Very high accuracy temperaments: Difference between revisions

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= Rank-2 temperaments =
= Rank-2 temperaments =
== Kwazy ==
== Kwazy ==
Subgroup: 2.3.5
Comma list: {{monzo| -53 10 16 }} = 9010162353515625 / 9007199254740992
Comma list: {{monzo| -53 10 16 }} = 9010162353515625 / 9007199254740992


Mapping: [<2 1 6|, <0 8 -5|]
Mapping: [{{val| 2 1 6 }}, {{val| 0 8 -5 }}]


POTE generator: ~1125/1024 = 162.743
POTE generator: ~1125/1024 = 162.743
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== Astro ==
== Astro ==
Comma list: |91 -12 -31>
Subgroup: 2.3.5
 
Comma list: {{monzo| 91 -12 -31 }}


Mapping: [<1 5 1|, <0 31 -12|]
Mapping: [{{val| 1 5 1 }}, {{val| 0 31 -12 }}]


POTE generator: ~296630859375/274877906944 = 132.1947
POTE generator: ~296630859375/274877906944 = 132.1947
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== Whoosh ==
== Whoosh ==
Comma list: |37 25 -33>
Subgroup: 2.3.5
 
Comma list: {{monzo| 37 25 -33 }}


Mapping: [<1 -16 -11|, <0 33 25|]
Mapping: [{{val| 1 -16 -11 }}, {{val| 0 33 25 }}]


POTE generator: ~864/625 = 560.5468
POTE generator: ~864/625 = 560.5468
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== Monzismic ==
== Monzismic ==
{{See also| Monzisma }}


: ''See also: [[Monzisma]]''
Subgroup: 2.3.5


Comma list: |54 -37 2> = 450359962737049600 / 450283905890997363
Comma list: {{monzo| 54 -37 2 }} = 450359962737049600 / 450283905890997363


Mapping: [<1 0 -27|, <0 2 37|]
Mapping: [{{val| 1 0 -27 }}, {{val| 0 2 37 }}]


POTE generator: ~387420489/335544320 = 249.0184
POTE generator: ~387420489/335544320 = 249.0184
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== Egads ==
== Egads ==
Comma list: |-36 -52 51>
Subgroup: 2.3.5


Mapping: [<1 15 16|, <0 -51 -52|]
Comma list: {{monzo| -36 -52 51 }}
 
Mapping: [{{val| 1 15 16 }}, {{val| 0 -51 -52 }}]


POTE generator: ~6/5 = 315.6479
POTE generator: ~6/5 = 315.6479
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== Fortune ==
== Fortune ==
Comma list: |-107 47 14>
Subgroup: 2.3.5


Mapping: [<1 -1 11|, <0 14 -47|]
Comma list: {{monzo| -107 47 14 }}
 
Mapping: [{{val| 1 -1 11 }}, {{val| 0 14 -47 }}]


POTE generator: ~8388608/7381125 = 221.5679
POTE generator: ~8388608/7381125 = 221.5679
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=== 7-limit ===
=== 7-limit ===
Comma list: 78125000/78121827, |-52 17 12 -1>
Subgroup: 2.3.5.7


Mapping: [<1 -1 11 63|, <0 14 -47 -326|]
Comma list: 78125000/78121827, {{monzo| -52 17 12 -1 }}
 
Mapping: [{{val| 1 -1 11 63 }}, {{val| 0 14 -47 -326 }}]


POTE generator: ~8388608/7381125 = 221.5680
POTE generator: ~8388608/7381125 = 221.5680
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=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 151263/151250, 21437500/21434787, 369140625/369098752
Comma list: 151263/151250, 21437500/21434787, 369140625/369098752


Mapping: [<1 -1 11 63 134|, <0 14 -47 -326 -707|]
Mapping: [{{val| 1 -1 11 63 134 }}, {{val| 0 14 -47 -326 -707 }}]


POTE generator: ~8388608/7381125 = 221.5681
POTE generator: ~8388608/7381125 = 221.5681
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== Senior ==
== Senior ==
Comma list: |-17 62 -35>
Subgroup: 2.3.5


Mapping: [<1 11 19|, <0 -35 -62|]
Comma list: {{monzo| -17 62 -35 }}
 
Mapping: [{{val| 1 11 19 }}, {{val| 0 -35 -62 }}]


POTE generator: ~94143178827/78125000000 = 322.8014
POTE generator: ~94143178827/78125000000 = 322.8014
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== Gross ==
== Gross ==
Comma list: |144 -22 -47>
Subgroup: 2.3.5


Mapping: [<1 -2 4|, <0 47 -22|]
Comma list: {{monzo| 144 -22 -47 }}
 
Mapping: [{{val| 1 -2 4 }}, {{val| 0 47 -22 }}]


POTE generator: ~1953125000000000/1853020188851841 = 91.5310
POTE generator: ~1953125000000000/1853020188851841 = 91.5310
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== Raider ==
== Raider ==
Comma list: |71 -99 37>
Subgroup: 2.3.5
 
Comma list: {{monzo| 71 -99 37 }}


Mapping: [<1 -9 -26|, <0 37 99|]
Mapping: [{{val| 1 -9 -26 }}, {{val| 0 37 99 }}]


POTE generator: ~8000/6561 = 343.2961
POTE generator: ~8000/6561 = 343.2961
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== Pirate ==
== Pirate ==
Comma list: |-90 -15 49>
Subgroup: 2.3.5
 
Comma list: {{monzo| -90 -15 49 }}


Mapping: [<1 -6 0|, <0 49 15|]
Mapping: [{{val| 1 -6 0 }}, {{val| 0 49 15 }}]


POTE generator: ~1358954496/1220703125 = 185.7542
POTE generator: ~1358954496/1220703125 = 185.7542
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{{see also | Kirnberger's atom }}
{{see also | Kirnberger's atom }}


Comma list: |161 -84 -12>
Subgroup: 2.3.5


Mapping: [<12 0 161|, <0 1 -7|]
Comma list: {{monzo| 161 -84 -12 }}
 
Mapping: [{{val| 12 0 161 }}, {{val| 0 1 -7 }}]


POTE generator: ~32805/32768 = 1.95516
POTE generator: ~32805/32768 = 1.95516
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=== 7-limit ===
=== 7-limit ===
Comma list: 250047/250000, |-55 30 2 1>
Subgroup: 2.3.5.7


Mapping: [<12 0 161 338|, <0 1 -7 -16|]
Comma list: 250047/250000, {{monzo| -55 30 2 1 }}
 
Mapping: [{{val| 12 0 161 338 }}, {{val| 0 1 -7 -16 }}]


POTE generator: ~32805/32768 = 1.94961
POTE generator: ~32805/32768 = 1.94961
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=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Comma list: 9801/9800, 151263/151250, 184549376/184528125
Comma list: 9801/9800, 151263/151250, 184549376/184528125


Mapping: [<12 0 161 338 517|, <0 1 -7 -16 -25|]
Mapping: [{{val| 12 0 161 338 517 }}, {{val| 0 1 -7 -16 -25 }}]


POTE generator: ~32805/32768 = 1.94799
POTE generator: ~32805/32768 = 1.94799
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= Rank-3 temperaments =
= Rank-3 temperaments =
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
== Sasaquinbizo-atriyo (171 & 1106 & 3566) ==
Subgroup: 2.3.5.7
Comma list: 282475249000/282429536481
Comma list: 282475249000/282429536481


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== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
== Saquadtrizo-asepgu (171 & 2019 & 3566) ==
Subgroup: 2.3.5.7
Comma list: 13841287201/13839609375
Comma list: 13841287201/13839609375


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== Laquinzo-aquadquadgu (171 & 441 & 4973) ==
== Laquinzo-aquadquadgu (171 & 441 & 4973) ==
Subgroup: 2.3.5.7
Comma list: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000
Comma list: {{monzo| -7 19 -16 5 }} = 19534128475869/19531250000000


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== Laleruyo (171 & 1547 & 3125) ==
== Laleruyo (171 & 1547 & 3125) ==
Subgroup: 2.3.5.7
Comma list: 3955078125/3954653486
Comma list: 3955078125/3954653486


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== Starscape or Latritriru-ayo ==
== Starscape or Latritriru-ayo ==
Subgroup: 2.3.5.7
Comma list: 645700815/645657712
Comma list: 645700815/645657712


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== Sepbizo-asegu (171 & 3566 & 4973) ==
== Sepbizo-asegu (171 & 3566 & 4973) ==
Subgroup: 2.3.5.7
Comma list: 6104007655641/6103515625000
Comma list: 6104007655641/6103515625000


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== Euzenius or Sabiruquinyo ==
== Euzenius or Sabiruquinyo ==
Subgroup: 2.3.5.7
Comma list: 78125000/78121827
Comma list: 78125000/78121827


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== Quinla-zoyoyo (612 & 1848 & 3125) ==
== Quinla-zoyoyo (612 & 1848 & 3125) ==
Subgroup: 2.3.5.7
Comma list: {{monzo| -55 30 2 1 }}
Comma list: {{monzo| -55 30 2 1 }}


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== Sa-twentythezo-atritribigu (171 & 1547 & 4973) ==
== Sa-twentythezo-atritribigu (171 & 1547 & 4973) ==
Subgroup: 2.3.5.7
Comma list: {{monzo| 1 -15 -18 23 }}
Comma list: {{monzo| 1 -15 -18 23 }}


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== Trisa-quinbiru-agu (441 & 1848 & 3125) ==
== Trisa-quinbiru-agu (441 & 1848 & 3125) ==
Subgroup: 2.3.5.7
Comma list: {{monzo| 51 -13 -1 -10 }}
Comma list: {{monzo| 51 -13 -1 -10 }}


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== Quinbisa-quinbizo-alegu (21480 & 33144 & 103169) ==
== Quinbisa-quinbizo-alegu (21480 & 33144 & 103169) ==
Subgroup: 2.3.5.7
Comma list: {{monzo| 110 -71 -11 10 }}
Comma list: {{monzo| 110 -71 -11 10 }}


Revision as of 14:29, 19 July 2021

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

See also: Monzisma

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

See also: Kirnberger's atom

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

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