68edo: Difference between revisions

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68edo's step is half of the step size of [[34edo]], which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of [[17edo]], which does well in the [[3-limit]], but not so well in the [[5-limit]]. The luck continues: 68 is a strong [[7-limit]] system, but does not do as well for in [[11-limit]]; though it's certainly usable for that purpose, it does not represent the 11-limit diamond [[consistent]]ly.

As a 7-limit system it tempers out [[Diaschisma|2048/2025]], [[245/243]], 4000/3969, [[15625/15552]], [[3136/3125]], [[6144/6125]] and [[2401/2400]]. It ~~supports~~ [[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.

As a 7-limit system it tempers out [[Diaschisma|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).

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 edo's step is half of the step size of [[34edo]], which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of [[17edo]], which does well in the [[3-limit]], but not so well in the [[5-limit]]. The luck continues: 68 is a strong [[7-limit]] system, but does not do as well for in [[11-limit]]; though it's certainly usable for that purpose, it does not represent the 11-limit diamond [[consistent]]ly.
-As a 7-limit system it tempers out [[Diaschisma|2048/2025]], [[245/243]], 4000/3969, [[15625/15552]], [[3136/3125]], [[6144/6125]] and [[2401/2400]]. It supports [[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.
+As a 7-limit system it tempers out [[Diaschisma|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).