Bird's eye view of temperaments by accuracy: Difference between revisions
m add generator tunings for garibaldi |
m add generator tunings for miracle |
||
| Line 143: | Line 143: | ||
=== [[Miracle]] === | === [[Miracle]] === | ||
Note count: 23 for {3, 5, 7, 9, 11, 15, 21} ([[10L 11s]] or [[10L 21s]]) | Note count: 23 for {3, 5, 7, 9, 11, 15, 21} ([[10L 11s]] or [[10L 21s]]) | ||
[[#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 [[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. | 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 [[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. | ||