Very high accuracy temperaments: Difference between revisions

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Line 173: Line 173:
Badness: 0.0160
Badness: 0.0160


=Rank three temperaments=
= Rank three temperaments =
==Sasaquinbizo-atriyo (171 & 1106 & 3566)==
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
Comma: 282475249000/282429536481
Comma list: 282475249000/282429536481


Map: [<1 0 9 -3|, <0 1 8 0|, <0 0 10 -3|]
Mapping: [{{val| 1 0 9 -3 }}, {{val| 0 1 8 0 }}, {{val| 0 0 10 -3 }}]


Vals: {{Val list| 171, 935, 1106, 1277, 2289, 2460, 3395, 3566, 3737}}
Vals: {{Val list| 171, 935, 1106, 1277, 2289, 2460, 3395, 3566, 3737}}
Line 183: Line 183:
Badness: 0.000281
Badness: 0.000281


==Saquadtrizo-asepgu (171 & 2019 & 3566)==
== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
Comma: 13841287201/13839609375
Comma list: 13841287201/13839609375


Map: [<1 0 0 0|, <0 1 7 5|, <0 0 12 7|]
Mapping: [{{val| 1 0 0 0 }}, {{val| 0 1 7 5 }}, {{val| 0 0 12 7 }}]


Vals: {{Val list| 171, 1547, 1677, 1718, 1848, 2019, 3395, 3566, 3737}}
Vals: {{Val list| 171, 1547, 1677, 1718, 1848, 2019, 3395, 3566, 3737}}
Line 192: Line 192:
Badness: 0.000135
Badness: 0.000135


==Laquinzo-aquadquadgu (171 & 441 & 4973)==
== Laquinzo-aquadquadgu (171 & 441 & 4973) ==
Comma: |-7 19 -16 5> = 19534128475869/19531250000000
Comma list: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000


Map: [<1 0 3 11|, <0 1 4 9|, <0 0 5 16|]
Mapping: [{{val| 1 0 3 11 }}, {{val| 0 1 4 9 }}, {{val| 0 0 5 16 }}]


Vals: {{Val list| 171, 270, 441, 612, 783, 4802, 4973, 5144}}
Vals: {{Val list| 171, 270, 441, 612, 783, 4802, 4973, 5144}}


Badness: 0.000297
Badness: 0.000297


==Laleruyo (171 & 1547 & 3125)==
== Laleruyo (171 & 1547 & 3125) ==
Comma: 3955078125/3954653486
Comma list: 3955078125/3954653486


Map: [<1 3 0 1|, <0 11 0 4|, <0 0 1 1|]
Mapping: [{{val| 1 3 0 1 }}, {{val| 0 11 0 4 }}, {{val| 0 0 1 1 }}]


Vals: {{Val list| 171, 1407, 1547, 1578, 1718, 2783, 2954, 3125, 3296}}
Vals: {{Val list| 171, 1407, 1547, 1578, 1718, 2783, 2954, 3125, 3296}}


Badness: 0.000114
Badness: 0.000114


==Starscape or Latritriru-ayo==
== Starscape or Latritriru-ayo ==
Comma: 645700815/645657712
Comma list: 645700815/645657712


Map: [<1 0 4 0|, <0 1 1 2|, <0 0 9 1|]
Mapping: [{{val| 1 0 4 0 }}, {{val| 0 1 1 2 }}, {{val| 0 0 9 1 }}]


Vals: {{Val list| 171, 1848, 2019, 2783, 2954, 3125, 3296, 4973, 5144}}
Vals: {{Val list| 171, 1848, 2019, 2783, 2954, 3125, 3296, 4973, 5144}}


Badness: 0.000545
Badness: 0.000545


==Sepbizo-asegu (171 & 3566 & 4973)==
== Sepbizo-asegu (171 & 3566 & 4973) ==
Comma: 6104007655641/6103515625000
Comma list: 6104007655641/6103515625000


Map: [<1 0 13 16|, <0 1 10 12|, <0 0 14 17|]
Mapping: [{{val| 1 0 13 16 }}, {{val| 0 1 10 12 }}, {{val| 0 0 14 17 }}]


Vals: {{Val list| 171, 1236, 1407, 3566, 3737, 3908, 4802, 4973, 8539, 8710}}
Vals: {{Val list| 171, 1236, 1407, 3566, 3737, 3908, 4802, 4973, 8539, 8710}}
Line 228: Line 228:
Badness: 0.000223
Badness: 0.000223


==Euzenius or Sabiruquinyo==
== Euzenius or Sabiruquinyo ==
Comma: 78125000/78121827
Comma list: 78125000/78121827


Map: [<1 0 0 -5|, <0 2 0 -13|, <0 0 1 5|]
Mapping: [{{val| 1 0 0 -5 }}, {{val| 0 2 0 -13 }}, {{val| 0 0 1 5 }}]


Vals: {{Val list| 171, 441, 612, 2954, 3125, 3566, 3737, 6520, 6691}}
Vals: {{Val list| 171, 441, 612, 2954, 3125, 3566, 3737, 6520, 6691}}


Badness: 0.000205
Badness: 0.000205


==Quinla-zoyoyo (612 & 1848 & 3125)==
== Quinla-zoyoyo (612 & 1848 & 3125) ==
Comma: |-55 30 2 1>
Comma list: {{monzo| -55 30 2 1 }}


Map: [<1 0 0 55|, <0 1 0 -30|, <0 0 1 -2|]
Mapping: [{{val| 1 0 0 55 }}, {{val| 0 1 0 -30 }}, {{val| 0 0 1 -2 }}]


Vals: {{Val list| 612, 665, 1236, 1277, 1848, 1889, 2460, 2513, 3125, 3737, 4973, 5585, 6862, 8098, 8710, 11835, 14960}}
Vals: {{Val list| 612, 665, 1236, 1277, 1848, 1889, 2460, 2513, 3125, 3737, 4973, 5585, 6862, 8098, 8710, 11835, 14960}}
Line 246: Line 246:
Badness: 0.000366
Badness: 0.000366


==Sa-twentythezo-atritribigu (171 & 1547 & 4973)==
== Sa-twentythezo-atritribigu (171 & 1547 & 4973) ==
Comma: |1 -15 -18 23>
Comma list: {{monzo| 1 -15 -18 23 }}


Map: [<1 0 9 7|, <0 1 3 3|, <0 0 23 18|]
Mapping: [{{val| 1 0 9 7 }}, {{val| 0 1 3 3 }}, {{val| 0 0 23 18 }}]


Vals: {{Val list| 171, 1547, 4802, 4973, 5144, 6520, 6691, 6862, 11493, 11664, 11835, 18184, 18355, 18526, 25046, 30019, 30190, 48545}}
Vals: {{Val list| 171, 1547, 4802, 4973, 5144, 6520, 6691, 6862, 11493, 11664, 11835, 18184, 18355, 18526, 25046, 30019, 30190, 48545}}
Line 255: Line 255:
Badness: 0.000114
Badness: 0.000114


==Trisa-quinbiru-agu (441 & 1848 & 3125)==
== Trisa-quinbiru-agu (441 & 1848 & 3125) ==
Comma: |51 -13 -1 -10>
Comma list: {{monzo| 51 -13 -1 -10 }}


Map: [<1 0 1 5|, <0 1 7 -2|, <0 0 10 -1|]
Mapping: [{{val| 1 0 1 5 }}, {{val| 0 1 7 -2 }}, {{val| 0 0 10 -1 }}]


Vals: {{Val list| 441, 1848, 3125, 3566, 4973, 6691, 8098, 8539, 9816, 11664, 14789, 15230, 18355, 21480, 30019, 33144, 39835, 51499}}
Vals: {{Val list| 441, 1848, 3125, 3566, 4973, 6691, 8098, 8539, 9816, 11664, 14789, 15230, 18355, 21480, 30019, 33144, 39835, 51499}}
Line 264: Line 264:
Badness: 0.000263
Badness: 0.000263


==Quinbisa-quinbizo-alegu (21480 & 33144 & 103169)==
== Quinbisa-quinbizo-alegu (21480 & 33144 & 103169) ==
Comma: |110 -71 -11 10>
Comma list: {{monzo| 110 -71 -11 10 }}


Map: [<1 0 0 -11|, <0 1 -1 6|, <0 0 10 11|]
Mapping: [{{val| 1 0 0 -11 }}, {{val| 0 1 -1 6 }}, {{val| 0 0 10 11 }}]


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}}

Revision as of 07:17, 11 April 2021

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

Rank two temperaments

Kwazy

Comma: |-53 10 16> = 9010162353515625 / 9007199254740992

POTE generator: ~1125/1024 = 162.743

Map: [<2 1 6|, <0 8 -5|]

EDOs: 118, 494, 612, 730, 848, 1342, 1954

Badness: 0.0141

Astro

Comma: |91 -12 -31>

POTE generator: ~296630859375/274877906944 = 132.1947

Map: [<1 5 1|, <0 31 -12|]

EDOs: 118, 935, 1053, 1171, 1289, 1407, 2224, 2460

Badness: 0.0628

Whoosh

Comma: |37 25 -33>

POTE generator: ~864/625 = 560.5468

Map: [<1 -16 -11|, <0 33 25|]

EDOs: 289, 441, 730, 1171, 1612, 1901, 2631

Badness: 0.0257

Monzismic

See also: Monzisma

Comma: |54 -37 2> = 450359962737049600 / 450283905890997363

POTE generator: ~387420489/335544320 = 249.0184

Map: [<1 0 -27|, <0 2 37|]

EDOs: 53, 506, 559, 612, 1783, 2954, 6520

Badness: 0.0104

Egads

Comma: |-36 -52 51>

POTE generator: ~6/5 = 315.6479

Map: [<1 15 16|, <0 -51 -52|]

EDOs: 441, 901, 1342, 1783, 2224, 3125, 4467, 4908

Badness: 0.0418

Fortune

Comma: |-107 47 14>

POTE generator: ~8388608/7381125 = 221.5679

Map: [<1 -1 11|, <0 14 -47|]

EDOs: 612, 1289, 1901, 2513, 3125, 3737, 4414, 5638

Badness: 0.0279

7-limit

Commas: 78125000/78121827, |-52 17 12 -1>

POTE generator: ~8388608/7381125 = 221.5680

Map: [<1 -1 11 63|, <0 14 -47 -326|]

EDOs: 612, 2513, 3125, 3737, 4349, 5638, 6862, 9987

Badness: 0.0237

11-limit

Commas: 151263/151250, 21437500/21434787, 369140625/369098752

POTE generator: ~8388608/7381125 = 221.5681

Map: [<1 -1 11 63 134|, <0 14 -47 -326 -707|]

EDOs: 612, 2513, 3125, 3737, 4349, 4961, 6862, 8086

Badness: 0.0366

Senior

Comma: |-17 62 -35>

POTE generator: ~94143178827/78125000000 = 322.8014

Map: [<1 11 19|, <0 -35 -62|]

EDOs: 171, 1171, 1342, 2513, 3684, 3855, 4855, 6197

Badness: 0.0212

Gross

Comma: |144 -22 -47>

POTE generator: ~1953125000000000/1853020188851841 = 91.5310

Map: [<1 -2 4|, <0 47 -22|]

EDOs: 118, 1783, 1901, 3684, 5467, 5585, 7250

Badness: 0.0463

Raider

Comma: |71 -99 37>

POTE generator: ~8000/6561 = 343.2961

Map: [<1 -9 -26|, <0 37 99|]

EDOs: 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355

Badness: 0.0129

Pirate

Comma: |-90 -15 49>

POTE generator: ~1358954496/1220703125 = 185.7542

Map: [<1 -6 0|, <0 49 15|]

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

Badness: 0.0057

Atomic

See also: Kirnberger's atom

Comma: |161 -84 -12>

POTE generator: ~32805/32768 = 1.95516

Map: [<12 0 161|, <0 1 -7|]

EDOs: 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

Commas: 250047/250000, |-55 30 2 1>

POTE generator: ~32805/32768 = 1.94961

Map: [<12 0 161 338|, <0 1 -7 -16|]

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

Badness: 0.0458

11-limit

Commas: 9801/9800, 151263/151250, 184549376/184528125

POTE generator: ~32805/32768 = 1.94799

Map: [<12 0 161 338 517|, <0 1 -7 -16 -25|]

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

Badness: 0.0160

Rank three temperaments

Sasaquinbizo-atriyo (171 & 1106 & 3566)

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)

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)

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)

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

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)

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

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)

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)

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)

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)

Comma list: [110 -71 -11 10⟩

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

Vals: Template:Val list

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