33edo: Difference between revisions
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{{Infobox ET | |||
| Prime factorization = 3 x 11 | |||
| Step size = 36.364¢ | |||
| Fifth = 19\33 = 690.909 | |||
| Major 2nd = 5\33 = 181.818¢ | |||
| Minor 2nd = 4\33 = 145.455¢ | |||
| Augmented 1sn = 1\33 = 36.364¢ | |||
}} | |||
'''33edo''' divides the [[octave]] into 33 equal parts of 36.3636 [[cent]]s each. It is not especially good at representing all rational intervals in the [[7-limit]], but it does very well on the 7-limit [[k*N_subgroups|3*33 subgroup]] 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as [[99edo]], and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the [[Chromatic_pairs#Terrain|terrain]] subgroup temperament can be tuned via the 5\33 generator. The full system of harmony provides the optimal patent val for [[Mint_temperaments#Slurpee|slurpee temperament]] in the 5, 7, 11 and 13 limits. | '''33edo''' divides the [[octave]] into 33 equal parts of 36.3636 [[cent]]s each. It is not especially good at representing all rational intervals in the [[7-limit]], but it does very well on the 7-limit [[k*N_subgroups|3*33 subgroup]] 2.27.15.21.11.13. On this subgroup it tunes things to the same tuning as [[99edo]], and as a subgroup patent val it tempers out the same commas. The 99 equal temperaments hemififths, amity, parakleismic, hemiwuerschmidt, ennealimmal and hendecatonic can be reduced to this subgroup and give various possibilities for MOS scales, etc. In particular, the [[Chromatic_pairs#Terrain|terrain]] subgroup temperament can be tuned via the 5\33 generator. The full system of harmony provides the optimal patent val for [[Mint_temperaments#Slurpee|slurpee temperament]] in the 5, 7, 11 and 13 limits. | ||