Orwellismic temperaments: Difference between revisions

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These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.
These temper out {{monzo| 6 3 -1 -3 }} = 1728/1715, the orwellisma.


Temperaments not discussed here include:
Temperaments discussed elsewhere include:
* ''[[beep]]'', {21/20, 27/25} → [[Bug family #Beep]]
* ''[[beep]]'', {21/20, 27/25} → [[Bug family #Beep]]
* ''[[doublewide]]'', {50/49, 875/864} → [[Jubilismic clan #Doublewide]]
* ''[[doublewide]]'', {50/49, 875/864} → [[Jubilismic clan #Doublewide]]
Line 8: Line 8:
* [[myna]], {126/125, 1728/1715} → [[Starling temperaments #Myna]]
* [[myna]], {126/125, 1728/1715} → [[Starling temperaments #Myna]]
* [[orwell]], {225/224, 1728/1715} → [[Semicomma family #Orwell]]
* [[orwell]], {225/224, 1728/1715} → [[Semicomma family #Orwell]]
* ''[[secund]]'', {405/392, 525/512} → [[Greenwoodmic temperaments #Secund]]
* ''[[buzzard]]'', {1728/1715, 5120/5103} → [[Hemifamity temperaments #Buzzard]]
* ''[[buzzard]]'', {1728/1715, 5120/5103} → [[Hemifamity temperaments #Buzzard]]


== Secant ==
== Secant ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 25: Line 26:
[[Badness]]: 0.095278
[[Badness]]: 0.095278


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 38: Line 39:
Badness: 0.046373
Badness: 0.046373


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 51: Line 52:
Badness: 0.025035
Badness: 0.025035


== Infraorwell ==
== Infraorwell ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 66: Line 67:
[[Badness]]: 0.117073
[[Badness]]: 0.117073


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 79: Line 80:
Badness: 0.040721
Badness: 0.040721


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 92: Line 93:
Badness: 0.023683
Badness: 0.023683


== Quartonic ==
== Quartonic ==
{{See also| Turkish maqam music temperaments #Yarman temperament}}
{{See also| Turkish maqam music temperaments #Yarman temperament}}


Line 107: Line 108:
[[Badness]]: 0.117250
[[Badness]]: 0.117250


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 122: Line 123:
[[Badness]]: 0.042632
[[Badness]]: 0.042632


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 135: Line 136:
Badness: 0.034031
Badness: 0.034031


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 148: Line 149:
Badness: 0.023875
Badness: 0.023875


=== Quarto ===
=== Quarto ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 161: Line 162:
Badness: 0.041786
Badness: 0.041786


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 174: Line 175:
Badness: 0.027692
Badness: 0.027692


=== Quartz ===
=== Quartz ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 187: Line 188:
Badness: 0.053285
Badness: 0.053285


==== 13-limit ====
==== 13-limit ====
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 200: Line 201:
Badness: 0.028818
Badness: 0.028818


== Sentinel ==
== Sentinel ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 213: Line 214:
[[Badness]]: 0.723413
[[Badness]]: 0.723413


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 228: Line 229:
[[Badness]]: 0.093805
[[Badness]]: 0.093805


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 241: Line 242:
Badness: 0.039595
Badness: 0.039595


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 254: Line 255:
Badness: 0.037408
Badness: 0.037408


== Diesic ==
== Diesic ==
Subgroup: 2.3.5
Subgroup: 2.3.5


Line 267: Line 268:
[[Badness]]: 1.344681
[[Badness]]: 1.344681


=== 7-limit ===
=== 7-limit ===
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Line 282: Line 283:
[[Badness]]: 0.107348
[[Badness]]: 0.107348


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Line 295: Line 296:
Badness: 0.044186
Badness: 0.044186


=== 13-limit ===
=== 13-limit ===
Subgroup: 2.3.5.7.11.13
Subgroup: 2.3.5.7.11.13


Line 308: Line 309:
Badness: 0.038116
Badness: 0.038116


== Pentorwell ==
== Pentorwell ==
Subgroup: 2.3.5.7
Subgroup: 2.3.5.7


Comma list: 1728/1715, 179200/177147
[[Comma list]]: 1728/1715, 179200/177147


Mapping: [{{val| 5 8 12 14 }}, {{val| 0 -1 -6 1 }}]
[[Mapping]]: [{{val| 5 8 12 14 }}, {{val| 0 -1 -6 1 }}]


POTE generator: ~7/4 = 975.0872
[[POTE generator]]: ~7/4 = 975.0872


{{Val list|legend=1| 5, 75, 80 }}
{{Val list|legend=1| 5, 75, 80 }}


Badness: 0.148665
[[Badness]]: 0.148665


=== 11-limit ===
=== 11-limit ===
Subgroup: 2.3.5.7.11
Subgroup: 2.3.5.7.11


Revision as of 11:12, 3 August 2021

These temper out [6 3 -1 -3⟩ = 1728/1715, the orwellisma.

Temperaments discussed elsewhere include:

Secant

Subgroup: 2.3.5.7

Comma list: 1728/1715, 177147/175000

Mapping: [⟨2 1 0 5], ⟨0 7 15 2]]

Wedgie: ⟨⟨ 14 30 4 15 -33 -75 ]]

POTE generator: ~10/9 = 185.885

Template:Val list

Badness: 0.095278

11-limit

Subgroup: 2.3.5.7.11

Comma list: 441/440, 1344/1331, 1728/1715

Mapping: [⟨2 1 0 5 6], ⟨0 7 15 2 3]]

POTE genertor: ~10/9 = 185.962

Vals: Template:Val list

Badness: 0.046373

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 351/350, 364/363, 441/440

Mapping: [⟨2 1 0 5 6 4], ⟨0 7 15 2 3 11]]

POTE generator: ~10/9 = 185.955

Vals: Template:Val list

Badness: 0.025035

Infraorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 28672/28125

Mapping: [⟨1 14 0 16], ⟨0 -16 3 -17]]

Wedgie: ⟨⟨ 16 -3 17 -42 -18 48 ]]

POTE generator: ~7/6 = 269.032

Template:Val list

Badness: 0.117073

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 1344/1331

Mapping: [⟨1 14 0 16 12], ⟨0 -16 3 -17 -11]]

POTE generator: ~7/6 = 269.036

Vals: Template:Val list

Badness: 0.040721

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 144/143, 176/175, 196/195, 364/363

Mapping: [⟨1 14 0 16 12 20], ⟨0 -16 3 -17 -11 -21]]

POTE generator: ~7/6 = 269.021

Vals: Template:Val list

Badness: 0.023683

Quartonic

See also: Turkish maqam music temperaments § Yarman temperament

Subgroup: 2.3.5

Comma list: 390625000/387420489

Mapping: [⟨1 2 3], ⟨0 -11 -18]]

POTE generator: ~250/243 = 45.233

Template:Val list

Badness: 0.117250

7-limit

Subgroup: 2.3.5.7

Comma list: 1728/1715, 4000/3969

Mapping: [⟨1 2 3 3], ⟨0 -11 -18 -5]]

Wedgie: ⟨⟨ 11 18 5 3 -23 -39 ]]

POTE generator: ~36/35 = 45.139

Template:Val list

Badness: 0.042632

11-limit

Subgroup: 2.3.5.7.11

Comma list: 176/175, 540/539, 2200/2187

Mapping: [⟨1 2 3 3 5], ⟨0 -11 -18 -5 -41]]

POTE generator: ~36/35 = 45.041

Vals: Template:Val list

Badness: 0.034031

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 169/168, 176/175, 325/324, 540/539

Mapping: [⟨1 2 3 3 5 4], ⟨0 -11 -18 -5 -41 -8]]

POTE generator: ~36/35 = 45.080

Vals: Template:Val list

Badness: 0.023875

Quarto

Subgroup: 2.3.5.7.11

Comma list: 100/99, 245/242, 864/847

Mapping: [⟨1 2 3 3 4], ⟨0 -11 -18 -5 -14]]

POTE generator: ~36/35 = 45.132

Vals: Template:Val list

Badness: 0.041786

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 78/77, 100/99, 144/143, 245/242

Mapping: [⟨1 2 3 3 4 4], ⟨0 -11 -18 -5 -14 -8]]

POTE generator: ~36/35 = 45.205

Vals: Template:Val list

Badness: 0.027692

Quartz

Subgroup: 2.3.5.7.11

Comma list: 99/98, 385/384, 4000/3969

Mapping: [⟨1 2 3 3 3], ⟨0 -11 -18 -5 12]]

POTE generator: ~36/35 = 45.385

Vals: Template:Val list

Badness: 0.053285

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 169/168, 275/273, 385/384

Mapping: [⟨1 2 3 3 3 4], ⟨0 -11 -18 -5 12 -8]]

POTE generator: ~36/35 = 45.387

Vals: Template:Val list

Badness: 0.028818

Sentinel

Subgroup: 2.3.5

Comma list: 8968066875/8589934592

Mapping: [⟨1 3 -3], ⟨0 -4 15]]

POTE generator: ~512/405 = 425.474

Template:Val list

Badness: 0.723413

7-limit

Subgroup: 2.3.5.7

Comma list: 1728/1715, 3645/3584

Mapping: [⟨1 3 -3 6], ⟨0 -4 15 -9]]

Wedgie: ⟨⟨ 4 -15 9 -33 3 63 ]]

POTE generator: ~9/7 = 425.596

Template:Val list

Badness: 0.093805

11-limit

Subgroup: 2.3.5.7.11

Comma list: 99/98, 243/242, 385/384

Mapping: [⟨1 3 -3 6 7], ⟨0 -4 15 -9 -10]]

POTE generator: ~9/7 = 425.550

Vals: Template:Val list

Badness: 0.039595

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 99/98, 105/104, 144/143, 243/242

Mapping: [⟨1 3 -3 6 7 3], ⟨0 -4 15 -9 -10 2]]

POTE generator: ~9/7 = 425.501

Vals: Template:Val list

Badness: 0.037408

Diesic

Subgroup: 2.3.5

Comma list: 10460353203/9765625000

Mapping: [⟨1 2 3], ⟨0 -13 -21]]

POTE generator: ~6561/6250 = 38.571

Template:Val list

Badness: 1.344681

7-limit

Subgroup: 2.3.5.7

Comma list: 1728/1715, 5103/5000

Mapping: [⟨1 2 3 3], ⟨0 -13 -21 -6]]

Wedgie: ⟨⟨ 13 21 6 3 -27 -45 ]]

POTE generator: ~36/35 = 38.567

Template:Val list

Badness: 0.107348

11-limit

Subgroup: 2.3.5.7.11

Comma list: 121/120, 441/440, 891/875

Mapping: [⟨1 2 3 3 4], ⟨0 -13 -21 -6 -17]]

POTE generator: ~36/35 = 38.565

Vals: Template:Val list

Badness: 0.044186

13-limit

Subgroup: 2.3.5.7.11.13

Comma list: 66/65, 121/120, 343/338, 441/440

Mapping: [⟨1 2 3 3 4 4], ⟨0 -13 -21 -6 -17 -9]]

POTE generator: ~36/35 = 38.444

Vals: Template:Val list

Badness: 0.038116

Pentorwell

Subgroup: 2.3.5.7

Comma list: 1728/1715, 179200/177147

Mapping: [⟨5 8 12 14], ⟨0 -1 -6 1]]

POTE generator: ~7/4 = 975.0872

Template:Val list

Badness: 0.148665

11-limit

Subgroup: 2.3.5.7.11

Comma list: 896/891, 1728/1715, 2200/2187

Mapping: [⟨5 8 12 14 17], ⟨0 -1 -6 1 5]]

POTE generator: ~7/4 = 975.1212

Vals: Template:Val list

Badness: 0.071702

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