Bird's eye view of temperaments by accuracy: Difference between revisions
→Orwell: made wording a bit better |
m →11-limit focus: fixed formatting |
||
| Line 166: | Line 166: | ||
[[#Generator tunings|Generator tunings]]: 3\31, 4\41, 7\72 | [[#Generator tunings|Generator tunings]]: 3\31, 4\41, 7\72 | ||
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 out {{nowrap| [[243/242|S9/S11 {{=}} (12/8)/(11/9)<sup>2</sup> {{=}} (3/2)/(11/9)<sup>2</sup> }} | 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 out {{nowrap| [[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 out [[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 out [[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 == | ||