Very high accuracy temperaments: Difference between revisions

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Below are listed some very high accuracy temperaments ([[Tenney-Euclidean temperament measures|TE error]] < 0.005 cents/octave).
Below are listed some very high accuracy temperaments ([[Tenney-Euclidean temperament measures|TE error]] < 0.005 cents/octave).


=Rank two temperaments=
= Rank-2 temperaments =
== Kwazy ==
Comma list: {{monzo| -53 10 16 }} = 9010162353515625 / 9007199254740992


==Kwazy==
Mapping: [<2 1 6|, <0 8 -5|]
Comma: |-53 10 16> = 9010162353515625 / 9007199254740992


POTE generator: ~1125/1024 = 162.743
POTE generator: ~1125/1024 = 162.743


Map: [<2 1 6|, <0 8 -5|]
Vals: {{Val list| 118, 494, 612, 730, 848, 1342, 1954 }}


EDOs: [[118edo|118]], [[494edo|494]], [[612edo|612]], [[730edo|730]], [[848edo|848]], [[1342edo|1342]], [[1954edo|1954]]
Badness: 0.0141


Badness: 0.0141
== Astro ==
Comma list: |91 -12 -31>


==Astro==
Mapping: [<1 5 1|, <0 31 -12|]
Comma: |91 -12 -31>


POTE generator: ~296630859375/274877906944 = 132.1947
POTE generator: ~296630859375/274877906944 = 132.1947


Map: [<1 5 1|, <0 31 -12|]
Vals: {{Val list| 118, 935, 1053, 1171, 1289, 1407, 2224, 2460 }}


EDOs: [[118edo|118]], [[935edo|935]], [[1053edo|1053]], [[1171edo|1171]], [[1289edo|1289]], [[1407edo|1407]], [[2224edo|2224]], [[2460edo|2460]]
Badness: 0.0628


Badness: 0.0628
== Whoosh ==
Comma list: |37 25 -33>


==Whoosh==
Mapping: [<1 -16 -11|, <0 33 25|]
Comma: |37 25 -33>


POTE generator: ~864/625 = 560.5468
POTE generator: ~864/625 = 560.5468


Map: [<1 -16 -11|, <0 33 25|]
Vals: {{Val list| 289, 441, 730, 1171, 1612, 1901, 2631 }}
 
EDOs: [[289edo|289]], [[441edo|441]], [[730edo|730]], [[1171edo|1171]], [[1612edo|1612]], [[1901edo|1901]], [[2631edo|2631]]


Badness: 0.0257
Badness: 0.0257


==Monzismic==
== Monzismic ==


: ''See also: [[Monzisma]]''
: ''See also: [[Monzisma]]''


Comma: |54 -37 2> = 450359962737049600 / 450283905890997363
Comma list: |54 -37 2> = 450359962737049600 / 450283905890997363
 
Mapping: [<1 0 -27|, <0 2 37|]


POTE generator: ~387420489/335544320 = 249.0184
POTE generator: ~387420489/335544320 = 249.0184


Map: [<1 0 -27|, <0 2 37|]
Vals: {{Val list| 53, 506, 559, 612, 1783, 2954, 6520 }}


EDOs: [[53edo|53]], [[506edo|506]], [[559edo|559]], [[612edo|612]], [[1783edo|1783]], [[2954edo|2954]], [[6520edo|6520]]
Badness: 0.0104


Badness: 0.0104
== Egads ==
Comma list: |-36 -52 51>


==Egads==
Mapping: [<1 15 16|, <0 -51 -52|]
Comma: |-36 -52 51>


POTE generator: ~6/5 = 315.6479
POTE generator: ~6/5 = 315.6479


Map: [<1 15 16|, <0 -51 -52|]
Vals: {{Val list| 441, 901, 1342, 1783, 2224, 3125, 4467, 4908 }}


EDOs: [[441edo|441]], [[901edo|901]], [[1342edo|1342]], [[1783edo|1783]], [[2224edo|2224]], [[3125edo|3125]], [[4467edo|4467]], [[4908edo|4908]]
Badness: 0.0418


Badness: 0.0418
== Fortune ==
Comma list: |-107 47 14>


==Fortune==
Mapping: [<1 -1 11|, <0 14 -47|]
Comma: |-107 47 14>


POTE generator: ~8388608/7381125 = 221.5679
POTE generator: ~8388608/7381125 = 221.5679


Map: [<1 -1 11|, <0 14 -47|]
Vals: {{Val list| 612, 1289, 1901, 2513, 3125, 3737, 4414, 5638 }}


EDOs: [[612edo|612]], [[1289edo|1289]], [[1901edo|1901]], [[2513edo|2513]], [[3125edo|3125]], [[3737edo|3737]], [[4414edo|4414]], [[5638edo|5638]]
Badness: 0.0279


Badness: 0.0279
=== 7-limit ===
Comma list: 78125000/78121827, |-52 17 12 -1>


===7-limit===
Mapping: [<1 -1 11 63|, <0 14 -47 -326|]
Commas: 78125000/78121827, |-52 17 12 -1>


POTE generator: ~8388608/7381125 = 221.5680
POTE generator: ~8388608/7381125 = 221.5680


Map: [<1 -1 11 63|, <0 14 -47 -326|]
Vals: {{Val list| 612, 2513, 3125, 3737, 4349, 5638, 6862, 9987 }}


EDOs: 612, 2513, 3125, 3737, 4349, 5638, 6862, 9987
Badness: 0.0237


Badness: 0.0237
=== 11-limit ===
Comma list: 151263/151250, 21437500/21434787, 369140625/369098752


===11-limit===
Mapping: [<1 -1 11 63 134|, <0 14 -47 -326 -707|]
Commas: 151263/151250, 21437500/21434787, 369140625/369098752


POTE generator: ~8388608/7381125 = 221.5681
POTE generator: ~8388608/7381125 = 221.5681


Map: [<1 -1 11 63 134|, <0 14 -47 -326 -707|]
Vals: {{Val list| 612, 2513, 3125, 3737, 4349, 4961, 6862, 8086 }}


EDOs: 612, 2513, 3125, 3737, 4349, 4961, 6862, 8086
Badness: 0.0366


Badness: 0.0366
== Senior ==
Comma list: |-17 62 -35>


==Senior==
Mapping: [<1 11 19|, <0 -35 -62|]
Comma: |-17 62 -35>


POTE generator: ~94143178827/78125000000 = 322.8014
POTE generator: ~94143178827/78125000000 = 322.8014


Map: [<1 11 19|, <0 -35 -62|]
Vals: {{Val list| 171, 1171, 1342, 2513, 3684, 3855, 4855, 6197 }}


EDOs: [[171edo|171]], [[1171edo|1171]], [[1342edo|1342]], [[2513edo|2513]], [[3684edo|3684]], [[3855edo|3855]], [[4855edo|4855]], [[6197edo|6197]]
Badness: 0.0212


Badness: 0.0212
== Gross ==
Comma list: |144 -22 -47>


==Gross==
Mapping: [<1 -2 4|, <0 47 -22|]
Comma: |144 -22 -47>


POTE generator: ~1953125000000000/1853020188851841 = 91.5310
POTE generator: ~1953125000000000/1853020188851841 = 91.5310


Map: [<1 -2 4|, <0 47 -22|]
Vals: {{Val list| 118, 1783, 1901, 3684, 5467, 5585, 7250 }}


EDOs: [[118edo|118]], [[1783edo|1783]], [[1901edo|1901]], [[3684edo|3684]], [[5467edo|5467]], [[5585edo|5585]], [[7250edo|7250]]
Badness: 0.0463


Badness: 0.0463
== Raider ==
Comma list: |71 -99 37>


==Raider==
Mapping: [<1 -9 -26|, <0 37 99|]
Comma: |71 -99 37>


POTE generator: ~8000/6561 = 343.2961
POTE generator: ~8000/6561 = 343.2961


Map: [<1 -9 -26|, <0 37 99|]
Vals: {{Val list| 1171, 1954, 3125, 4296, 5467, 7421, 9763, 14059, 18355 }}


EDOs: [[1171edo|1171]], [[1954edo|1954]], [[3125edo|3125]], [[4296edo|4296]], [[5467edo|5467]], [[7421edo|7421]], [[9763edo|9763]], [[14059edo|14059]], [[18355edo|18355]]
Badness: 0.0129


Badness: 0.0129
== Pirate ==
Comma list: |-90 -15 49>


==Pirate==
Mapping: [<1 -6 0|, <0 49 15|]
Comma: |-90 -15 49>


POTE generator: ~1358954496/1220703125 = 185.7542
POTE generator: ~1358954496/1220703125 = 185.7542


Map: [<1 -6 0|, <0 49 15|]
Vals: {{Val list| 730, 1783, 2513, 4296, 6079, 6809, 10375, 11105 }}
 
EDOs: [[730edo|730]], [[1783edo|1783]], [[2513edo|2513]], [[4296edo|4296]], [[6079edo|6079]], [[6809edo|6809]], [[10375edo|10375]], [[11105edo|11105]]


Badness: 0.0057
Badness: 0.0057
Line 141: Line 140:
{{see also | Kirnberger's atom }}
{{see also | Kirnberger's atom }}


Comma: |161 -84 -12>
Comma list: |161 -84 -12>
 
Mapping: [<12 0 161|, <0 1 -7|]


POTE generator: ~32805/32768 = 1.95516
POTE generator: ~32805/32768 = 1.95516


Map: [<12 0 161|, <0 1 -7|]
Vals: {{Val list| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 3684, 4296, 4308, 4908, 7980, 12276, 16572, 20868, 25164, 29460, 33756, 46032 }}


EDOs: [[12edo|12]], [[612edo|612]], [[624edo|624]], [[1236edo|1236]], [[1848edo|1848]], [[2460edo|2460]], [[3072edo|3072]], [[3084edo|3084]], [[3684edo|3684]], [[4296edo|4296]], [[4308edo|4308]], [[4908edo|4908]], [[7980edo|7980]], [[12276edo|12276]], [[16572edo|16572]], [[20868edo|20868]], [[25164edo|25164]], [[29460edo|29460]], [[33756edo|33756]], [[46032edo|46032]]
Badness: 0.0038


Badness: 0.0038
=== 7-limit ===
Comma list: 250047/250000, |-55 30 2 1>


===7-limit===
Mapping: [<12 0 161 338|, <0 1 -7 -16|]
Commas: 250047/250000, |-55 30 2 1>


POTE generator: ~32805/32768 = 1.94961
POTE generator: ~32805/32768 = 1.94961


Map: [<12 0 161 338|, <0 1 -7 -16|]
Vals: {{Val list| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308 }}


EDOs: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308
Badness: 0.0458


Badness: 0.0458
=== 11-limit ===
Comma list: 9801/9800, 151263/151250, 184549376/184528125


===11-limit===
Mapping: [<12 0 161 338 517|, <0 1 -7 -16 -25|]
Commas: 9801/9800, 151263/151250, 184549376/184528125


POTE generator: ~32805/32768 = 1.94799
POTE generator: ~32805/32768 = 1.94799


Map: [<12 0 161 338 517|, <0 1 -7 -16 -25|]
Vals: {{Val list| 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308 }}
 
EDOs: 12, 612, 624, 1236, 1848, 2460, 3072, 3084, 4308


Badness: 0.0160
Badness: 0.0160


= Rank three temperaments =
= Rank-3 temperaments =
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
Comma list: 282475249000/282429536481
Comma list: 282475249000/282429536481
Line 271: Line 270:
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:todo:add definition]]
{{Todo| add definition | intro }}
[[category:todo:intro]]

Revision as of 14:23, 19 July 2021

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

Rank-2 temperaments

Kwazy

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

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

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

See also: Monzisma

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

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

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

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

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

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

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

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

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

See also: Kirnberger's atom

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

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

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)

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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