Diaslen: Difference between revisions

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The standard untempered 2.3.7 interpretation for diaslen has L = [[9/8]], m = [[49/48]], s = [[64/63]].

=== ~~Huntmic~~ (2.3.7.13/5[640/637, 676/675]) ===

=== Buzzard (2.3.7.13/5[640/637, 676/675]) ===

[[~~Huntmic~~]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. 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]] and [[676/675]]. [[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, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

[[Buzzard]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. 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]] and [[676/675]]. [[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, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.

== External links ==

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 The standard untempered 2.3.7 interpretation for diaslen has L = [[9/8]], m = [[49/48]], s = [[64/63]].
-=== Huntmic (2.3.7.13/5[640/637, 676/675]) ===
+=== Buzzard (2.3.7.13/5[640/637, 676/675]) ===
-[[Huntmic]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. 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]] and [[676/675]]. [[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, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.
+[[Buzzard]] is an important temperament for diaslen offering an elegant combination of interordinals and making 7/4 sharper in systems exaggerating [[49/48]] and splitting it into two equal parts. 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]] and [[676/675]]. [[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, 58edo has better 7/6, 9/7, 15/13, and 13/10 as well as giving you a free 11:13:15.
 == External links ==