Varunismic temperaments: Difference between revisions
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Mapping: [{{val| 2 10 27 23 33 }}, {{val| 0 -11 -36 -28 -42 }}] | Mapping: [{{val| 2 10 27 23 33 }}, {{val| 0 -11 -36 -28 -42 }}] | ||
Optimal GPV sequence: {{Val list| 58, 132de, 190, 248, 438d }} | |||
Badness: 0.046447 | Badness: 0.046447 | ||
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Mapping: [{{val| 2 10 27 23 33 31 }}, {{val| 0 -11 -36 -28 -42 -38 }}] | Mapping: [{{val| 2 10 27 23 33 31 }}, {{val| 0 -11 -36 -28 -42 -38 }}] | ||
Optimal GPV sequence: {{Val list| 58, 132de, 190, 248, 438d }} | |||
Badness: 0.026107 | Badness: 0.026107 | ||
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POTE generator: ~121/84 = 633.755 | POTE generator: ~121/84 = 633.755 | ||
Optimal GPV sequence: {{Val list| 32c, 72, 176, 248, 320 }} | |||
Badness: 0.030159 | Badness: 0.030159 | ||
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POTE generator: ~75/52 = 633.742 | POTE generator: ~75/52 = 633.742 | ||
Optimal GPV sequence: {{Val list| 72, 176f, 248, 320 }} | |||
Badness: 0.027632 | Badness: 0.027632 | ||
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POTE generator: ~13/9 = 633.8370 | POTE generator: ~13/9 = 633.8370 | ||
Optimal GPV sequence: {{Val list| 32cf, 72, 176, 248f }} | |||
Badness: 0.030192 | Badness: 0.030192 | ||
Revision as of 01:58, 19 March 2022
This is a collection of rank-2 temperaments tempering out the varunisma, 321489/320000 = [-9 8 -4 2⟩.
Temperaments discussed elsewhere are:
- Injera, {50/49, 81/80} → Meantone family
- Diaschismic, {126/125, 2048/2025} → Diaschismic family
- Compton, {225/224, 250047/250000} → Compton family
- Bamity, {245/243, 64827/64000} → Amity family
- Unidec, {1029/1024, 4375/4374} → Gamelismic clan
- Harry, {2401/2400, 19683/19600} → Gravity family and Breedsmic temperaments
- Bischismic, {3136/3125, 32805/32768} → Schismatic family
- Bison, {6144/6125, 78732/78125} → Sensipent family
- Commatic, {10976/10935, 50421/50000} → Hemimage temperaments
- Narayana, {65625/65536, 321489/320000} → Vishnuzmic family
- Decal, {235298/234375, 321489/320000} → Pental family
- Bosonic, {321489/320000, 589824/588245} → 26th-octave temperaments
Essence
Essence is of interest because of the abundant supply of essentially tempered chords. Specifically, werckismic chords, squbemic chords, cuthbert triad, sinbadmic chords, and petrmic triad in the 13-odd-limit, in addition to nicolic chords in the 15-odd-limit.
Subgroup: 2.3.5.7
Comma list: 321489/320000, 823543/820125
Mapping: [⟨2 10 27 23], ⟨0 -11 -36 -28]]
Wedgie: ⟨⟨ 22 72 56 63 27 -72 ]]
POTE generator: ~243/196 = 372.597
Badness: 0.173565
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 456533/455625
POTE generator: ~150/121 = 372.599
Mapping: [⟨2 10 27 23 33], ⟨0 -11 -36 -28 -42]]
Optimal GPV sequence: Template:Val list
Badness: 0.046447
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 729/728, 847/845, 1001/1000
POTE generator: ~26/21 = 372.602
Mapping: [⟨2 10 27 23 33 31], ⟨0 -11 -36 -28 -42 -38]]
Optimal GPV sequence: Template:Val list
Badness: 0.026107
Octowerck
Subgroup: 2.3.5.7
Comma list: 321489/320000, 420175/419904
Mapping: [⟨8 0 -11 14], ⟨0 3 7 2]]
Mapping generators: ~160/147, ~350/243
POTE generator: ~350/243 = 633.738
Badness: 0.102295
11-limit
Subgroup: 2.3.5.7.11
Comma list: 441/440, 8019/8000, 41503/41472
Mapping: [⟨8 0 -11 14 15], ⟨0 3 7 2 3]]
POTE generator: ~121/84 = 633.755
Optimal GPV sequence: Template:Val list
Badness: 0.030159
13-limit
Subgroup: 2.3.5.7.11.13
Comma list: 441/440, 729/728, 1001/1000, 6656/6655
Mapping: [⟨8 0 -11 14 15 -38], ⟨0 3 7 2 3 16]]
POTE generator: ~75/52 = 633.742
Optimal GPV sequence: Template:Val list
Badness: 0.027632
Octowerckis
Subgroup: 2.3.5.7.11.13
Comma list: 351/350, 364/363, 441/440, 2197/2187
Mapping: [⟨8 0 -11 14 15 0], ⟨0 3 7 2 3 7]]
POTE generator: ~13/9 = 633.8370
Optimal GPV sequence: Template:Val list
Badness: 0.030192