Miscellaneous 7-limit temperaments: Difference between revisions
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== Avicennmic == | == Avicennmic == | ||
Avicennmic tempers out the [[avicennma]] in the 7-limit. It equates [[32/21]] with a stack of two [[5/4]]'s, and [[12/7]] with a stack of two [[15/8]]'s octave reduced. This implies [[prime interval|primes]] [[3/1|3]], [[5/1|5]] and [[7/1|7]] should all be tuned flat. A rank-2 temperament that does that is [[flattone]], which introduces little extra [[damage]] over avicennmic. | Avicennmic tempers out the [[avicennma]] in the 7-limit. It equates [[32/21]] with a stack of two [[5/4]]'s, and [[12/7]] with a stack of two [[15/8]]'s octave reduced. This implies [[prime interval|primes]] [[3/1|3]], [[5/1|5]] and [[7/1|7]] should all be tuned flat. A rank-2 temperament that does that is [[flattone]], which introduces little extra [[damage]] over avicennmic. | ||
One possible extension of avicennmic to the 11-limit is via [[45/44]] and [[385/384]], using the identity 525/512 = (45/44)⋅(385/384), but the result is somewhat less accurate. Instead, it is more natural to extend it to the [[2.3.5.7.13 subgroup]] by tempering out [[65/64]] and [[105/104]], using the identity 525/512 = (65/64)⋅(105/104). | |||
[[Subgroup]]: 2.3.5.7 | [[Subgroup]]: 2.3.5.7 | ||