68edo: Difference between revisions

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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.

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)

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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.
+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)