68edo: Difference between revisions

The '''68 equal temperament''', often abbreviated '''68-tET''', '''68-EDO''', or '''68-ET''', is the scale derived by dividing the octave into 68 equally-sized steps. Each step represents a frequency ratio of 17.65 cents; this is half of the step size of [[34edo|34edo]], which does well in the 5-limit but not so well in the 7-limit, and one quarter the size of [[17edo|17edo]], which does well in the [[3-limit|3-limit]], but not so well in the [[5-limit|5-limit]]. The luck continues: 68 is a strong [[7-limit|7-limit]] system, but does not do as well for in [[11-limit|11-limit]]; though it's certainly usable for that purpose, it does not represent the 11-limit diamond [[consistent|consistent]]ly.

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

[[Category:clyde]]

[[Category:hemikleismic]]

[[Category:hemiwuerschmidt]]

[[Category:neptune]]

[[Category:octacot]]

[[Category:shrutar]]