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. | ||
[[Comma]]: 50/49 | = Jubilismic = | ||
[[Comma list]]: 50/49 | |||
7 and 9 limit | Minimax tuning: | ||
* 7- and 9-odd-limit | |||
: [{{monzo| 1 0 0 0 }}, {{monzo| 0 1 0 0 }}, {{monzo| -1/4 0 1/2 1/2 }}, {{monzo| 1/4 0 1/2 1/2 }}] | |||
: [[Eigenmonzo]]s: 2, 3/2, 35/32 | |||
[| | [[Mapping]]: [{{val| 2 0 0 1 }}, {{val| 0 1 0 0 }}, {{val| 0 0 1 1 }}] | ||
[[ | Mapping [[generator]]s: ~7/5, ~3, ~5 | ||
{{Val list|legend=1| 10, 12, 22, 26, 38, 48 }} | |||
[[ | Scales: [[jubilismic10]], [[jubilismic12]] | ||
= Jubilee = | |||
Comma list: 50/49, 99/98 | |||
Mapping: [{{val| 2 0 0 1 4 }}, {{val| 0 1 0 0 -2 }}, {{val| 0 0 1 1 2 }}] | |||
= | {{Val list|legend=1| 12, 22, 48 }} | ||
Badness: 0.600 × 10<sup>-3</sup> | |||
= Festival = | |||
Comma list: 50/49, 45/44 | |||
Mapping: [{{val| 2 0 0 1 -4 }}, {{val| 0 1 0 0 2 }}, {{val| 0 0 1 1 1 }}] | |||
= | {{Val list|legend=1| 10, 12, 26 }} | ||
Badness: 0.689 × 10<sup>-3</sup> | |||
= Fiesta = | |||
Comma list: 50/49, 56/55 | |||
Mapping: [{{val| 2 0 0 1 7 }}, {{val| 0 1 0 0 0 }}, {{val| 0 0 1 1 0 }}] | |||
= | {{Val list|legend=1| 10, 12 }} | ||
Badness: 0.717 × 10<sup>-3</sup> | |||
= Jamboree = | |||
Comma list: 50/49, 55/54 | |||
Mapping: [{{val| 2 0 0 1 2 }}, {{val| 0 1 0 0 3 }}, {{val| 0 0 1 1 -1 }}] | |||
= | {{Val list|legend=1| 10, 22 }} | ||
Badness: 0.781 × 10<sup>-3</sup> | |||
Badness: 0. | |||
[[Category:Theory]] | [[Category:Theory]] | ||
[[Category:Temperament family]] | [[Category:Temperament family]] | ||
[[Category:Jubilismic]] | [[Category:Jubilismic]] | ||
[[Category:Rank 3]] | |||
{{todo| improve readability }} | |||
Revision as of 03:37, 17 March 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
Comma list: 50/49
Minimax tuning:
- 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
Mapping: [⟨2 0 0 1], ⟨0 1 0 0], ⟨0 0 1 1]]
Mapping generators: ~7/5, ~3, ~5
Scales: jubilismic10, jubilismic12
Jubilee
Comma list: 50/49, 99/98
Mapping: [⟨2 0 0 1 4], ⟨0 1 0 0 -2], ⟨0 0 1 1 2]]
Badness: 0.600 × 10-3
Festival
Comma list: 50/49, 45/44
Mapping: [⟨2 0 0 1 -4], ⟨0 1 0 0 2], ⟨0 0 1 1 1]]
Badness: 0.689 × 10-3
Fiesta
Comma list: 50/49, 56/55
Mapping: [⟨2 0 0 1 7], ⟨0 1 0 0 0], ⟨0 0 1 1 0]]
Badness: 0.717 × 10-3
Jamboree
Comma list: 50/49, 55/54
Mapping: [⟨2 0 0 1 2], ⟨0 1 0 0 3], ⟨0 0 1 1 -1]]
Badness: 0.781 × 10-3