21edo: Difference between revisions
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Since 21edo contains sub-edos of 3 and 7, it contains no heptatonic [[MOS scale]]s (other than 7edo and a few very [[Step ratio|hard]] scales) and a wealth of scales that repeat at a 1/3-octave period. | Since 21edo contains sub-edos of 3 and 7, it contains no heptatonic [[MOS scale]]s (other than 7edo and a few very [[Step ratio|hard]] scales) and a wealth of scales that repeat at a 1/3-octave period. | ||
For 7-limit harmony (based on a chord of 0-7-12-17 approximating 4:5:6:7), using 1/3-octave period scales (i.e. those related to augmented temperament) yields the most harmonically-efficient scales. The 9-tone [[3L 6s]] scale (related to Tcherepnin's scale in [[12edo]]) is an excellent example. | For 7-limit harmony (based on a chord of 0-7-12-17 approximating 4:5:6:7), using 1/3-octave period scales (i.e. those related to [[augmented (temperament)|augmented]] temperament) yields the most harmonically-efficient scales. The 9-tone [[3L 6s]] scale (related to Tcherepnin's scale in [[12edo]]) is an excellent example. | ||
For scales with a full-octave period, only 6 degrees of 21edo generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7edo, 3edo, or a repetition of one of the other scales. | For scales with a full-octave period, only 6 degrees of 21edo generate unique scales: 1\21, 2\21, 4\21, 5\21, 8\21, and 10\21. Other degrees generate either 7edo, 3edo, or a repetition of one of the other scales. | ||
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| 3 | | 3 | ||
| 1\21 | | 1\21 | ||
| [[ | | [[Hemiug]] | ||
|- | |- | ||
| 3 | | 3 | ||
| 2\21 | | 2\21 | ||
| [[Augmented]] / [[august]] | | [[Augmented (temperament)|Augmented]] / [[august]] | ||
|- | |- | ||
| 3 | | 3 | ||