68edo: Difference between revisions

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As a 7-limit system it tempers out [[2048/2025]], [[245/243]], 4000/3969, [[15625/15552]], [[3136/3125]], [[6144/6125]] and [[2401/2400]]. It [[support]]s [[octacot]], [[shrutar]], [[hemiwürschmidt]], [[hemikleismic]], [[clyde]] and [[neptune]] temperaments, and supplies the [[optimal patent val]] for 11-limit [[hemikleismic]]. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp.

The 3rd degree of 68edo can be used as a generator for [[23edo and octave stretching|stretched 23edo]]. It results in a 23edo scale with octaves stretched by 1 step of 68edo (octaves of 1217.65 cents). It ~~can~~ also ~~be thought of~~ as a ~~stretched version of~~ [[~~33/32 equal step tuning~~]].

The 3rd degree of 68edo can be used as a generator for [[23edo and octave stretching|stretched 23edo]], which also acts as the [[The Quartercache#Quartkeenlig|quartkeenlig]] temperament tempering out the quartisma, 385/384 and 6250/6237. It results in a 23edo scale with octaves stretched by 1 step of 68edo (octaves of 1217.65 cents). It also works as a [[22L 1s]] MOS of the quartkeenlig temperament.

=== Prime harmonics ===

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Superpyth: 12 12 4 12 12 12 4

~~Superpyth quarter octave: 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1~~

Flattone: 10 10 9 10 10 10 9

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Inverse half octave: 4 4 7 4 4 4 4 7 4 4 7 4 4 4 4 7

Superpyth quarter octave: 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1

=== Other ===

Quartkeenlig (Stretched 23edo): 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2

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

[[Category:Clyde]]

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 As a 7-limit system it tempers out [[2048/2025]], [[245/243]], 4000/3969, [[15625/15552]], [[3136/3125]], [[6144/6125]] and [[2401/2400]]. It [[support]]s [[octacot]], [[shrutar]], [[hemiwürschmidt]], [[hemikleismic]], [[clyde]] and [[neptune]] temperaments, and supplies the [[optimal patent val]] for 11-limit [[hemikleismic]]. It is a sharp-tending system, with the third, fifth and seventh harmonics all sharp.
-The 3rd degree of 68edo can be used as a generator for [[23edo and octave stretching|stretched 23edo]]. It results in a 23edo scale with octaves stretched by 1 step of 68edo (octaves of 1217.65 cents). It can also be thought of as a stretched version of [[33/32 equal step tuning]].
+The 3rd degree of 68edo can be used as a generator for [[23edo and octave stretching|stretched 23edo]], which also acts as the [[The Quartercache#Quartkeenlig|quartkeenlig]] temperament tempering out the quartisma, 385/384 and 6250/6237. It results in a 23edo scale with octaves stretched by 1 step of 68edo (octaves of 1217.65 cents). It also works as a [[22L 1s]] MOS of the quartkeenlig temperament.
 === Prime harmonics ===
@@ Line 354: / Line 354: @@
 Superpyth: 12 12 4 12 12 12 4
-Superpyth quarter octave: 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1
 Flattone: 10 10 9 10 10 10 9
@@ Line 363: / Line 361: @@
 Inverse half octave: 4 4 7 4 4 4 4 7 4 4 7 4 4 4 4 7
+Superpyth quarter octave: 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1 3 3 1 3 3 3 1
+=== Other ===
+Quartkeenlig (Stretched 23edo): 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 2
 [[Category:Equal divisions of the octave|##]] <!-- 2-digit number -->
 [[Category:Clyde]]