Very high accuracy temperaments

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:

• WE: ~94921875/67108864 = 600.003398 ¢, ~1125/1024 = 162.743548 ¢

error map: ⟨+0.0068 -0.0032 -0.0111]

• CWE: ~94921875/67108864 = 600.000000 ¢, ~1125/1024 = 162.742801 ¢

error map: ⟨0.0000 -0.0126 -0.0277]

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 -26 13], ⟨0 31 -12]]

mapping generators: ~2, ~[39 -5 -13⟩

Optimal tunings:

• WE: ~2 = 1199.994636 ¢, ~[39 -5 -13⟩ = 1067.800558 ¢

error map: ⟨-0.0054 +0.0018 +0.0099]

• CWE: ~2 = 1200.000000 ¢, ~[39 -5 -13⟩ = 1067.805278 ¢

error map: ⟨0.0000 +0.0086 +0.0230]

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 -8 -34], ⟨0 19 72]]

mapping generators: ~2, ~[-18 19 -5⟩

Optimal tunings:

• WE: ~2 = 1200.002817 ¢, ~[-18 19 -5⟩ = 605.366856 ¢

error map: ⟨+0.0028 -0.0073 +0.0041]

• CWE: ~2 = 1200.000000 ¢, ~[-18 19 -5⟩ = 605.365482 ¢

error map: ⟨0.0000 -0.0108 +0.0010]

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

Badness (Sintel): TBD

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 -16 -11], ⟨0 33 25]]

mapping generators: ~2, ~625/432

Optimal tunings:

• WE: ~2 = 1199.997806 ¢, ~625/432 = 639.452005 ¢

error map: ⟨-0.0022 -0.0037 +0.0106]

• CWE: ~2 = 1200.000000 ¢, ~625/432 = 639.453117 ¢

error map: ⟨0.0000 -0.0022 +0.0142]

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:

• WE: ~2 = 1199.997524 ¢, ~[27 -18 1⟩ = 950.979631 ¢

error map: ⟨-0.0025 +0.0043 -0.0005]

• CWE: ~2 = 1200.000000 ¢, ~[27 -18 1⟩ = 950.981535 ¢

error map: ⟨0.0000 +0.0081 +0.0031]

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 -36 -36], ⟨0 51 52]]

mapping generators: ~2, ~5/3

Optimal tunings:

• WE: ~2 = 1200.000553 ¢, ~5/3 = 884.352488 ¢

error map: ⟨+0.0006 +0.0020 -0.0042]

• CWE: ~2 = 1200.000000 ¢, ~5/3 = 844.352090 ¢

error map: ⟨0.0000 +0.0016 -0.0050]

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): TBD

Hemiegads

Subgroup: 2.3.5.7

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

Mapping: [⟨1 -87 -88 127], ⟨0 102 104 -143]]

mapping generators: ~2, ~67108864/36756909

Optimal tunings:

• WE: ~2 = 1200.000308 ¢, ~67108864/36756909 = 1042.176313 ¢
• CWE: ~2 = 1200.000000 ¢, ~67108864/36756909 = 1042.176046 ¢

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

Badness (Sintel): TBD

Catabolic

Subgroup: 2.3.5.13

Comma list: 140625/140608, [-4 20 -9 0 0 -4⟩

Mapping: [⟨1 -36 -36 -98], ⟨0 51 52 138]]

Optimal tunings:

• WE: ~2 = 1200.000308 ¢, ~5/3 = 884.354064 ¢
• CWE: ~2 = 1200.000000 ¢, ~5/3 = 884.351835 ¢

Optimal ET sequence: 19, …, 441, 460, 901, 1342

Badness (Sintel): 0.222

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 -1 11], ⟨0 14 -47]]

mapping generators: ~2, ~8388608/7381125

Optimal tunings:

• WE: ~2 = 1200.000553 ¢, ~8388608/7381125 = 221.568202 ¢

error map: ⟨+0.0016 -0.0018 -0.0012]

• CWE: ~2 = 1200.000000 ¢, ~8388608/7381125 = 221.567889 ¢

error map: ⟨0.0000 -0.0046 -0.0045]

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

Badness (Sintel): TBD

7-limit

Subgroup: 2.3.5.7

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

Mapping: [⟨1 -1 11 63], ⟨0 14 -47 -326]]

Optimal tunings:

• WE: ~2 = 1200.001970 ¢, ~8388608/7381125 = 221.568395 ¢
• CWE: ~2 = 1200.000000 ¢, ~8388608/7381125 = 221.568026 ¢

Optimal ET sequence: 65d, …, 612, 1901, 2513, 3125, 6862, 9987, 13112, 36211, 49323

Badness (Sintel): TBD

11-limit

Subgroup: 2.3.5.7.11

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

Mapping: [⟨1 -1 11 63 134], ⟨0 14 -47 -326 -707]]

Optimal tunings:

• WE: ~2 = 1200.003854 ¢, ~8388608/7381125 = 221.568850 ¢
• CWE: ~2 = 1200.000000 ¢, ~8388608/7381125 = 221.568133 ¢

Optimal ET sequence: 65dee, …, 612, 2513, 3125, 3737, 8086, 19909d

Badness (Sintel): TBD

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 -24 -43], ⟨0 35 62]]

mapping generators: ~2, ~[7 -23 13⟩

Optimal tunings:

• WE: ~2 = 1200.000236 ¢, ~[7 -23 13⟩ = 877.198814 ¢

error map: ⟨+0.0002 -0.0022 +0.0026]

• CWE: ~2 = 1200.000000 ¢, ~[7 -23 13⟩ = 877.198647 ¢

error map: ⟨0.0000 -0.0024 -0.0024]

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

Badness (Sintel): TBD

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 -2 4], ⟨0 47 -22]]

mapping generators: ~2, ~[46 -7 -15⟩

Optimal tunings:

• WE: ~2 = 1199.998956 ¢, ~[46 -7 -15⟩ = 91.530922 ¢

error map: ⟨-0.0010 +0.0004 +0.0018]

• CWE: ~2 = 1200.000000 ¢, ~[46 -7 -15⟩ = 91.530995 ¢

error map: ⟨0.0000 +0.0018 +0.0044]

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): TBD

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:

• WE: ~2 = 1199.999902567 ¢, ~3/2 = 701.955253373 ¢

error map: ⟨-0.000097 +0.000155 -0.000001]

• CWE: ~2 = 1200.000000000 ¢, ~3/2 = 701.955310152 ¢

error map: ⟨0.000000 +0.000309 +0.000149]

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

Badness (Sintel): TBD

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:

• WE: ~2 = 1199.979407 ¢, ~3/2 = 701.943437 ¢
• CWE: ~2 = 1200.000000 ¢, ~3/2 = 701.955457 ¢

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

Badness (Sintel): TBD

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:

• WE: ~2 = 1200.010750 ¢, ~3/2 = 701.961041 ¢
• CWE: ~2 = 1200.000000 ¢, ~3/2 = 701.954771 ¢

Optimal ET sequence: 306d, 359cd, 665

Badness (Sintel): TBD

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:

• WE: ~2 = 1200.000184840 ¢, ~3/2 = 701.954524421 ¢

error map: ⟨+0.000185 -0.000292 -0.000002]

• CWE: ~2 = 1200.000000000 ¢, ~3/2 = 701.954415845 ¢

error map: ⟨0.000000 -0.000585 -0.000289]

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

Badness (Sintel): TBD

Raider

See also: Syntonic–chromatic equivalence continuum

Subgroup: 2.3.5

Comma list: [71 -99 37⟩

Mapping: [⟨1 -9 -26], ⟨0 37 99]]

mapping generators: ~2, ~8000/6561

Optimal tunings:

• WE: ~2 = 1199.999880537 ¢, ~8000/6561 = 343.296063356 ¢

error map: ⟨-0.000119 +0.000418 -0.000336]

• CWE: ~2 = 1200.000000000 ¢, ~8000/6561 = 343.296095985 ¢

error map: ⟨0.000000 +0.000551 -0.000211]

Optimal ET sequence: 7, …, 381, 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355, 22651, 26947, 31243, 35539, 66782, 102321, 137860

Badness (Sintel): TBD

Pirate

See also: Hemfiness temperaments § Piracy

Subgroup: 2.3.5

Comma list: [-90 -15 49⟩

Mapping: [⟨1 -6 0], ⟨0 49 15]]

mapping generators: ~2, ~[24 4 -13⟩

Optimal tunings:

• WE: ~2 = 1200.000195604 ¢, ~[24 4 -13⟩ = 185.754209314 ¢

error map: ⟨-0.000196 +0.000418 -0.000336]

• CWE: ~2 = 1200.000000000 ¢, ~[24 4 -13⟩ = 185.754209314 ¢

error map: ⟨0.000000 +0.000082 -0.000574]

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

Badness (Sintel): TBD

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:

• WE: ~[-67 35 5⟩ = 99.999995361 ¢, ~3/2 = 701.955129505 ¢ (~32805/32768 = 1.955161980 ¢)

error map: ⟨-0.000056 +0.000072 +0.000022]

• CWE: ~[-67 35 5⟩ = 100.000000000 ¢, ~3/2 = 701.955166184 ¢ (~32805/32768 = 1.955166184 ¢)

error map: ⟨0.000000 +0.000165 +0.000123]

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

Badness (Sintel): TBD

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:

• WE: ~30375/28672 = 99.999866 ¢, ~3/2 = 701.948670 ¢ (~32805/32768 = 1.949605 ¢)
• CWE: ~30375/28672 = 100.000000 ¢, ~3/2 = 701.949698 ¢ (~32805/32768 = 1.949698 ¢)

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:

• WE: ~30375/28672 = 99.999760 ¢, ~3/2 = 701.946301 ¢ (~32805/32768 = 1.947983 ¢)
• CWE: ~30375/28672 = 100.000000 ¢, ~3/2 = 701.948121 ¢ (~32805/32768 = 1.948121 ¢)

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

Badness (Sintel): 0.530

Revopentic

See also: Revopentisma

Subgroup: 2.3.7

Comma list: [47 4 -19⟩

Subgroup-val mapping: [⟨1 -7 1], ⟨0 19 4]]

mapping generators: ~2, ~16807/12288

Optimal tunings:

• WE: ~2 = 1199.998821 ¢, ~16807/12288 = 542.207710 ¢

error map: ⟨-0.0012 -0.0003 +0.0038]

• CWE: ~2 = 1200.000000 ¢, ~16807/12288 = 542.208204 ¢

error map: ⟨0.0000 +0.0009 +0.0069]

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 -7 132 1], ⟨0 19 -287 4]]

Optimal tunings:

• WE: ~2 = 1200.000110 ¢, ~16807/12288 = 542.208018 ¢
• CWE: ~2 = 1200.000000 ¢, ~16807/12288 = 542.207968 ¢

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

Badness (Sintel): TBD

Nanic

See also: Nanisma

Subgroup: 2.3.7

Comma list: [109 -67 -1⟩

Subgroup-val mapping: [⟨1 0 109], ⟨0 1 -67]]

mapping generators: ~2, ~3

Optimal tunings:

• WE: ~2 = 1199.999111 ¢, ~3/2 = 701.957264 ¢

error map: ⟨-0.0009 +0.0014 +0.0001]

• CWE: ~2 = 1200.000000 ¢, ~3/2 = 701.957796 ¢

error map: ⟨0.0000 +0.0028 +0.0018]

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

Badness (Sintel): TBD

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⟩

Subgroup-val mapping: [⟨1 -36 -32], ⟨0 71 64]]

mapping generators: ~3, ~[-4 -9 10⟩

Optimal tunings:

• WE: ~3 = 1901.955003 ¢, ~[-4 -9 10⟩ = 1003.615406 ¢

error map: ⟨+0.0000 +0.0000 -0.0000]

• CWE: ~3 = 1901.955001 ¢, ~[-4 -9 10⟩ = 1003.615405 ¢

error map: ⟨0.0000 -0.0000 -0.0000]

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

Badness (Sintel): TBD

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

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

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

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

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 & 3737 & 6079)

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 = 1200.000 ¢, ~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

Septrongismic

See also: Septrongisma

Subgroup: 2.3.5.7

Comma list: [-7 30 -9 -7⟩ = 205891132094649/205885750000000

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

Optimal tuning (CWE): ~2 = 1200.000 ¢, ~3/2 = 701.954 ¢, ~1715000/1594323 = 126.337 ¢

Optimal ET sequence: 171, 2783, 2954, 3125, 8539, 11664, 14789, …

Badness (Sintel): 0.320