21edo: Difference between revisions
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==Moment-of-Symmetry Scales== | ==Moment-of-Symmetry Scales== | ||
Since 21-EDO contains sub-EDOs of 3 and 7, it contains no heptatonic MOS scales (other than 7-EDO) and a wealth of scales that repeat at a 1/3-octave period. | Since 21-EDO contains sub-EDOs of 3 and 7, it contains no heptatonic MOS scales (other than 7-EDO) and a wealth of scales that repeat at a 1/3-octave period. | ||
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For scales with a full-octave period, only 6 degrees of 21-EDO generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7-EDO, 3-EDO, or a repetition of one of the other scales. | For scales with a full-octave period, only 6 degrees of 21-EDO generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7-EDO, 3-EDO, or a repetition of one of the other scales. | ||
21edo has the [[oneirotonic]] (5L 3s) MOS with generator 8\21; it is notable for approximating 9:10:11:13 and 16:23:30. | 21edo has the [[oneirotonic]] (5L 3s) MOS with generator 8\21; it is notable for approximating 9:10:11:13 and 16:23:30. | ||
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! | Periods per octave | ! | Periods per octave | ||
! | Generator | ! | Generator | ||
! | | ! | MOSes | ||
|- | |- | ||
| | 1 | | | 1 | ||