21edo: Difference between revisions

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Inthar (talk | contribs)
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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.
Examples:
*[[augment6]]
*[[augment9]]
*[[augment12]]


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
! | Temperaments
! | MOSes
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| | 1
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