Very high accuracy temperaments

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

Rank-2 temperaments

Kwazy

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

Subgroup: 2.3.5

Comma list: [-53 10 16 = 9010162353515625 / 9007199254740992

Mapping: [2 1 6], 0 8 -5]]

POTE generator: ~1125/1024 = 162.742626

Vals: 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934

Badness: 0.014091

Astro

Subgroup: 2.3.5

Comma list: [91 -12 -31

Mapping: [1 5 1], 0 -31 12]]

POTE generator: ~296630859375/274877906944 = 132.194668

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

Badness: 0.062778

Whoosh

Whoosh temperament (152&289) tempers out the whoosh comma, [37 25 -33 (saletrigu). 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]]

POTE generator: ~864/625 = 560.546826

Vals: 15, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c

Badness: 0.025653

Monzismic

Monzismic temperament (53&559) tempers out the monzisma, [54 -37 2. 7-limit extensions of the monzismic temperament include monzism.

Subgroup: 2.3.5

Comma list: [54 -37 2 = 450359962737049600 / 450283905890997363

Mapping: [1 0 -27], 0 2 37]]

POTE generator: ~387420489/335544320 = 249.018406

Vals: 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520

Badness: 0.010391

Egads

Subgroup: 2.3.5

Comma list: [-36 -52 51

Mapping: [1 15 16], 0 -51 -52]]

POTE generator: ~6/5 = 315.647919

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

Badness: 0.041819

Fortune

Fortune temperament tempers out the fortune comma, [-107 47 14 (tritrila-sepbiyo). 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]]

POTE generator: ~8388608/7381125 = 221.567899

Vals: 65, 352, 417, 482, 547, 612, 1901, 2513, 5638, 8151

Badness: 0.027876

7-limit

Subgroup: 2.3.5.7

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

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

POTE generator: ~8388608/7381125 = 221.568031

Vals: 612, 1901, 2513, 3125, 6862, 9987

Badness: 0.023704

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]]

POTE generator: ~8388608/7381125 = 221.568139

Vals: 612, 2513, 3125, 3737, 8086

Badness: 0.036641

Senior

Senior temperament (171&1171) tempers out the senior comma, [-17 62 -35 (quadla-sepquingu). 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]]

POTE generator: ~94143178827/78125000000 = 322.801358

Vals: 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680

Badness: 0.021220

Gross

Gross temperament (118&1783) tempers out the gross comma, [144 -22 -47, by which a stack of 22 tritaves (third harmonic) and 47 pentaves (fifth harmonic) falls short of 144 (gross) octaves.

Subgroup: 2.3.5

Comma list: [144 -22 -47

Mapping: [1 -2 4], 0 47 -22]]

POTE generator: ~1953125000000000/1853020188851841 = 91.531001

Vals: 13, 105, 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467

Badness: 0.046315

Raider

See also: Syntonic-chromatic equivalence continuum

Subgroup: 2.3.5

Comma list: [71 -99 37

Mapping: [1 -9 -26], 0 37 99]]

POTE generator: ~8000/6561 = 343.2961

Vals: 388, 783, 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355

Badness: 0.0129

Pirate

Subgroup: 2.3.5

Comma list: [-90 -15 49

Mapping: [1 -6 0], 0 49 15]]

POTE generator: ~1358954496/1220703125 = 185.7542

Vals: 730, 1783, 2513, 4296, 6079, 6809, 10375, 11105

Badness: 0.0057

Atomic

See also: Kirnberger's atom

Subgroup: 2.3.5

Comma list: [161 -84 -12

Mapping: [12 0 161], 0 1 -7]]

POTE generator: ~32805/32768 = 1.95516

Vals: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, 46032

Badness: 0.0038

7-limit

Subgroup: 2.3.5.7

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

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

POTE generator: ~32805/32768 = 1.94961

Vals: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308

Badness: 0.0458

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]]

POTE generator: ~32805/32768 = 1.94799

Vals: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308

Badness: 0.0160

Rank-3 temperaments

Sasaquinbizo-atriyo (171 & 1106 & 3566)

Subgroup: 2.3.5.7

Comma list: 282475249000/282429536481

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

Vals: 171, 935, 1106, 1277, 2289, 2460, 3395, 3566, 3737

Badness: 0.000281

Saquadtrizo-asepgu (171 & 2019 & 3566)

Subgroup: 2.3.5.7

Comma list: 13841287201/13839609375

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

Vals: 171, 1547, 1677, 1718, 1848, 2019, 3395, 3566, 3737

Badness: 0.000135

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]]

Vals: 171, 270, 441, 612, 783, 4802, 4973, 5144

Badness: 0.000297

Laleruyo (171 & 1547 & 3125)

Subgroup: 2.3.5.7

Comma list: 3955078125/3954653486

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

Vals: 171, 1407, 1547, 1578, 1718, 2783, 2954, 3125, 3296

Badness: 0.000114

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]]

Vals: 171, 1848, 2019, 2783, 2954, 3125, 3296, 4973, 5144

Badness: 0.000545

Sepbizo-asegu (171 & 3566 & 4973)

Subgroup: 2.3.5.7

Comma list: 6104007655641/6103515625000

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

Vals: 171, 1236, 1407, 3566, 3737, 3908, 4802, 4973, 8539, 8710

Badness: 0.000223

Euzenius or Sabiruquinyo

Subgroup: 2.3.5.7

Comma list: 78125000/78121827

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

Vals: 171, 441, 612, 2954, 3125, 3566, 3737, 6520, 6691

Badness: 0.000205

Quinla-zoyoyo (612 & 1848 & 3125)

Subgroup: 2.3.5.7

Comma list: [-55 30 2 1

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

Vals: 612, 665, 1236, 1277, 1848, 1889, 2460, 2513, 3125, 3737, 4973, 5585, 6862, 8098, 8710, 11835, 14960

Badness: 0.000366

Sa-twentythezo-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]]

Vals: 171, 1547, 4802, 4973, 5144, 6520, 6691, 6862, 11493, 11664, 11835, 18184, 18355, 18526, 25046, 30019, 30190, 48545

Badness: 0.000114

Trisa-quinbiru-agu (441 & 1848 & 3125)

Subgroup: 2.3.5.7

Comma list: [51 -13 -1 -10

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

Vals: 441, 1848, 3125, 3566, 4973, 6691, 8098, 8539, 9816, 11664, 14789, 15230, 18355, 21480, 30019, 33144, 39835, 51499

Badness: 0.000263

Quinbisa-quinbizo-alegu (21480 & 33144 & 103169)

Subgroup: 2.3.5.7

Comma list: [110 -71 -11 10

Mapping: [1 0 0 -11], 0 1 -1 6], 0 0 10 11]]

Vals: 11664, 21480, 33144, 36881, 48545, 54624, 70025, 81689, 91505, 103169