Diaslen: Difference between revisions
No edit summary |
|||
| Line 30: | Line 30: | ||
|} | |} | ||
== Tunings and interpretations == | == Tunings and interpretations == | ||
=== Untempered 2.3.7 === | |||
The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]]. | The standard untempered 2.3.7 interpretation for diamech has L = [[9/8]], m = [[49/48]], s = [[64/63]]. | ||
=== Huntmic (2.3.7.13/5[640/637]) === | |||
[[Huntmic]] is a particularly elegant temperament for diamech. Assuming the 2.3.7 interpretation above and the constraint m:s = 2:1 makes L + m = 147/128 exactly half of 2L + m + 2s = 4/3, making it natural to set 147/128 equal to 15/13, tempering out [[640/637]]. [[53edo]] (9:2:1) and [[58edo]] (10:2:1) offer particularly good tunings for this interpretation; while the 58edo tuning's s step is smaller than that of the 53edo tuning, the former tuning has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15. | |||
[[Category:Rank-3 scales]] | [[Category:Rank-3 scales]] | ||
[[Category:Aberrismic theory]] | [[Category:Aberrismic theory]] | ||