Jubilismic family: Difference between revisions
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
Cmloegcmluin (talk | contribs) "optimal GPV sequence" → "optimal ET sequence", per Talk:Optimal_ET_sequence |
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: [[Eigenmonzo]]s (unchanged-intervals): 2, 3/2, 35/32 | : [[Eigenmonzo]]s (unchanged-intervals): 2, 3/2, 35/32 | ||
{{ | {{Optimal ET sequence|legend=1| 4, 8d, 10, 12, 22, 34d, 48 }} | ||
Scales: [[jubilismic10]], [[jubilismic12]] | Scales: [[jubilismic10]], [[jubilismic12]] | ||
| Line 32: | Line 32: | ||
[[POTE generator]]s: ~3/2 = 703.4155, ~5/4 = 380.6973 | [[POTE generator]]s: ~3/2 = 703.4155, ~5/4 = 380.6973 | ||
{{ | {{Optimal ET sequence|legend=1| 4, 8d, 10e, 12, 22, 34d, 48 }} | ||
[[Badness]]: 0.600 × 10<sup>-3</sup> | [[Badness]]: 0.600 × 10<sup>-3</sup> | ||
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[[POTE generator]]s: ~3/2 = 693.6257, ~5/4 = 371.2658 | [[POTE generator]]s: ~3/2 = 693.6257, ~5/4 = 371.2658 | ||
{{ | {{Optimal ET sequence|legend=1| 10, 12, 22e, 26 }} | ||
[[Badness]]: 0.689 × 10<sup>-3</sup> | [[Badness]]: 0.689 × 10<sup>-3</sup> | ||
| Line 60: | Line 60: | ||
[[POTE generator]]s: ~3/2 = 713.5853, ~5/4 = 397.6952 | [[POTE generator]]s: ~3/2 = 713.5853, ~5/4 = 397.6952 | ||
{{ | {{Optimal ET sequence|legend=1| 8d, 10, 12, 22e }} | ||
[[Badness]]: 0.717 × 10<sup>-3</sup> | [[Badness]]: 0.717 × 10<sup>-3</sup> | ||
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[[POTE generator]]s: ~3/2 = 706.6559, ~5/4 = 376.8308 | [[POTE generator]]s: ~3/2 = 706.6559, ~5/4 = 376.8308 | ||
{{ | {{Optimal ET sequence|legend=1| 8d, 10, 12e, 14c, 22 }} | ||
[[Badness]]: 0.781 × 10<sup>-3</sup> | [[Badness]]: 0.781 × 10<sup>-3</sup> | ||
Revision as of 18:10, 7 May 2023
The jubilismic family contains temperaments that temper out the jubilisma (50/49) (also called tritonic diesis, or septimal sixth-tone). It therefore identifies the two septimal tritones 7/5 and 10/7, an identification familiar from 12edo. While most rank-three temperaments are planar, a jubilismic temperament divides the octave in two.
Jubilismic
Subgroup: 2.3.5.7
Comma list: 50/49
Mapping: [⟨2 0 0 1], ⟨0 1 0 0], ⟨0 0 1 1]]
Mapping generators: ~7/5, ~3, ~5
POTE generators: ~3/2 = 702.9804, ~5/4 = 380.8399
- 7- and 9-odd-limit
- [[1 0 0 0⟩, [0 1 0 0⟩, [-1/4 0 1/2 1/2⟩, [1/4 0 1/2 1/2⟩]
- Eigenmonzos (unchanged-intervals): 2, 3/2, 35/32
Optimal ET sequence: 4, 8d, 10, 12, 22, 34d, 48
Scales: jubilismic10, jubilismic12
Jubilee
Subgroup: 2.3.5.7.11
Comma list: 50/49, 99/98
Mapping: [⟨2 0 0 1 4], ⟨0 1 0 0 -2], ⟨0 0 1 1 2]]
POTE generators: ~3/2 = 703.4155, ~5/4 = 380.6973
Optimal ET sequence: 4, 8d, 10e, 12, 22, 34d, 48
Badness: 0.600 × 10-3
Festival
Subgroup: 2.3.5.7.11
Comma list: 45/44, 50/49
Mapping: [⟨2 0 0 1 -4], ⟨0 1 0 0 2], ⟨0 0 1 1 1]]
POTE generators: ~3/2 = 693.6257, ~5/4 = 371.2658
Optimal ET sequence: 10, 12, 22e, 26
Badness: 0.689 × 10-3
Fiesta
Subgroup: 2.3.5.7.11
Comma list: 50/49, 56/55
Mapping: [⟨2 0 0 1 7], ⟨0 1 0 0 0], ⟨0 0 1 1 0]]
POTE generators: ~3/2 = 713.5853, ~5/4 = 397.6952
Optimal ET sequence: 8d, 10, 12, 22e
Badness: 0.717 × 10-3
Jamboree
Subgroup: 2.3.5.7.11
Comma list: 50/49, 55/54
Mapping: [⟨2 0 0 1 2], ⟨0 1 0 0 3], ⟨0 0 1 1 -1]]
POTE generators: ~3/2 = 706.6559, ~5/4 = 376.8308
Optimal ET sequence: 8d, 10, 12e, 14c, 22
Badness: 0.781 × 10-3