Orwellismic temperaments
These temper out [6 3 -1 -3⟩ = 1728/1715, the orwellisma.
Temperaments discussed elsewhere include:
- Beep, {21/20, 27/25} → Bug family #Beep
- Doublewide, {50/49, 875/864} → Jubilismic clan #Doublewide
- Superpyth, {64/63, 245/243} → Archytas clan #Superpyth
- Mothra, {81/80, 1029/1024} → Meantone family #Mothra
- Myna, {126/125, 1728/1715} → Starling temperaments #Myna
- Orwell, {225/224, 1728/1715} → Semicomma family #Orwell
- Secund, {405/392, 525/512} → Greenwoodmic temperaments #Secund
- Buzzard, {1728/1715, 5120/5103} → Hemifamity temperaments #Buzzard
- Trimabila, {1728/1715, 268435456/263671875} → Mabila family #Trimabila
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
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.023683
Quartonic
Quartonic tempers out saleyo comma, [3 -18 11⟩ = 390625000/387420489 in the 5-limit. This temperament can be described as 26&27 temperament, which tempers out the orwellisma and the octagar comma, 4000/3969. The name "quartonic" means quarter-tone, which is the generator of this temperament (representing ~36/35 and ~40/39). Alternative extension yarman (80&159) slices the quartonic generator in three.
Subgroup: 2.3.5
Comma list: 390625000/387420489
Mapping: [⟨1 2 3], ⟨0 -11 -18]]
POTE generator: ~250/243 = 45.233
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
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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.028818
Biquartonic
Subgroup: 2.3.5.7.11
Comma list: 1728/1715, 2420/2401, 2560/2541
Mapping: [⟨2 4 6 6 7], ⟨0 -11 -18 -5 -1]]
POTE generator: ~36/35 = 45.129
Optimal GPV sequence: Template:Val list
Badness: 0.060737
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 169/168, 325/324, 364/363, 640/637
Mapping: [⟨2 4 6 6 7 8], ⟨0 -11 -18 -5 -1 -8]]
POTE generator: ~36/35 = 45.153
Optimal GPV sequence: Template:Val list
Badness: 0.039891
Sentinel
- For the 5-limit version of this temperament, see High badness temperaments #Sentinel.
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
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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.037408
Diesic
- For the 5-limit version of this temperament, see High badness temperaments #Diesic.
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
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
Optimal GPV sequence: 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
Optimal GPV sequence: Template:Val list
Badness: 0.038116
Phillips
- For the 5-limit version of this temperament, see High badness temperaments #Phillips.
Subgroup: 2.3.5.7
Comma list: 1728/1715, 6561/6272
Mapping: [⟨2 0 33 -7], ⟨0 1 -9 4]]
Wedgie: ⟨⟨ 2 -18 8 -33 7 69 ]]
POTE generator: ~3/2 = 691.174
Badness: 0.228602
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 385/384, 729/704
Mapping: [⟨2 0 33 -7 -12], ⟨0 1 -9 4 6]]
POTE generator: ~3/2 = 691.040
Optimal GPV sequence: Template:Val list
Badness: 0.095777
Triskaidekic
- For the 5-limit version of this temperament, see High badness temperaments #Triskaidekic.
Subgroup: 2.3.5.7
Comma list: 1728/1715, 1875/1792
Mapping: [⟨13 0 30 16], ⟨0 1 0 1]]
Wedgie: ⟨⟨ 13 0 13 -30 -16 30 ]]
POTE generator: ~3/2 = 694.143
Badness: 0.219050
11-limit
Subgroup: 2.3.5.7.11
Comma list: 99/98, 125/121, 385/384
Mapping: [⟨13 0 30 16 45], ⟨0 1 0 1 0]]
POTE generator: ~3/2 = 696.296
Optimal GPV sequence: Template:Val list
Badness: 0.098847
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 78/77, 99/98, 125/121, 1200/1183
Mapping: [⟨13 0 30 16 45 48], ⟨0 1 0 1 0 0]]
POTE generator: ~3/2 = 695.879
Optimal GPV sequence: Template:Val list
Badness: 0.059216
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
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
Optimal GPV sequence: Template:Val list
Badness: 0.071702