Bird's eye view of temperaments by accuracy: Difference between revisions
m →5-limit focus: add srutal archagall |
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== 7-limit focus == | == 7-limit focus == | ||
== 11-limit focus == | == 11-limit focus == | ||
=== [[Miracle]] === | |||
Note count: 23 for {3, 5, 7, 9, 11, 15, 21} ([[10L 11s]] or [[10L 21s]]) | |||
Subgroup: 2.3.5.7.11 | |||
Miracle is an elegant temperament that splits [[3/2]] into six equal parts that can be derived as the most natural and efficient way of doing so through [[S-expression]]s by splitting 3/2 into two by tempering [[243/242|S9/S11 = (12/8)/(11/9)<sup>2</sup> = (3/2)/(11/9)<sup>2</sup>]], splitting 3/2 into three by tempering [[1029/1024|S7/S8 = (9/6)/(8/7)<sup>3</sup> = (3/2)/(8/7)<sup>3</sup>]] and then splitting the [[~]][[8/7]] in two by tempering [[225/224|S15 = (15/14)/(16/15)]] so that [[15/14]] and [[16/15]] are equated. [[72edo]] is a very good tuning of miracle, though [[31edo]] and [[41edo]] may be preferred for smaller note counts and for the various things they support, EG [[meantone]] for 31edo and [[garibaldi]] for 41edo. | |||
== ~17-limit focus == | == ~17-limit focus == | ||
== Higher-limit focus == | == Higher-limit focus == | ||