73edo: Difference between revisions

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== Theory ==

73edo has a very sharp tendency, with the approximations of [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] and [[262144/253125]] in the [[5-limit]]; [[126/125]] and [[245/243]] in the [[7-limit]]; [[176/175]], [[441/440]] and [[4000/3993]] in the [[11-limit]]; [[91/90]], [[169/168]], [[196/195]], [[325/324]], [[351/350]], and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[marrakesh]] temperament, though [[104edo]] and [[135edo]] ~~tunes~~ it better.

73edo has a very sharp tendency, with the approximations of [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] and [[262144/253125]] in the [[5-limit]]; [[126/125]] and [[245/243]] in the [[7-limit]]; [[176/175]], [[441/440]] and [[4000/3993]] in the [[11-limit]]; [[91/90]], [[169/168]], [[196/195]], [[325/324]], [[351/350]], and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[marrakesh]] temperament, though [[104edo]] and [[135edo]] tune it better.

73edo can be used as a tuning of [[trismegistus]] or [[mavila]], by the 9:5 relation in the [[7L 2s|superdiatonic]] scheme, though neither of these use the most accurate 3/2. It is also notable for supporting the 2.3.5.7.13 version of [[sensi]] entirely by patent val.

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; [[Bryan Deister]]

* [https://www.youtube.com/shorts/meZYE1Yj2pY ''microtonal improvisation in 73edo''] (2025)

* ''Waltz in 73edo'' (2026)

** [https://www.youtube.com/shorts/sRZEJVBuDl0 ''<nowiki>[short]</nowiki>''] (Lumatone view)

** [https://www.youtube.com/watch?v=Z-3a5LJlul8 ''<nowiki>[full version]</nowiki>'']

; [[Claudi Meneghin]]

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 == Theory ==
-edo has a very sharp tendency, with the approximations of [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] and [[262144/253125]] in the [[5-limit]]; [[126/125]] and [[245/243]] in the [[7-limit]]; [[176/175]], [[441/440]] and [[4000/3993]] in the [[11-limit]]; [[91/90]], [[169/168]], [[196/195]], [[325/324]], [[351/350]], and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[marrakesh]] temperament, though [[104edo]] and [[135edo]] tunes it better.
+edo has a very sharp tendency, with the approximations of [[3/1|3]], [[5/1|5]], [[7/1|7]], [[11/1|11]] all sharp. The equal temperament [[tempering out|tempers out]] [[78732/78125]] and [[262144/253125]] in the [[5-limit]]; [[126/125]] and [[245/243]] in the [[7-limit]]; [[176/175]], [[441/440]] and [[4000/3993]] in the [[11-limit]]; [[91/90]], [[169/168]], [[196/195]], [[325/324]], [[351/350]], and [[352/351]] in the [[13-limit]]. It provides the [[optimal patent val]] for the [[marrakesh]] temperament, though [[104edo]] and [[135edo]] tune it better.
 edo can be used as a tuning of [[trismegistus]] or [[mavila]], by the 9:5 relation in the [[7L 2s|superdiatonic]] scheme, though neither of these use the most accurate 3/2. It is also notable for supporting the 2.3.5.7.13 version of [[sensi]] entirely by patent val.
@@ Line 57: / Line 57: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/shorts/meZYE1Yj2pY ''microtonal improvisation in 73edo''] (2025)
+* ''Waltz in 73edo'' (2026)
+** [https://www.youtube.com/shorts/sRZEJVBuDl0 ''<nowiki>[short]</nowiki>''] (Lumatone view)
+** [https://www.youtube.com/watch?v=Z-3a5LJlul8 ''<nowiki>[full version]</nowiki>'']
 ; [[Claudi Meneghin]]