Bird's eye view of temperaments by accuracy: Difference between revisions
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== 7-limit focus == | == 7-limit focus == | ||
== 11-limit focus == | == 11-limit focus == | ||
=== [[Mohaha]] === | |||
Note counts: | |||
* 9 for {3, 5, 9, 11(, 33, 35)} ([[7L 3s]], note odd 35 comes from the [[mohajira]] specifically) | |||
* 20 for adding {7, 15, 21(, 35} ([[7L 10s]] and [[7L 17s]]) | |||
Mohaha is a 2.3.5.11 (no-7's [[11-limit]]) "hemi-meantone" temperament that splits [[#Meantone]]'s fifth into two [[~]][[11/9]]'s by tempering [[243/242|S9/S11 = (12/8)/(11/9)<sup>2</sup> = (3/2)/(11/9)<sup>2</sup>]], which as [[81/80|S9 = (9/8)/(10/9)]] is tempered implies tempering [[121/120|S11 = (11/10)/(12/11) = (11/8)/(15/11)]] as well. It has two main extensions to the full 11-limit; if you accept the [[#Septimal meantone]] mapping of 7 you get [[migration]], but maybe more natural is if you instead equate the flat [[~]][[33/32]] interval with S6 = [[36/35]] = ([[6/5]])/([[7/6]]), which results in [[mohajira]], which finds 7 at a negative number of gens so that composite harmonics of 7 are simpler to find (as primes 3, 5 and 11 are all found at a positive number of gens). | |||
== ~17-limit focus == | == ~17-limit focus == | ||
== Higher-limit focus == | == Higher-limit focus == | ||