93edo: Difference between revisions

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== Theory ==

93 = 3 × 31, and 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[prajapati]] and 13-limit [[kumhar]] temperaments, and the 11- and 13-limit [[superpine]] (43 & 50) temperament. It is the 13th no-3s [[zeta peak edo]].

Since 93edo has good approximations of [[13/1|13th]], [[17/1|17th]] and [[19/1|19th]] [[harmonic]]s unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.

=== Odd harmonics ===

93 = 3 * 31, and 93 is a [[contorted]] 31 through the 7 limit. In the 11-limit the patent val tempers out 4000/3993 and in the 13-limit 144/143, 1188/1183 and 364/363. It provides the optimal patent val for the 11-limit prajapati and 13-limit kumhar temperaments, and the 11 and 13 limit 43&50 temperament. It is the 13th no-3s zeta peak edo.

Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.

== Intervals ==

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* 980.645

* 1200.000

~~== See Also ==~~

== See also ==

* [[93edo and stretched hemififths]]

~~[[Category:Equal divisions of the octave|##]] ~~

@@ Line 3: / Line 3: @@
 == Theory ==
+= 3 × 31, and 93edo is a [[contorted]] [[31edo]] through the [[7-limit]]. In the 11-limit the [[patent val]] [[tempering out|tempers out]] [[4000/3993]] and in the 13-limit [[144/143]], [[1188/1183]] and [[364/363]]. It provides the [[optimal patent val]] for the 11-limit [[prajapati]] and 13-limit [[kumhar]] temperaments, and the 11- and 13-limit [[superpine]] (43 &amp; 50) temperament. It is the 13th no-3s [[zeta peak edo]].
+Since 93edo has good approximations of [[13/1|13th]], [[17/1|17th]] and [[19/1|19th]] [[harmonic]]s unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.
+=== Odd harmonics ===
 {{Harmonics in equal|93}}
-= 3 * 31, and 93 is a [[contorted]] 31 through the 7 limit. In the 11-limit the patent val tempers out 4000/3993 and in the 13-limit 144/143, 1188/1183 and 364/363. It provides the optimal patent val for the 11-limit prajapati and 13-limit kumhar temperaments, and the 11 and 13 limit 43&amp;50 temperament. It is the 13th no-3s zeta peak edo.
-Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710{{cent}}, 103.226{{cent}}, and 296.774{{cent}} respectively, [[octave-reduced]]), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.
 == Intervals ==
@@ Line 69: / Line 71: @@
 * 980.645
 * 1200.000
-== See Also ==
+== See also ==
 * [[93edo and stretched hemififths]]
-[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->