Varunismic temperaments

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

Optimal ET sequence: 58, 132d, 190, 248, 438d, 686d

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 ET sequence: 58, 132de, 190, 248, 438d

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 ET sequence: 58, 132de, 190, 248, 438d

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

Optimal ET sequence: 32c, 72, 176, 248, 320

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 ET sequence: 32c, 72, 176, 248, 320

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 ET sequence: 72, 176f, 248, 320

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 ET sequence: 32cf, 72, 176, 248f

Badness: 0.030192