359edo: Difference between revisions

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'''~~359EDO~~''' is the [[EDO|equal division of the octave]] into 359 parts of 3.34262 [[cent]]s each.

The '''359 equal divisions of the octave''' ('''359edo''') is the [[EDO|equal division of the octave]] into 359 parts of 3.34262 [[cent]]s each.

=~~359 tone equal temperament~~=

== Theory ==

~~359EDO~~ contains a very close approximation of the pure 3/2 fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. ~~359EDO~~ supports a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in ~~359EDO~~ this is the step 203\359 of 678.55153¢.

359edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. It provides the [[optimal patent val]] for the 11-limit [[hera]] temperament.

359edo supports a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in 359edo this is the step 203\359 of 678.55153¢.

Pythagorean diatonic scale: 61 61 27 61 61 61 27

Exaggerated Hornbostel superdiatonic scale: 47 47 47 15 47 47 47 47 15 (fails in the position of Phi and the square root of Pi [+1\359 step of each one]).

Exaggerated Hornbostel superdiatonic scale: 47 47 47 15 47 47 47 47 15 (fails in the position of Phi and the square root of Pi [+1\359 step of each one]{{clarify}}).

359edo is the 72nd [[prime EDO]].

~~359EDO is the 72nd [[prime EDO]].~~

=== Prime harmonics ===

[[Category:Equal divisions of the octave]]

[[Category:Prime EDO]]

[[Category:~~nano]]~~

[[Category:Hera]]

~~[[Category:theory~~]]

@@ Line 1: / Line 1: @@
-'''359EDO''' is the [[EDO|equal division of the octave]] into 359 parts of 3.34262 [[cent]]s each.
+The '''359 equal divisions of the octave''' ('''359edo''') is the [[EDO|equal division of the octave]] into 359 parts of 3.34262 [[cent]]s each.
-=359 tone equal temperament=
+== Theory ==
-EDO contains a very close approximation of the pure 3/2 fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. 359EDO supports a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in 359EDO this is the step 203\359 of 678.55153¢.
+edo contains a very close approximation of the pure [[3/2]] fifth of 701.955 cents, with the 210\359 step of 701.94986 cents. It provides the [[optimal patent val]] for the 11-limit [[hera]] temperament.
+edo supports a type of exaggerated Hornbostel mode, with an approximation of the blown fifth that he described of the pan flutes of some regions of South America; the Pythagorean fifth (701.955¢) minus the Pythagorean comma (23.46¢) = 678.495¢; in 359edo this is the step 203\359 of 678.55153¢.
 Pythagorean diatonic scale: 61 61 27 61 61 61 27
-Exaggerated Hornbostel superdiatonic scale: 47 47 47 15 47 47 47 47 15 (fails in the position of Phi and the square root of Pi [+1\359 step of each one]).
+Exaggerated Hornbostel superdiatonic scale: 47 47 47 15 47 47 47 47 15 (fails in the position of Phi and the square root of Pi [+1\359 step of each one]{{clarify}}).
+edo is the 72nd [[prime EDO]].
-EDO is the 72nd [[prime EDO]].
+=== Prime harmonics ===
+{{Primes in edo|359}}
 [[Category:Equal divisions of the octave]]
 [[Category:Prime EDO]]
-[[Category:nano]]
+[[Category:Hera]]
-[[Category:theory]]