comma, [-53 10 16⟩. 7-limit extensions of the kwazy temperament include gwazy, bisupermajor, and crazy.

Subgroup: 2.3.5

Comma list: [-53 10 16⟩

Mapping: [⟨2 1 6], ⟨0 8 -5]]

mapping generators: ~94921875/67108864, ~1125/1024

Optimal tunings:

CTE: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.743279
POTE: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.742626

Optimal ET sequence: 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934

Badness (Sintel): 0.331

Astro

Astro temperament tempers out the astro comma, [91 -12 -31⟩. 7-limit extensions of the astro temperament include kastro.

Subgroup: 2.3.5

Comma list: [91 -12 -31⟩

Mapping: [⟨1 5 1], ⟨0 -31 12]]

mapping generators: ~2, ~[-38 5 13⟩

Optimal tunings:

CTE: ~2 = 1200.000000, ~[-38 5 13⟩ = 132.194857
POTE: ~2 = 1200.000000, ~[-38 5 13⟩ = 132.194668

Optimal ET sequence: 9, …, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c

Badness (Sintel): 1.47

Gaster

Main article: Gaster temperament

See also: Mirkwai clan § Gaster

Subgroup: 2.3.5

Comma list: [-70 72 -19⟩

Mapping: [⟨1 11 38], ⟨0 -19 -72]]

mapping generators: ~2, ~[19 -19 5⟩

Optimal tunings:

CTE: ~2 = 1200.000000, ~[19 -19 5⟩ = 594.634456
POTE: ~2 = 1200.000000, ~[19 -19 5⟩ = 594.634565

Optimal ET sequence: 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630

Badness (Sintel): 2.08

Whoosh

Whoosh (152 & 289) tempers out the whoosh comma, [37 25 -33⟩. 7-limit extensions of the whoosh temperament include whoops.

Subgroup: 2.3.5

Comma list: [37 25 -33⟩

Mapping: [⟨1 17 14], ⟨0 -33 -25]]

mapping generators: ~2, ~864/625

Optimal tunings:

CTE: ~2 = 1200.000000, ~864/625 = 560.546952
POTE: ~2 = 1200.000000, ~864/625 = 560.546826

Optimal ET sequence: 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c

Badness (Sintel): 0.602

Monzismic

Monzismic (53 & 612) tempers out the monzisma, [54 -37 2⟩. For its 7-limit extension, see Ragismic microtemperaments #Monzismic.

Subgroup: 2.3.5

Comma list: [54 -37 2⟩

Mapping: [⟨1 0 -27], ⟨0 2 37]]

mapping generators: ~2, ~[27 -18 1⟩

Optimal tunings:

CTE: ~2 = 1200.000000, ~[27 -18 1⟩ = 950.981427
POTE: ~2 = 1200.000000, ~[27 -18 1⟩ = 950.981594

Optimal ET sequence: 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520

Badness (Sintel): 0.244

Egads

Subgroup: 2.3.5

Comma list: [-36 -52 51⟩

Mapping: [⟨1 15 16], ⟨0 -51 -52]]

mapping generators: ~2, ~6/5

Optimal tunings:

CTE: ~2 = 1200.000000, ~6/5 = 315.647899
POTE: ~2 = 1200.000000, ~6/5 = 315.647919

Optimal ET sequence: 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127

Badness (Sintel): 0.981

Hemiegads

Subgroup: 2.3.5.7

Comma list: 78125000/78121827, [-48 0 11 8⟩

Mapping: [⟨1 15 16 -16], ⟨0 -102 -104 143]]

Optimal tunings:

CTE: ~2 = 1200.000000, ~36756909/33554432 = 157.823952
CWE: ~2 = 1200.000000, ~36756909/33554432 = 157.823954

Optimal ET sequence: 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c

Badness (Sintel): 0.313

Fortune

Fortune tempers out the fortune comma, [-107 47 14⟩. It can be described as 612 & 2513 temperament, which tempers out 78125000/78121827 (euzenius comma) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.

Subgroup: 2.3.5

Comma list: [-107 47 14⟩

Mapping: [⟨1 13 -36], ⟨0 -14 47]]

mapping generators: ~2, 7381125/4194304

Optimal tunings:

CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.567861
POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.567899

Optimal ET sequence: 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc

Badness (Sintel): 0.654

7-limit

Subgroup: 2.3.5.7

Comma list: 78125000/78121827, [-52 17 12 -1⟩

Mapping: [⟨1 13 -36 -263], ⟨0 -14 47 326]]

Optimal tunings:

CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568013
POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568031

Optimal ET sequence: 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323

Badness (Sintel): 0.600

11-limit

Subgroup: 2.3.5.7.11

Comma list: 151263/151250, 21437500/21434787, 369140625/369098752

Mapping: [⟨1 13 -36 -263 -573], ⟨0 -14 47 326 707]]

Optimal tunings:

CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568116
POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568139

Optimal ET sequence: 612, 2513, 3125, 3737, 8086, 19909d

Badness (Sintel): 1.21

Senior

Senior (171 & 1171) tempers out the senior comma, [-17 62 -35⟩. 7-limit extensions of the senior temperament include seniority.

Subgroup: 2.3.5

Comma list: [-17 62 -35⟩

Mapping: [⟨1 11 19], ⟨0 -35 -62]]

mapping generators: ~2, ~[-6 23 -13⟩

Optimal tunings:

CTE: ~2 = 1200.000000, ~[-6 23 -13⟩ = 322.801349
POTE: ~2 = 1200.000000, ~[-6 23 -13⟩ = 322.801358

Optimal ET sequence: 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680

Badness (Sintel): 0.498

Gross

Gross (118 & 1783) tempers out the gross comma, [144 -22 -47⟩, by which a stack of 22 3rd harmonics and 47 5th harmonics falls short of 144 (gross) octaves.

Subgroup: 2.3.5

Comma list: [144 -22 -47⟩

Mapping: [⟨1 45 -18], ⟨0 -47 22]]

mapping generators: ~2, ~[-45 7 15⟩

Optimal tunings:

CTE: ~2 = 1200.000000, ~[46 -7 -15⟩ = 91.530979
POTE: ~2 = 1200.000000, ~[46 -7 -15⟩ = 91.531001

Optimal ET sequence: 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c

Badness (Sintel): 1.09

Music

Gross temperament EP (2023) by Francium – Spotify | Bandcamp | YouTube – 2-piece extended play

Quectismic

See also: Quectisma

Subgroup: 2.3.5

Comma list: [554 -351 1⟩

Mapping: [⟨1 0 -554], ⟨0 1 351]]

mapping generators: ~2, ~3

Optimal tunings:

CTE: ~2 = 1200.000000, ~3/2 = 701.955310
CWE: ~2 = 1200.000000, ~3/2 = 701.955310

Optimal ET sequence: 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551

Badness (Sintel): 8.74

Nanoquectismic

Subgroup: 2.3.5.7

Comma list: 43046721/43025920, [82 -19 -3 -16⟩

Mapping: [⟨1 0 -554 109], ⟨0 1 351 -67]]

Optimal tunings:

CTE: ~2 = 1200.000000, ~3/2 = 701.955371
CWE: ~2 = 1200.000000, ~3/2 = 701.955457

Optimal ET sequence: 306, 665, 1636, 2301, 2966

Badness (Sintel): 15.3

Conanoquectismic

Subgroup: 2.3.5.7

Comma list: [33 -26 12 -7⟩, [-32 13 17 -10⟩

Mapping: [⟨1 0 -554 -945], ⟨0 1 351 598]]

Optimal tunings:

CTE: ~2 = 1200.000000, ~3/2 = 701.954810
CWE: ~2 = 1200.000000, ~3/2 = 701.954771

Optimal ET sequence: 306d, 359cd, 665

Badness (Sintel): 55.0

Counterquectismic

See also: Counterquectisma

Subgroup: 2.3.5

Comma list: [-500 314 1⟩

Mapping: [⟨1 0 500], ⟨0 1 -314]]

mapping generators: ~2, ~3

Optimal tunings:

CTE: ~2 = 1200.000000, ~3/2 = 701.954415
CWE: ~2 = 1200.000000, ~3/2 = 701.954416

Optimal ET sequence: 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486

Badness (Sintel): 12.0

Raider

See also: Syntonic–chromatic equivalence continuum

Subgroup: 2.3.5

Comma list: [71 -99 37⟩

Mapping: [⟨1 28 73], ⟨0 -37 -99]]

mapping generators: ~2, ~6561/4000

Optimal tunings:

CTE: ~2 = 1200.000000, ~8000/6561 = 343.296094
POTE: ~2 = 1200.000000, ~8000/6561 = 343.296098

Optimal ET sequence: 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860

Badness (Sintel): 0.302

Pirate

See also: Hemfiness temperaments § Piracy

Subgroup: 2.3.5

Comma list: [-90 -15 49⟩

Mapping: [⟨1 43 15], ⟨0 -49 -15]]

Mapping generators: ~2, ~[-23 -4 13⟩

Optimal tunings:

CTE: ~2 = 1200.000000, ~[24 4 -13⟩ = 185.754186
POTE: ~2 = 1200.000000, ~[24 4 -13⟩ = 185.754179

Optimal ET sequence: 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 …

Badness (Sintel): 0.133

Atomic

See also: Kirnberger's atom

Atomic observes the schisma, and the 3/2 is one schisma sharp of its 12edo value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the Pythagorean comma is twelve schismas, and hence 81/80, the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.

Atomic extensions discussed elsewhere include minutes and hafnium.

Subgroup: 2.3.5

Comma list: [161 -84 -12⟩

Mapping: [⟨12 0 161], ⟨0 1 -7]]

mapping generators: ~[-67 35 5⟩, ~3

Optimal tunings:

CTE: ~[-67 35 5⟩ = 100.000000, ~3/2 = 701.955176 (~32805/32768 = 1.955176)
POTE: ~[-67 35 5⟩ = 100.000000, ~3/2 = 701.955162 (~32805/32768 = 1.955162)

Optimal ET sequence: 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032

Badness (Sintel): 0.0892

7-limit

Subgroup: 2.3.5.7

Comma list: 250047/250000, [-55 30 2 1⟩

Mapping: [⟨12 0 161 338], ⟨0 1 -7 -16]]

Optimal tunings:

CTE: ~30375/28672 = 100.000000, ~3/2 = 701.949917 (or ~32805/32768 = 1.949917)
POTE: ~30375/28672 = 100.000000, ~3/2 = 701.949608 (or ~32805/32768 = 1.949608)

Optimal ET sequence: 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd

Badness (Sintel): 1.16

11-limit

Subgroup: 2.3.5.7.11

Comma list: 9801/9800, 151263/151250, 184549376/184528125

Mapping: [⟨12 0 161 338 517], ⟨0 1 -7 -16 -25]]

Optimal tunings:

CTE: ~30375/28672 = 100.000000, ~3/2 = 701.948456 (or ~32805/32768 = 1.948456)
POTE: ~30375/28672 = 100.000000, ~3/2 = 701.947988 (or ~32805/32768 = 1.947988)

Optimal ET sequence: 12, …, 600e, 612, 1236, 1848

Badness (Sintel): 0.530

Revopentic (2.3.7)

See also: Revopentisma

Subgroup: 2.3.7

Comma list: 11399736556781568/11398895185373143

Sval mapping: [⟨1 12 5], ⟨0 -19 -4]]

mapping generators: ~2, ~24576/16807

Optimal tunings:

CTE: ~2 = 1200.000000, ~24576/16807 = 657.791865
CWE: ~2 = 1200.000000, ~24576/16807 = 657.791796

Optimal ET sequence: 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, …

Badness (Sintel): 0.0704

Revopent

Revopent can be described as the 1848 & 3125 temperament.

Subgroup: 2.3.5.7

Comma list: 645700815/645657712, [51 -13 -1 -10⟩

Mapping: [⟨1 12 -155 5], ⟨0 -19 287 -4]]

Optimal tunings:

CTE: ~2 = 1200.000000, ~24576/16807 = 657.792032
CWE: ~2 = 1200.000000, ~24576/16807 = 657.792032

Optimal ET sequence: 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d

Badness (Sintel): 0.665

Nanic

See also: Nanisma

Subgroup: 2.3.7

Comma list: [109 -67 -1⟩

Sval mapping: [⟨1 0 109], ⟨0 1 -67]]

sval mapping generators: ~2, ~3

Optimal tunings:

CTE: ~2 = 1200.000000, ~3/2 = 701.957820
POTE: ~2 = 1200.000000, ~3/2 = 701.957784

Optimal ET sequence: 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733

Badness (Sintel): 0.474

Icarus

This temperament is named after a very distant star. Curiously, the names of two even more distant stars coincide with named temperaments, those being godzilla and mothra.

Subgroup: 3.5.7

Comma list: [-32 -64 71⟩

Mapping: [⟨1 35 32], ⟨0 -71 -64]]

Optimal tunings:

CTE: ~3 = 1901.955, ~[5 9 -10⟩ = 898.340
CWE: ~3 = 1901.955, ~[5 9 -10⟩ = 898.340

Optimal ET sequence: b163cd, b199c, b235, b271, b4643, b4914, …, b8708, b8979, b18229, b27208, b99853, b127061, b154269, b181477, b208685, b390162

Badness (Sintel): 0.00493

Rank-3 temperaments

Sasaquinbizo-atriyo (171 & 1106 & 3566)

Subgroup: 2.3.5.7

Comma list: [3 -24 3 10⟩ (282475249000/282429536481)

Mapping: [⟨1 0 9 -3], ⟨0 1 8 0], ⟨0 0 10 -3]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9624, ~6561/3430 = 1122.9387

Optimal ET sequence: 171, 764, 935, 1106, 1277, 2118, 2289, 2460, 3224, 3395, 3566, 26068, 26239, 29634, 29805, 33200, 33371, 36937, 40503, 44069

Badness (Sintel): 1.24

Saquadtrizo-asepgu (171 & 2019 & 3566)

Subgroup: 2.3.5.7

Comma list: [0 -11 -7 12⟩ (13841287201/13839609375)

Mapping: [⟨1 0 0 0], ⟨0 1 7 5], ⟨0 0 -12 -7]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9584, ~16807/10125 = 877.2825

Optimal ET sequence: 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d

Badness (Sintel): 0.595

Laquinzo-aquadquadgu (171 & 441 & 4973)

Subgroup: 2.3.5.7

Comma list: [-7 19 -16 5⟩ (19534128475869/19531250000000)

Mapping: [⟨1 0 3 11], ⟨0 1 4 9], ⟨0 0 5 16]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9501, ~250/189 = 484.2956

Optimal ET sequence: 171, 441, 612, 2696, 2795, 2867, 2966, 3137, 3308, 3407, 3479, 3578, 3749, 3920, 4091, 4190, 4361, 4532, 4703, 4802, 4973, 5144, 10117, 10558, 15531, 15702, 52079, 62637, 67781, 78339

Badness (Sintel): 1.31

Laleruyo (171 & 1547 & 3125)

Subgroup: 2.3.5.7

Comma list: [-1 4 11 -11⟩ (3955078125/3954653486)

Mapping: [⟨1 3 0 1], ⟨0 -11 0 -4], ⟨0 0 1 1]]

Optimal tuning (CTE): ~2 = 1200.0000, ~375/343 = 154.3678, ~5/4 = 386.3070

Optimal ET sequence: 171, 863, 894, 1034, 1065, 1205, 1236, 1376, 1407, 1547, 1578, 1718, 2612, 2783, 2954, 3125, 12329, 15454, 18579, 21704, 40283, 61987

Badness (Sintel): 0.501

Starscape or Latritriru-ayo

Subgroup: 2.3.5.7

Comma list: 645700815/645657712

Mapping: [⟨1 0 4 0], ⟨0 1 1 2], ⟨0 0 -9 -1]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9514, ~9/7 = 435.0709

Optimal ET sequence: 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634

Badness (Sintel): 0.240

Sepbizo-asegu (171 & 3566 & 4973)

Subgroup: 2.3.5.7

Comma list: [-3 2 -17 14⟩ (6104007655641/6103515625000)

Mapping: [⟨1 0 13 16], ⟨0 1 10 12], ⟨0 0 -14 -17]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9548, ~31250/16807 = 1073.8021

Optimal ET sequence: 171, 894, 1065, 1236, 1407, 1578, 3053, 3224, 3395, 3566, 5144, 8368, 8539, 8710, 17249, 20815, 29525, 38064, 67589, 105653

Badness (Sintel): 0.982

Euzenius or Sabiruquinyo

See also: Euzenius comma

Subgroup: 2.3.5.7

Comma list: 78125000/78121827

Mapping: [⟨1 1 0 -5], ⟨0 2 0 -13], ⟨0 0 1 5]]

Optimal tuning (CTE): ~2 = 1200.0000, ~6250/5103 = 350.9787, ~5/4 = 386.3099

Optimal ET sequence: 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654

Badness (Sintel): 0.0902

Nommismic or Quinla-zoyoyo

See also: Nommisma

Subgroup: 2.3.5.7

Comma list: [-55 30 2 1⟩

Mapping: [⟨1 0 0 55], ⟨0 1 0 -30], ⟨0 0 1 -2]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9516, ~5/4 = 386.3132

Optimal ET sequence: 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, …

Badness (Sintel): 1.62

Satwethezo-atritribigu (171 & 1547 & 4973)

Subgroup: 2.3.5.7

Comma list: [1 -15 -18 23⟩

Mapping: [⟨1 0 9 7], ⟨0 1 3 3], ⟨0 0 -23 -18]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9551, ~56953125/40353607 = 596.5022

Optimal ET sequence: 171, 863, 1034, 1205, 1376, 1547, 1718, 3255, 3426, 3597, 4460, 4631, 4802, 4973, 5144, 6520, 6691, 11664, 18355, 48374, 48545, 66900, 145464, …

Badness (Sintel): 0.505

Technologismic or Trisa-quinbiru-agu

Subgroup: 2.3.5.7

Comma list: [51 -13 -1 -10⟩

Mapping: [⟨1 0 1 5], ⟨0 1 7 -2], ⟨0 0 -10 1]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.9553, ~63/32 = 1172.7374

Optimal ET sequence: 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, …

Badness (Sintel): 0.116

Quinbisa-quinbizo-alegu (1848 & 11664 & 21480)

Subgroup: 2.3.5.7

Comma list: [110 -71 -11 10⟩

Mapping: [⟨1 0 0 -11], ⟨0 1 9 17], ⟨0 0 -10 -11]]

Optimal tuning (CTE): ~2 = 1200.0000, ~3/2 = 701.955, ~32805/28672 = 233.128

Optimal ET sequence: 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, …

Badness (Sintel): 0.538

@@ Line 1: / Line 1: @@
-Below are listed some very high accuracy temperaments ([[Tenney-Euclidean temperament measures|TE error]] &lt; 0.005 cents/octave).
+{{Technical data page}}
+Below are listed some very high accuracy temperaments (Breed's [[Tenney-Euclidean temperament measures|TE error]] < 0.005 cents/octave).
 = Rank-2 temperaments =
 == Kwazy ==
-Kwazy (118 &amp; 612) tempers out the kwazy comma, {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[Hemimage temperaments #Bisupermajor|bisupermajor]] and [[Marvel temperaments #Gwazy|gwazy]].
+Kwazy ({{nowrap| 118 & 612 }}) tempers out the [[kwazy comma]], {{monzo| -53 10 16 }}. 7-limit extensions of the kwazy temperament include [[marvel temperaments #Gwazy|gwazy]],  [[hemimage temperaments #Bisupermajor|bisupermajor]], and [[ragismic microtemperaments #Crazy|crazy]].
 [[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| -53 10 16 }} = 9010162353515625 / 9007199254740992
+[[Comma list]]: {{monzo| -53 10 16 }}
 {{Mapping|legend=1| 2 1 6 | 0 8 -5 }}
@@ Line 13: / Line 14: @@
 : mapping generators: ~94921875/67108864, ~1125/1024
-[[Optimal tuning]] ([[CTE]]): ~94921875/67108864 = 1\2, ~1125/1024 = 162.7433
+[[Optimal tuning]]s:
+* [[CTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.743279
+* [[POTE]]: ~94921875/67108864 = 600.000000, ~1125/1024 = 162.742626
 {{Optimal ET sequence|legend=1| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }}
-[[Badness]]: 0.014091
+[[Badness]] (Sintel): 0.331
 == Astro ==
-Astro temperament tempers out the astro comma, {{monzo| 91 -12 -31 }}. 7-limit extensions of the astro temperament include [[Horwell temperaments #Kastro|kastro]].
+Astro temperament tempers out the [[astro comma]], {{monzo| 91 -12 -31 }}. 7-limit extensions of the astro temperament include [[Horwell temperaments #Kastro|kastro]].
 [[Subgroup]]: 2.3.5
@@ Line 30: / Line 33: @@
 : mapping generators: ~2, ~{{monzo| -38 5 13 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| -38 5 13 }} = 132.1949
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194857
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -38 5 13 }} = 132.194668
-{{Optimal ET sequence|legend=1| 9, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}
+{{Optimal ET sequence|legend=1| 9, …, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }}
-[[Badness]]: 0.062778
+[[Badness]] (Sintel): 1.47
 == Gaster ==
@@ Line 48: / Line 53: @@
 : mapping generators: ~2, ~{{monzo| 19 -19 5 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 19 -19 5 }} = 594.6345
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634456
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 19 -19 5 }} = 594.634565
 {{Optimal ET sequence|legend=1| 111, 224, 335, 559, 1342, 1901, 3243, 8387, 11630 }}
-[[Badness]]: 0.088530
+[[Badness]] (Sintel): 2.08
 == Whoosh ==
-Whoosh (152 &amp; 289) tempers out the whoosh comma, {{monzo| 37 25 -33 }}. 7-limit extensions of the whoosh temperament include [[Porwell temperaments #Whoops|whoops]].
+Whoosh ({{nowrap| 152 & 289 }}) tempers out the [[whoosh comma]], {{monzo| 37 25 -33 }}. 7-limit extensions of the whoosh temperament include [[Porwell temperaments #Whoops|whoops]].
 [[Subgroup]]: 2.3.5
@@ Line 65: / Line 72: @@
 : mapping generators: ~2, ~864/625
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~864/625 = 560.546826
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~864/625 = 560.546952
+* [[POTE]]: ~2 = 1200.000000, ~864/625 = 560.546826
-{{Optimal ET sequence|legend=1| 15, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
+{{Optimal ET sequence|legend=1| 15, …, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }}
-[[Badness]]: 0.025653
+[[Badness]] (Sintel): 0.602
 == Monzismic ==
-Monzismic (53 &amp; 612) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}. For its 7-limit extension, see [[Ragismic microtemperaments #Monzismic]].
+Monzismic ({{nowrap| 53 & 612 }}) tempers out the [[monzisma]], {{monzo| 54 -37 2 }}. For its 7-limit extension, see [[Ragismic microtemperaments #Monzismic]].
 [[Subgroup]]: 2.3.5
-[[Comma list]]: {{monzo| 54 -37 2 }} = 450359962737049600 / 450283905890997363
+[[Comma list]]: {{monzo| 54 -37 2 }}
 {{Mapping|legend=1| 1 0 -27 | 0 2 37 }}
@@ Line 82: / Line 91: @@
 : mapping generators: ~2, ~{{monzo| 27 -18 1 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 27 -18 1 }} = 950.9814
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981427
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 27 -18 1 }} = 950.981594
 {{Optimal ET sequence|legend=1| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }}
-[[Badness]]: 0.010391
+[[Badness]] (Sintel): 0.244
 == Egads ==
@@ Line 97: / Line 108: @@
 : mapping generators: ~2, ~6/5
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~6/5 = 315.6479
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~6/5 = 315.647899
+* [[POTE]]: ~2 = 1200.000000, ~6/5 = 315.647919
-{{Optimal ET sequence|legend=1| 19, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
+{{Optimal ET sequence|legend=1| 19, …, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908, 45955, 50863, 55771, 60679, 65587, 70495, 75403, 80311, 85219, 90127 }}
-[[Badness]]: 0.041819
+[[Badness]] (Sintel): 0.981
 === Hemiegads ===
@@ Line 110: / Line 123: @@
 Mapping: {{mapping| 1 15 16 -16 | 0 -102 -104 143 }}
-Optimal tuning (CTE): ~2 = 1\1, ~36756909/33554432 = 157.8240
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~36756909/33554432 = 157.823952
+* CWE: ~2 = 1200.000000, ~36756909/33554432 = 157.823954
-{{Optimal ET sequence|legend=1| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
+{{Optimal ET sequence|legend=0| 38, 403, 441, 1802, 2243, 2684, 3125, 6691, 9816, 16507, 75844, 125365c }}
-Badness: 0.0124
+Badness (Sintel): 0.313
 == Fortune ==
-Fortune tempers out the fortune comma, {{monzo| -107 47 14 }}. It can be described as 612 &amp; 2513 temperament, which tempers out 78125000/78121827 (euzenius comma) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.
+Fortune tempers out the [[fortune comma]], {{monzo| -107 47 14 }}. It can be described as {{nowrap| 612 & 2513 }} temperament, which tempers out 78125000/78121827 ([[euzenius comma]]) in the 7-limit; 151263/151250, 21437500/21434787, and 369140625/369098752 in the 11-limit.
 [[Subgroup]]: 2.3.5
@@ Line 127: / Line 142: @@
 : mapping generators: ~2, 7381125/4194304
-Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5679
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567861
+* [[POTE]]: ~2 = 1200.000000, ~8388608/7381125 = 221.567899
 {{Optimal ET sequence|legend=1| 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151, 18815, 45781, 64596, 110377, 174973bc }}
-[[Badness]]: 0.027876
+[[Badness]] (Sintel): 0.654
 === 7-limit ===
@@ Line 140: / Line 157: @@
 Mapping: {{mapping| 1 13 -36 -263 | 0 -14 47 326 }}
-Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5680
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568013
+* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568031
-{{Optimal ET sequence|legend=1| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
+{{Optimal ET sequence|legend=0| 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323 }}
-Badness: 0.023704
+Badness (Sintel): 0.600
 === 11-limit ===
@@ Line 153: / Line 172: @@
 Mapping: {{mapping| 1 13 -36 -263 -573 | 0 -14 47 326 707 }}
-Optimal tuning (CTE): ~2 = 1\1, ~8388608/7381125 = 221.5681
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568116
+* POTE: ~2 = 1200.000000, ~8388608/7381125 = 221.568139
 {{Optimal ET sequence|legend=1| 612, 2513, 3125, 3737, 8086, 19909d }}
-Badness: 0.036641
+Badness (Sintel): 1.21
 == Senior ==
-Senior (171 &amp; 1171) tempers out the senior comma, {{monzo| -17 62 -35 }}. 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]].
+Senior ({{nowrap| 171 & 1171 }}) tempers out the [[senior comma]], {{monzo| -17 62 -35 }}. 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]].
 [[Subgroup]]: 2.3.5
@@ Line 170: / Line 191: @@
 : mapping generators: ~2, ~{{monzo| -6 23 -13 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| -6 23 -13 }} = 322.8013
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801349
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| -6 23 -13 }} = 322.801358
-{{Optimal ET sequence|legend=1| 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
+{{Optimal ET sequence|legend=1| 26, …, 145, 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }}
-[[Badness]]: 0.021220
+[[Badness]] (Sintel): 0.498
 == Gross ==
-Gross (118 &amp; 1783) tempers out the gross comma, {{monzo| 144 -22 -47 }}, by which a stack of 22 [[3/1|3rd harmonics]] and 47 [[5/1|5th harmonics]] falls short of 144 (gross) octaves.
+Gross ({{nowrap| 118 & 1783 }}) tempers out the gross comma, {{monzo| 144 -22 -47 }}, by which a stack of 22 [[3/1|3rd harmonics]] and 47 [[5/1|5th harmonics]] falls short of 144 (gross) octaves.
 [[Subgroup]]: 2.3.5
@@ Line 187: / Line 210: @@
 : mapping generators: ~2, ~{{monzo| -45 7 15 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 46 -7 -15 }} = 91.5310
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.530979
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 46 -7 -15 }} = 91.531001
-{{Optimal ET sequence|legend=1| 13, 105, 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}
+{{Optimal ET sequence|legend=1| 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467, 36486, 41953, 47420, 52887, 63821, 69288, 74755, 144043c, 218798c }}
-[[Badness]]: 0.046315
+[[Badness]] (Sintel): 1.09
+; Music
+* ''Gross temperament EP'' (2023) by [[User:Francium|Francium]] – [https://open.spotify.com/album/02Fz6IIJ2x9k7bEvFylZ2A Spotify] | [https://francium223.bandcamp.com/album/gross-temperament-ep Bandcamp] | [https://youtube.com/playlist?list=PLLZE7hMjEXRZy_JWYbZxbsxPsXahiEJA2&si=RttlCFpkeN4Rl7Tj YouTube] – 2-piece extended play
 == Quectismic ==
@@ Line 204: / Line 232: @@
 : mapping generators: ~2, ~3
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9553
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.955310
+* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.955310
 {{Optimal ET sequence|legend=1| 306, 359c, 665, 2301, 2966, 3631, 4296, 46591, 50887, 55183, 59479, 63775, 68071, 72367, 76663, 80959, 85255, 89551 }}
-[[Badness]]: 0.372
+[[Badness]] (Sintel): 8.74
 === Nanoquectismic ===
@@ Line 217: / Line 247: @@
 Mapping: {{mapping| 1 0 -554 109 | 0 1 351 -67 }}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.955
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~3/2 = 701.955371
+* CWE: ~2 = 1200.000000, ~3/2 = 701.955457
 {{Optimal ET sequence|legend=1| 306, 665, 1636, 2301, 2966 }}
-Badness: 0.604
+Badness (Sintel): 15.3
 === Conanoquectismic ===
@@ Line 230: / Line 262: @@
 Mapping: {{mapping| 1 0 -554 -945 | 0 1 351 598 }}
-Optimal tuning (CTE): ~2 = 1\1, ~3/2 = 701.9548
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~3/2 = 701.954810
+* CWE: ~2 = 1200.000000, ~3/2 = 701.954771
 {{Optimal ET sequence|legend=1| 306d, 359cd, 665 }}
-Badness: 2.17
+Badness (Sintel): 55.0
+== Counterquectismic ==
+{{See also| Counterquectisma }}
+[[Subgroup]]: 2.3.5
+[[Comma list]]: {{monzo| -500 314 1 }}
+{{Mapping|legend=1| 1 0 500 | 0 1 -314 }}
+: mapping generators: ~2, ~3
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.954415
+* [[CWE]]: ~2 = 1200.000000, ~3/2 = 701.954416
+{{Optimal ET sequence|legend=1| 306c, 359, 665, 2354, 3019, 3684, 11717, 15401, 19085, 34486 }}
+[[Badness]] (Sintel): 12.0
 == Raider ==
-{{See also| Syntonic-chromatic equivalence continuum }}
+{{See also| Syntonic–chromatic equivalence continuum }}
 [[Subgroup]]: 2.3.5
@@ Line 247: / Line 300: @@
 : mapping generators: ~2, ~6561/4000
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~8000/6561 = 343.2961
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296094
+* [[POTE]]: ~2 = 1200.000000, ~8000/6561 = 343.296098
 {{Optimal ET sequence|legend=1| 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860 }}
-[[Badness]]: 0.012867
+[[Badness]] (Sintel): 0.302
 == Pirate ==
+{{See also| Hemfiness temperaments #Piracy }}
 [[Subgroup]]: 2.3.5
@@ Line 260: / Line 317: @@
 {{Mapping|legend=1| 1 43 15 | 0 -49 -15 }}
-: mapping generators: ~2, ~{{monzo| -23 -4 13 }}
+: Mapping generators: ~2, ~{{monzo| -23 -4 13 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~{{monzo| 24 4 -13 }} = 185.7542
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754186
+* [[POTE]]: ~2 = 1200.000000, ~{{monzo| 24 4 -13 }} = 185.754179
 {{Optimal ET sequence|legend=1| 84, 239, 323, 730, 1783, 2513, 4296, 15401, 19697, 23993, 52282, 76275, 128557, 204832 … }}
-[[Badness]]: 0.005656
+[[Badness]] (Sintel): 0.133
 == Atomic ==
 {{See also | Kirnberger's atom }}
+Atomic observes the [[schisma]], and the 3/2 is one schisma sharp of its [[12edo]] value. In atomic, since twelve fifths are sharp of seven octaves by twelve schismas, the [[Pythagorean comma]] is twelve schismas, and hence [[81/80]], the Didymus comma, is eleven schismas. In fact eleven schismas is sharp of 81/80, and twelve schismas of the Pythaorean comma, by the microscopic interval of the atom, which atomic tempers out. Extremely accurate.
 Atomic extensions discussed elsewhere include [[minutes]] and [[72nd-octave temperaments#Hafnium|hafnium]].
@@ Line 281: / Line 342: @@
 : mapping generators: ~{{monzo| -67 35 5 }}, ~3
-[[Optimal tuning]] ([[CTE]]): ~{{monzo| -67 35 5 }} = 1\12, ~3/2 = 701.9552 (or ~32805/32768 = 1.9552)
+[[Optimal tuning]]s:
+* [[CTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955176 (~32805/32768 = 1.955176)
+* [[POTE]]: ~{{monzo| -67 35 5 }} = 100.000000, ~3/2 = 701.955162 (~32805/32768 = 1.955162)
 {{Optimal ET sequence|legend=1| 12, …, 576, 588, 600, 612, 2460, 3072, 3684, 4296, 12276, 16572, 20868, 25164, 46032 }}
-[[Badness]]: 0.003803
+[[Badness]] (Sintel): 0.0892
 === 7-limit ===
@@ Line 294: / Line 357: @@
 Mapping: {{mapping| 12 0 161 338 | 0 1 -7 -16 }}
-Optimal tuning (CTE): ~30375/28672 = 1\12, ~3/2 = 701.9499 (or ~32805/32768 = 1.9499)
+Optimal tunings:
+* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.949917 (or ~32805/32768 = 1.949917)
+* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.949608 (or ~32805/32768 = 1.949608)
-{{Optimal ET sequence|legend=1| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
+{{Optimal ET sequence|legend=0| 12, …, 600, 612, 1236, 1848, 4308, 10464, 14772, 25236c, 40008ccd }}
-Badness: 0.045818
+Badness (Sintel): 1.16
 === 11-limit ===
@@ Line 307: / Line 372: @@
 Mapping: {{mapping| 12 0 161 338 517 | 0 1 -7 -16 -25 }}
-Optimal tuning (CTE): ~30375/28672 = 1\12, ~3/2 = 701.9485 (or ~32805/32768 = 1.9485)
+Optimal tunings:
+* CTE: ~30375/28672 = 100.000000, ~3/2 = 701.948456 (or ~32805/32768 = 1.948456)
+* POTE: ~30375/28672 = 100.000000, ~3/2 = 701.947988 (or ~32805/32768 = 1.947988)
+{{Optimal ET sequence|legend=0| 12, …, 600e, 612, 1236, 1848 }}
+Badness (Sintel): 0.530
+== Revopentic (2.3.7) ==
+{{See also| Revopentisma }}
+Subgroup: 2.3.7
+Comma list: 11399736556781568/11398895185373143
+{{Mapping|legend=2| 1 12 5 | 0 -19 -4 }}
+: mapping generators: ~2, ~24576/16807
-{{Optimal ET sequence|legend=1| 12, …, 600e, 612, 1236, 1848 }}
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~24576/16807 = 657.791865
+* [[CWE]]: ~2 = 1200.000000, ~24576/16807 = 657.791796
-Badness: 0.016029
+{{Optimal ET sequence|legend=1| 31, 73, 104, 135, 436, 571, 706, 1277, 8233, 9510, 10787, 12064, 13341, 14618, 15895, 33067, 48962, 113819d, 162781d, … }}
-== Revopent ==
+[[Badness]] (Sintel): 0.0704
-Described as the 1848 & 3125 temperament, revopent is named because the year 1848 is known for revolutions while 3125 is 5 to the 5.
+=== Revopent ===
+Revopent can be described as the {{nowrap| 1848 & 3125 }} temperament.
 Subgroup: 2.3.5.7
@@ Line 322: / Line 408: @@
 Mapping: {{mapping| 1 12 -155 5 | 0 -19 287 -4 }}
-Optimal tuning (CTE): ~24576/16807 = 657.792
+Optimal tunings:
+* CTE: ~2 = 1200.000000, ~24576/16807 = 657.792032
+* CWE: ~2 = 1200.000000, ~24576/16807 = 657.792032
-{{Optimal ET sequence|legend=1| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
+{{Optimal ET sequence|legend=0| 135, 436c, 571, 1277, 1848, 3125, 8098, 11223, 25571, 36794, 121605d }}
-Badness: 0.263
+Badness (Sintel): 0.665
 == Nanic ==
@@ Line 335: / Line 423: @@
 [[Comma list]]: {{monzo| 109 -67 -1 }}
-{{Mapping|legend=1| 1 0 109 | 0 1 -67 }}
+{{Mapping|legend=2| 1 0 109 | 0 1 -67 }}
 : sval mapping generators: ~2, ~3
-[[Optimal tuning]] ([[POTE]]): ~3/2 = 701.9578
+[[Optimal tuning]]s:
+* [[CTE]]: ~2 = 1200.000000, ~3/2 = 701.957820
+* [[POTE]]: ~2 = 1200.000000, ~3/2 = 701.957784
 {{Optimal ET sequence|legend=1| 53, 200, 253, 306, 665, 971, 1277, 6691, 7968, 9245, 10522, 11799, 13076, 40505, 53581, 66657, 79733 }}
-[[Badness]]: 0.0138
+[[Badness]] (Sintel): 0.474
+== Icarus ==
+This temperament is named after a very distant star. Curiously, the names of two even more distant stars coincide with named temperaments, those being [[godzilla]] and [[mothra]].
+[[Subgroup]]: 3.5.7
+[[Comma list]]: {{monzo| -32 -64 71 }}
+{{Mapping|legend=1| 1 35 32 | 0 -71 -64 }}
+[[Optimal tuning]]s:
+* [[CTE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
+* [[CWE]]: ~3 = 1901.955, ~{{monzo| 5 9 -10 }} = 898.340
+[[Optimal ET sequence]]: [[163edt|b163cd]], [[199edt|b199c]], [[235edt|b235]], [[271edt|b271]], [[4643edt|b4643]], [[4914edt|b4914]], …, [[8708edt|b8708]], [[8979edt|b8979]], [[18229edt|b18229]], [[27208edt|b27208]], [[99853edt|b99853]], [[127061edt|b127061]], [[154269edt|b154269]], [[181477edt|b181477]], [[208685edt|b208685]], [[390162edt|b390162]]
+[[Badness]] (Sintel): 0.00493
 = Rank-3 temperaments =
-== Sasaquinbizo-atriyo (171 &amp; 1106 &amp; 3566) ==
+== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| 3 -24 3 10 }} = 282475249000/282429536481
+[[Comma list]]: {{monzo| 3 -24 3 10 }} (282475249000/282429536481)
 {{Mapping|legend=1| 1 0 9 -3 | 0 1 8 0 | 0 0 10 -3 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9624, ~6561/3430 = 1122.9387
 {{Optimal ET sequence|legend=1| 171, 764, 935, 1106, 1277, 2118, 2289, 2460, 3224, 3395, 3566, 26068, 26239, 29634, 29805, 33200, 33371, 36937, 40503, 44069 }}
-[[Badness]]: 0.281 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.24
-== Saquadtrizo-asepgu (171 &amp; 2019 &amp; 3566) ==
+== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| 0 -11 -7 12 }} = 13841287201/13839609375
+[[Comma list]]: {{monzo| 0 -11 -7 12 }} (13841287201/13839609375)
-{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 12 7 }}
+{{Mapping|legend=1| 1 0 0 0 | 0 1 7 5 | 0 0 -12 -7 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9584, ~16807/10125 = 877.2825
 {{Optimal ET sequence|legend=1| 171, 814, 985, 1034, 1205, 1376, 1547, 1718, 1848, 2019, 3224, 3395, 3566, 8980, 9151, 12717, 47131, 50697, 59848d, 63414d, 76131d }}
-[[Badness]]: 0.135 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.595
-== Laquinzo-aquadquadgu (171 &amp; 441 &amp; 4973) ==
+== Laquinzo-aquadquadgu (171 & 441 & 4973) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000
+[[Comma list]]: {{monzo| -7 19 -16 5 }} (19534128475869/19531250000000)
 {{Mapping|legend=1| 1 0 3 11 | 0 1 4 9 | 0 0 5 16 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9501, ~250/189 = 484.2956
 {{Optimal ET sequence|legend=1| 171, 441, 612, 2696, 2795, 2867, 2966, 3137, 3308, 3407, 3479, 3578, 3749, 3920, 4091, 4190, 4361, 4532, 4703, 4802, 4973, 5144, 10117, 10558, 15531, 15702, 52079, 62637, 67781, 78339 }}
-[[Badness]]: 0.297 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.31
-== Laleruyo (171 &amp; 1547 &amp; 3125) ==
+== Laleruyo (171 & 1547 & 3125) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| -1 4 11 -11 }} = 3955078125/3954653486
+[[Comma list]]: {{monzo| -1 4 11 -11 }} (3955078125/3954653486)
-{{Mapping|legend=1| 1 3 0 1 | 0 11 0 4 | 0 0 1 1 }}
+{{Mapping|legend=1| 1 3 0 1 | 0 -11 0 -4 | 0 0 1 1 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~375/343 = 154.3678, ~5/4 = 386.3070
 {{Optimal ET sequence|legend=1| 171, 863, 894, 1034, 1065, 1205, 1236, 1376, 1407, 1547, 1578, 1718, 2612, 2783, 2954, 3125, 12329, 15454, 18579, 21704, 40283, 61987 }}
-[[Badness]]: 0.114 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.501
 == Starscape or Latritriru-ayo ==
@@ Line 395: / Line 510: @@
 [[Comma list]]: 645700815/645657712
-{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 9 1 }}
+{{Mapping|legend=1| 1 0 4 0 | 0 1 1 2 | 0 0 -9 -1 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9514, ~9/7 = 435.0709
 {{Optimal ET sequence|legend=1| 171, 742, 764, 935, 1106, 1277, 1677, 1848, 2019, 2783, 2954, 3125, 8098, 11223, 25571, 33840, 36794, 45063, 48188, 59411, 70634 }}
-[[Badness]]: 0.545 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.240
-== Sepbizo-asegu (171 &amp; 3566 &amp; 4973) ==
+== Sepbizo-asegu (171 & 3566 & 4973) ==
 [[Subgroup]]: 2.3.5.7
-[[Comma list]]: {{monzo| -3 2 -17 14 }} = 6104007655641/6103515625000
+[[Comma list]]: {{monzo| -3 2 -17 14 }} (6104007655641/6103515625000)
-{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 14 17 }}
+{{Mapping|legend=1| 1 0 13 16 | 0 1 10 12 | 0 0 -14 -17 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9548, ~31250/16807 = 1073.8021
 {{Optimal ET sequence|legend=1| 171, 894, 1065, 1236, 1407, 1578, 3053, 3224, 3395, 3566, 5144, 8368, 8539, 8710, 17249, 20815, 29525, 38064, 67589, 105653 }}
-[[Badness]]: 0.223 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.982
 == Euzenius or Sabiruquinyo ==
@@ Line 419: / Line 538: @@
 [[Comma list]]: 78125000/78121827
-{{Mapping|legend=1| 1 0 0 -5 | 0 2 0 -13 | 0 0 1 5 }}
+{{Mapping|legend=1| 1 1 0 -5 | 0 2 0 -13 | 0 0 1 5 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~6250/5103 = 350.9787, ~5/4 = 386.3099
 {{Optimal ET sequence|legend=1| 171, 441, 612, 1730, 1901, 2072, 2171, 2342, 2513, 2684, 2783, 2954, 3125, 6520, 6691, 9816, 16336, 16507, 23027, 26152, 32843, 42659, 58995, 68811, 101654 }}
-[[Badness]]: 0.205 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.0902
 == Nommismic or Quinla-zoyoyo ==
@@ Line 434: / Line 555: @@
 {{Mapping|legend=1| 1 0 0 55 | 0 1 0 -30 | 0 0 1 -2 }}
-[[Optimal tuning]] ([[CTE]]): ~2 = 1\1, ~3/2 = 701.9516, ~5/4 = 386.3132
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9516, ~5/4 = 386.3132
 {{Optimal ET sequence|legend=1| 612, 1236, 1277, 1848, 2513, 3125, 6862, 8098, 8710, 11835, 14960, 26795, 195663b, }} …
-[[Badness]]: 0.366 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 1.62
-== Satwethezo-atritribigu (171 &amp; 1547 &amp; 4973)  ==
+== Satwethezo-atritribigu (171 & 1547 & 4973)  ==
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: {{monzo| 1 -15 -18 23 }}
-{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 23 18 }}
+{{Mapping|legend=1| 1 0 9 7 | 0 1 3 3 | 0 0 -23 -18 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9551, ~56953125/40353607 = 596.5022
 {{Optimal ET sequence|legend=1| 171, 863, 1034, 1205, 1376, 1547, 1718, 3255, 3426, 3597, 4460, 4631, 4802, 4973, 5144, 6520, 6691, 11664, 18355, 48374, 48545, 66900, 145464, }} …
-[[Badness]]: 0.114 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.505
-== Trisa-quinbiru-agu (441 &amp; 1848 &amp; 3125) ==
+== Technologismic or Trisa-quinbiru-agu ==
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: {{monzo| 51 -13 -1 -10 }}
-{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 10 -1 }}
+{{Mapping|legend=1| 1 0 1 5 | 0 1 7 -2 | 0 0 -10 1 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.9553, ~63/32 = 1172.7374
 {{Optimal ET sequence|legend=1| 441, 966, 1277, 1407, 1718, 1848, 2684, 3125, 6691, 9816, 11664, 14789, 18355, 33144, 51499, 124478, 175977, }} …
-[[Badness]]: 0.263 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.116
-== Quinbisa-quinbizo-alegu (1848 &amp; 11664 &amp; 21480) ==
+== Quinbisa-quinbizo-alegu (1848 & 11664 & 21480) ==
 [[Subgroup]]: 2.3.5.7
 [[Comma list]]: {{monzo| 110 -71 -11 10 }}
-{{Mapping|legend=1| 1 0 0 -11 | 0 1 -1 6 | 0 0 10 11 }}
+{{Mapping|legend=1| 1 0 0 -11 | 0 1 9 17 | 0 0 -10 -11 }}
+[[Optimal tuning]] ([[CTE]]): ~2 = 1200.0000, ~3/2 = 701.955, ~32805/28672 = 233.128
 {{Optimal ET sequence|legend=1| 1848, 3737, 5585, 6079, 7927, 9816, 11664, 21480, 33144, 54624, 70025, 81689, 103169, }} …
-[[Badness]]: 0.122 × 10<sup>-3</sup>
+[[Badness]] (Sintel): 0.538
 [[Category:Temperament collections]]
+[[Category:Pages with mostly numerical content]]

Very high accuracy temperaments: Difference between revisions

Latest revision as of 15:37, 14 July 2025

Rank-2 temperaments

Kwazy

Astro

Gaster

Whoosh

Monzismic

Egads

Hemiegads

Fortune

7-limit

11-limit

Senior

Gross

Quectismic

Nanoquectismic

Conanoquectismic

Counterquectismic

Raider

Pirate

Atomic

7-limit

11-limit

Revopentic (2.3.7)

Revopent

Nanic

Icarus

Rank-3 temperaments

Sasaquinbizo-atriyo (171 & 1106 & 3566)

Saquadtrizo-asepgu (171 & 2019 & 3566)

Laquinzo-aquadquadgu (171 & 441 & 4973)

Laleruyo (171 & 1547 & 3125)

Starscape or Latritriru-ayo

Sepbizo-asegu (171 & 3566 & 4973)

Euzenius or Sabiruquinyo

Nommismic or Quinla-zoyoyo

Satwethezo-atritribigu (171 & 1547 & 4973)

Technologismic or Trisa-quinbiru-agu

Quinbisa-quinbizo-alegu (1848 & 11664 & 21480)

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