Miscellaneous 7-limit temperaments: Difference between revisions
→Avicennmic: note about some possible extensions |
→Greenwoodmic: note det chord and 11-limit extension |
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== Greenwoodmic == | == Greenwoodmic == | ||
Greenwoodmic tempers out the [[greenwoodma]] in the 7-limit. It equates [[5/2]] with a stack of two [[14/9]]'s. This implies [[prime interval|primes]] [[3/1|3]] and [[5/1|5]] should be tuned flat, and [[7/1|7]] should be tuned sharp. A rank-2 temperament that does that is [[injera]], which introduces little extra [[damage]] over greenwoodmic. | Greenwoodmic tempers out the [[greenwoodma]] in the 7-limit. It equates [[5/2]] with a stack of two [[14/9]]'s. This implies [[prime interval|primes]] [[3/1|3]] and [[5/1|5]] should be tuned flat, and [[7/1|7]] should be tuned sharp. A rank-2 temperament that does that is [[injera]], which introduces little extra [[damage]] over greenwoodmic. | ||
In contrast to [[sensamagic]], where two [[9/7]]'s stack to [[5/3]], here two 9/7's stack to [[8/5]]. As such, greenwoodmic induces [[essentially tempered chord]]s in the [[9-odd-limit]]. An obvious 11-limit extension then equates [[5/4]] with [[11/9]] and equates 9/7 with [[14/11]], tempering out [[45/44]] as well as [[99/98]] using the identity 405/392 = (45/44)⋅(99/98). | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||