93edo: Difference between revisions

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~~The~~ 93 equal ~~division divides the octave into~~ 93 ~~equal parts of 12.903 cents each.~~ 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.

== Theory ==

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.

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

~~{{harmonics in equal|93}}~~

== Temperament properties ==

Since 93edo has a step of 12.903 ~~cents~~, it also allows one to use its MOS scales as circulating temperaments, which it is the first edo to do. It is also the first edo to allow one to use a syntonic or Mavila MOS scale or a 17 tone MOS scale similar to a median between [http://www.neuroscience-of-music.se/pelog_main.htm Pelog] and the theories of Sundanese composer-musicologist-teacher [http://en.wikipedia.org/wiki/Raden_Machjar_Angga_Koesoemadinata Raden Machjar Angga Koesoemadinata] as a circulating temperament.

Since 93edo has a step of 12.903{{cent}}, it also allows one to use its MOS scales as circulating temperaments, which it is the first edo to do. It is also the first edo to allow one to use a syntonic or Mavila MOS scale or a 17 tone MOS scale similar to a median between [http://www.neuroscience-of-music.se/pelog_main.htm Pelog] and the theories of Sundanese composer-musicologist-teacher [http://en.wikipedia.org/wiki/Raden_Machjar_Angga_Koesoemadinata Raden Machjar Angga Koesoemadinata] as a circulating temperament.

{| class="wikitable"

|+Circulating temperaments in 93edo

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|19L 55s

|}

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

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-The 93 equal division divides the octave into 93 equal parts of 12.903 cents each. 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.
+{{EDO intro|93}}
+== Theory ==
+{{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.
-Since 93edo has good approximations of 13th, 17th and 19th harmonics unlike 31edo (as 838.710¢, 103.226¢, and 296.774¢ respectively), it also allows one to give a clearer harmonic identity to [[31edo]]'s excellent approximation of 13:17:19.
-{{harmonics in equal|93}}
 == Temperament properties ==
-Since 93edo has a step of 12.903 cents, it also allows one to use its MOS scales as circulating temperaments, which it is the first edo to do. It is also the first edo to allow one to use a syntonic or Mavila MOS scale or a 17 tone MOS scale similar to a median between [http://www.neuroscience-of-music.se/pelog_main.htm Pelog] and the theories of Sundanese composer-musicologist-teacher [http://en.wikipedia.org/wiki/Raden_Machjar_Angga_Koesoemadinata Raden Machjar Angga Koesoemadinata] as a circulating temperament.
+Since 93edo has a step of 12.903{{cent}}, it also allows one to use its MOS scales as circulating temperaments, which it is the first edo to do. It is also the first edo to allow one to use a syntonic or Mavila MOS scale or a 17 tone MOS scale similar to a median between [http://www.neuroscience-of-music.se/pelog_main.htm Pelog] and the theories of Sundanese composer-musicologist-teacher [http://en.wikipedia.org/wiki/Raden_Machjar_Angga_Koesoemadinata Raden Machjar Angga Koesoemadinata] as a circulating temperament.
 {| class="wikitable"
 |+Circulating temperaments  in 93edo
@@ Line 236: / Line 240: @@
 |19L 55s
 |}
+[[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->