Varunismic temperaments: Difference between revisions
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[[Mapping]]: [{{val| 8 0 -11 14 }}, {{val| 0 3 7 2 }}] | [[Mapping]]: [{{val| 8 0 -11 14 }}, {{val| 0 3 7 2 }}] | ||
Mapping generators: ~160/147, ~350/243 | |||
[[POTE generator]]: ~350/243 = 633.738 | [[POTE generator]]: ~350/243 = 633.738 | ||
{{Val list|legend=1| 72, 176, 248, 320 }} | {{Val list|legend=1| 32c, 72, 176, 248, 320 }} | ||
[[Badness]]: 0.102295 | [[Badness]]: 0.102295 | ||
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POTE generator: ~121/84 = 633.755 | POTE generator: ~121/84 = 633.755 | ||
Vals: {{Val list| 72, 176, 248, 320 }} | Vals: {{Val list| 32c, 72, 176, 248, 320 }} | ||
Badness: 0.030159 | Badness: 0.030159 | ||
=== 13-limit === | ==== 13-limit ==== | ||
Subgroup: 2.3.5.7.11.13 | Subgroup: 2.3.5.7.11.13 | ||
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Badness: 0.027632 | Badness: 0.027632 | ||
==== Octowerckis ==== | |||
Subgroup: 2.3.5.7.11.13 | |||
Comma list: 351/350, 364/363, 441/440, 2197/2187 | |||
Mapping: [{{val| 8 0 -11 14 15 0 }}, {{val| 0 3 7 2 3 7 }}] | |||
POTE generator: ~13/9 = 633.8370 | |||
Vals: {{Val list| 32cf, 72, 176, 248f }} | |||
Badness: 0.0302 | |||
[[Category:Regular temperament theory]] | [[Category:Regular temperament theory]] | ||
Revision as of 13:54, 24 September 2021
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 #Injera
- diaschismic, {126/125, 2048/2025} → Diaschismic family #Diaschismic
- compton, {225/224, 250047/250000} → Compton family #Compton
- bamity, {245/243, 64827/64000} → Amity family #Bamity
- unidec, {1029/1024, 4375/4374} → Gamelismic clan #Unidec
- harry, {2401/2400, 19683/19600} → Breedsmic temperaments #Harry
- bischismic, {3136/3125, 32805/32768} → Schismatic family #Bischismic
- bison, {6144/6125, 78732/78125} → Sensipent family #Bison
- commatic, {10976/10935, 50421/50000} → Hemimage temperaments #Commatic
- decal, {235298/234375, 321489/320000} → Pental family #Decal
- bosonic, {321489/320000, 589824/588245} → 26th-octave temperaments #Bosonic
Essence
Essence is of interest because of the abundant supply of essentially tempered chords.
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]]
Vals: 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]]
Vals: 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
Vals: 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
Vals: 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
Vals: Template:Val list
Badness: 0.0302