Very high accuracy temperaments: Difference between revisions
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= Rank-2 temperaments = | = Rank-2 temperaments = | ||
== Kwazy == | == Kwazy == | ||
Kwazy temperament (118&612) tempers out the kwazy comma, {{Monzo|-53 10 16}} (quadla-quadquadyo). 7-limit extensions of the kwazy temperament include [[Hemimage temperaments #Bisupermajor|bisupermajor]] and [[Marvel temperaments #Gwazy|gwazy]]. | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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Mapping: [{{val| 2 1 6 }}, {{val| 0 8 -5 }}] | Mapping: [{{val| 2 1 6 }}, {{val| 0 8 -5 }}] | ||
POTE generator: ~1125/1024 = 162. | POTE generator: ~1125/1024 = 162.742626 | ||
Vals: {{Val list| 118, 494, 612, | Vals: {{Val list| 22, 74, 96, 118, 376, 494, 612, 1342, 3296, 4638, 7934 }} | ||
Badness: 0. | Badness: 0.014091 | ||
== Astro == | == Astro == | ||
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Comma list: {{monzo| 91 -12 -31 }} | Comma list: {{monzo| 91 -12 -31 }} | ||
Mapping: [{{val| 1 5 1 }}, {{val| 0 31 | Mapping: [{{val| 1 5 1 }}, {{val| 0 -31 12 }}] | ||
POTE generator: ~296630859375/274877906944 = 132. | POTE generator: ~296630859375/274877906944 = 132.194668 | ||
Vals: {{Val list| 118, 935, 1053, 1171, | Vals: {{Val list| 9, 109, 118, 699, 817, 935, 1053, 1171, 13934, 15105, 16276, 17447, 18618, 19789, 20960, 22131, 23302, 24473, 25644, 26815, 27986c }} | ||
Badness: 0. | Badness: 0.062778 | ||
== Whoosh == | == Whoosh == | ||
Whoosh temperament (152&289) tempers out the whoosh comma, {{Monzo|37 25 -33}} (saletrigu). 7-limit extensions of the whoosh temperament include [[Porwell temperamtents #Whoosh|whoosh]]. | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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Mapping: [{{val| 1 -16 -11 }}, {{val| 0 33 25 }}] | Mapping: [{{val| 1 -16 -11 }}, {{val| 0 33 25 }}] | ||
POTE generator: ~864/625 = 560. | POTE generator: ~864/625 = 560.546826 | ||
Vals: {{Val list| 289, 441, 730, 1171, | Vals: {{Val list| 15, 122, 137, 152, 289, 441, 730, 1171, 1901, 3072, 4243, 7315, 25017, 32332, 39647c }} | ||
Badness: 0. | Badness: 0.025653 | ||
== Monzismic == | == Monzismic == | ||
{{ | Monzismic temperament (53&559) tempers out the [[monzisma]], {{Monzo|54 -37 2}}. 7-limit extensions of the monzismic temperament include [[Ragismic microtemperamtents #Monzism|monzism]]. | ||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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Mapping: [{{val| 1 0 -27 }}, {{val| 0 2 37 }}] | Mapping: [{{val| 1 0 -27 }}, {{val| 0 2 37 }}] | ||
POTE generator: ~387420489/335544320 = 249. | POTE generator: ~387420489/335544320 = 249.018406 | ||
Vals: {{Val list| 53, 506, 559, 612, 1783, | Vals: {{Val list| 53, 347, 400, 453, 506, 559, 612, 1171, 1783, 4737, 6520 }} | ||
Badness: 0. | Badness: 0.010391 | ||
== Egads == | == Egads == | ||
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Mapping: [{{val| 1 15 16 }}, {{val| 0 -51 -52 }}] | Mapping: [{{val| 1 15 16 }}, {{val| 0 -51 -52 }}] | ||
POTE generator: ~6/5 = 315. | POTE generator: ~6/5 = 315.647919 | ||
Vals: {{Val list| 441, 901, 1342, 1783 | Vals: {{Val list| 19, 365, 384, 403, 422, 441, 901, 1342, 1783, 3125, 4908 }} | ||
Badness: 0. | Badness: 0.041819 | ||
== Fortune == | == Fortune == | ||
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== Senior == | == Senior == | ||
Senior temperament (171&1171) tempers out the senior comma, {{Monzo|-17 62 -35}} (quadla-sepquingu). 7-limit extensions of the senior temperament include [[Ragismic microtemperaments #Seniority|seniority]]. | |||
Subgroup: 2.3.5 | Subgroup: 2.3.5 | ||
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Mapping: [{{val| 1 11 19 }}, {{val| 0 -35 -62 }}] | Mapping: [{{val| 1 11 19 }}, {{val| 0 -35 -62 }}] | ||
POTE generator: ~94143178827/78125000000 = 322. | POTE generator: ~94143178827/78125000000 = 322.801358 | ||
Vals: {{Val list| 171, 1171, | Vals: {{Val list| 171, 658, 829, 1000, 1171, 2513, 6197, 39695, 45892, 52089, 58286, 64483, 70680 }} | ||
Badness: 0. | Badness: 0.021220 | ||
== Gross == | == Gross == | ||
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Vals: {{Val list| 11664, 21480, 33144, 36881, 48545, 54624, 70025, 81689, 91505, 103169}} | Vals: {{Val list| 11664, 21480, 33144, 36881, 48545, 54624, 70025, 81689, 91505, 103169}} | ||
[[Category:Temperament collection]] | |||
{{Todo| add definition | intro }} | {{Todo| add definition | intro }} | ||
Revision as of 08:13, 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 whoosh.
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
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
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
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