Jubilismic family: Difference between revisions
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The '''jubilismic family''' contains temperaments that temper out the [[jubilisma|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. | The '''jubilismic family''' contains temperaments that temper out the [[jubilisma|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 = | == Jubilismic == | ||
Subgroup: 2.3.5.7 | Subgroup: 2.3.5.7 | ||
| Line 22: | Line 22: | ||
Scales: [[jubilismic10]], [[jubilismic12]] | Scales: [[jubilismic10]], [[jubilismic12]] | ||
= Jubilee = | == Jubilee == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 36: | Line 36: | ||
[[Badness]]: 0.600 × 10<sup>-3</sup> | [[Badness]]: 0.600 × 10<sup>-3</sup> | ||
= Festival = | == Festival == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 50: | Line 50: | ||
[[Badness]]: 0.689 × 10<sup>-3</sup> | [[Badness]]: 0.689 × 10<sup>-3</sup> | ||
= Fiesta = | == Fiesta == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
| Line 64: | Line 64: | ||
[[Badness]]: 0.717 × 10<sup>-3</sup> | [[Badness]]: 0.717 × 10<sup>-3</sup> | ||
= Jamboree = | == Jamboree == | ||
Subgroup: 2.3.5.7.11 | Subgroup: 2.3.5.7.11 | ||
Revision as of 15:09, 31 May 2021
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: 2, 3/2, 35/32
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
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
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
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
Badness: 0.781 × 10-3