Very high accuracy temperaments

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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): 1.473

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): 2.077

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): 0.981

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): 0.313

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): 0.654

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): 0.600

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): 1.211

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): 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 -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): 1.086

Music

Septarium

Septarium splits the octave in seven, and tempers out the septarium comma, [73 77 -84⟩. It can be described as 441 & 2513 temperament, which tempers out 78125000/78121827 and [47 -7 -7 -7⟩ (akjaysma) in the 7-limit.

Subgroup: 2.3.5

Comma list: [73 77 -84⟩

Mapping: [⟨7 1 7], ⟨0 12 11]]

mapping generators: ~[21 22 -24⟩, ~[-20 -21 23⟩

Optimal tunings:

  • WE: ~[21 22 -24⟩ = 171.429 ¢, ~[-20 -21 23⟩ = 144.210 ¢
  • CWE: ~[21 22 -24⟩ = 171.429 ¢, ~[-20 -21 23⟩ = 144.210 ¢

Optimal ET sequence: 133, 308, 441, 1631, 2072, 2513, 5467, 7980

Badness (Sintel): 1.395

7-limit

Subgroup: 2.3.5.7

Comma list: 78125000/78121827, 140737488355328/140710042265625

Mapping: [⟨7 1 7 39], ⟨0 12 11 -23]]

Optimal tunings:

  • WE: ~1157625/1048576 = 171.428 ¢, ~2097152/1929375 = 144.211 ¢
  • CWE: ~1157625/1048576 = 171.429 ¢, ~2097152/1929375 = 144.212 ¢

Optimal ET sequence: 133, 308, 441, 1631, 2072, 2513, 2954

Badness (Sintel): 0.777

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): 0.302

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): 0.133

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): 11.971

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): 8.736

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): 15.285

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): 54.974

Atomic

For extensions, see Landscape microtemperaments #Atomic.

Atomic tempers out Kirnberger's atom, the microscopic interval separating eleven schismas and a syntonic comma, or twelfth schismas and a Pythagorean comma. It is a member of the schismic–commatic equivalence continuum with n = 12. In this extremely accurate temperament, the perfect fifth is one schisma sharp of its 12edo value.

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): 0.0892

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): 0.665

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

Akjaysmic

See also: Akjaysma

Subgroup: 2.3.5.7

Comma list: [47 -7 -7 -7⟩

Mapping: [⟨7 0 0 47], ⟨0 1 0 -1], ⟨0 0 1 -1]]

mapping generators: ~1157625/1048576, ~3, ~5

Optimal tunings:

  • WE: ~1157625/1048576 = 171.427811 ¢, ~3/2 = 701.962313 ¢, ~5/4 = 386.328628 ¢
error map: ⟨-0.0053 +0.0020 +0.0043 +0.0062]
  • CWE: ~1157625/1048576 = 171.428571 ¢, ~3/2 = 701.964859 ¢, ~5/4 = 386.330310 ¢
error map: ⟨0.0000 +0.0099 +0.0166 +0.0218]

Optimal ET sequence: 140, 217, 224, 301, 441, 966, 1106, 1407, 1547, 1848, 2513, 2954, 6349, 9303, 11151, 14105, 17500, 20454

Badness (Sintel): 2.22

11-limit

Subgroup: 2.3.5.7.11

Comma list: 184549376/184528125, 199297406/199290375

Mapping: [⟨7 0 0 47 -168], ⟨0 1 0 -1 10], ⟨0 0 1 -1 5]]

mapping generators: ~29160/26411, ~3, ~5

Optimal tunings:

  • WE: ~29160/26411 = 171.427802 ¢, ~3/2 = 701.964561 ¢, ~5/4 = 386.329837 ¢
  • CWE: ~29160/26411 = 171.428571 ¢, ~3/2 = 701.967291 ¢, ~5/4 = 386.331624 ¢

Optimal ET sequence: 301, 441, 665e, 742, 1106, 1547, 1848, 3395, 4501, 5243, 6349, 17941, 24290, 30639, 45185cde, 63126bcde, 69475bccdde, 75824bccddee

Badness (Sintel): 1.32

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

Izarismic

This temperament is identical to the izar in the no-twos subgroup, but has an independent generator for prime 2. It can be described as 41 & 49 & 130 temperament, and tempers out the izar comma, [0 -11 -7 12⟩.

Subgroup: 2.3.5.7

Comma list: 13841287201/13839609375

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

mapping generators: ~2, ~3, ~16807/10125

Optimal tunings:

  • TE: ~2 = 1200.0000 ¢, ~3/2 = 701.9584 ¢, ~16807/10125 = 877.2825 ¢
  • WE: ~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

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