68edo: Difference between revisions
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Wikispaces>xenwolf **Imported revision 602894314 - Original comment: Reverted to Sep 17, 2016 10:36 am: reverted last (destructive) change** |
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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. | 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. | ||
Diatonic scales: | Diatonic scales: | ||
Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5) | Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5) | ||
Superpyth: 12 12 4 12 12 12 4 | Superpyth: 12 12 4 12 12 12 4 | ||
Flattone: 10 10 9 10 10 10 9 | Flattone: 10 10 9 10 10 10 9 | ||
Inverse: 8 8 14 8 8 8 14 | |||
Inverse: 8 8 14 8 8 8 14 | |||
[[Category:clyde]] | |||
[[Category:edo]] | |||
[[Category:hemikleismic]] | |||
[[Category:hemiwuerschmidt]] | |||
[[Category:neptune]] | |||
[[Category:octacot]] | |||
[[Category:shrutar]] | |||
Revision as of 00:00, 17 July 2018
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, 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 consistently.
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.
Diatonic scales:
Negative semitone: 14 14 -1 14 14 14 -1 (E is sharper than F, and B is sharper than C5)
Superpyth: 12 12 4 12 12 12 4
Flattone: 10 10 9 10 10 10 9
Inverse: 8 8 14 8 8 8 14