Very high accuracy temperaments: Difference between revisions
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POTE generator: ~6/5 = 315.647919 | POTE generator: ~6/5 = 315.647919 | ||
Vals: {{Val list| 19, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908 }} | Vals: {{Val list| 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: 0.041819 | ||
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POTE generator: ~1953125000000000/1853020188851841 = 91.531001 | POTE generator: ~1953125000000000/1853020188851841 = 91.531001 | ||
Vals: {{Val list| 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467 }} | Vals: {{Val list| 13, 105, 118, 957, 1075, 1193, 1311, 1429, 1547, 1665, 1783, 3684, 5467 }} | ||
Badness: 0.046315 | Badness: 0.046315 | ||
Revision as of 09:23, 25 July 2021
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
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: Template:Val list
Badness: 0.046315
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