Very high accuracy temperaments

Revision as of 14:34, 19 July 2021 by FloraC (talk | contribs) (+two more vals and a link by community request)

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

Rank-2 temperaments

Kwazy

Subgroup: 2.3.5

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

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

POTE generator: ~1125/1024 = 162.743

Vals: Template:Val list

Badness: 0.0141

Astro

Subgroup: 2.3.5

Comma list: [91 -12 -31

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

POTE generator: ~296630859375/274877906944 = 132.1947

Vals: Template:Val list

Badness: 0.0628

Whoosh

Subgroup: 2.3.5

Comma list: [37 25 -33

Mapping: [1 -16 -11], 0 33 25]]

POTE generator: ~864/625 = 560.5468

Vals: Template:Val list

Badness: 0.0257

Monzismic

Subgroup: 2.3.5

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

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

POTE generator: ~387420489/335544320 = 249.0184

Vals: Template:Val list

Badness: 0.0104

Egads

Subgroup: 2.3.5

Comma list: [-36 -52 51

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

POTE generator: ~6/5 = 315.6479

Vals: Template:Val list

Badness: 0.0418

Fortune

Subgroup: 2.3.5

Comma list: [-107 47 14

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

POTE generator: ~8388608/7381125 = 221.5679

Vals: Template:Val list

Badness: 0.0279

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 = 221.5680

Vals: Template:Val list

Badness: 0.0237

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 = 221.5681

Vals: Template:Val list

Badness: 0.0366

Senior

Subgroup: 2.3.5

Comma list: [-17 62 -35

Mapping: [1 11 19], 0 -35 -62]]

POTE generator: ~94143178827/78125000000 = 322.8014

Vals: Template:Val list

Badness: 0.0212

Gross

Subgroup: 2.3.5

Comma list: [144 -22 -47

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

POTE generator: ~1953125000000000/1853020188851841 = 91.5310

Vals: Template:Val list

Badness: 0.0463

Raider

Subgroup: 2.3.5

Comma list: [71 -99 37

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

POTE generator: ~8000/6561 = 343.2961

Vals: Template:Val list

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: Template:Val list

Badness: 0.0057

Atomic

Subgroup: 2.3.5

Comma list: [161 -84 -12

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

POTE generator: ~32805/32768 = 1.95516

Vals: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list

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: Template:Val list