Augene: Difference between revisions
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Cmloegcmluin (talk | contribs) →Spectrum of Augene Tunings by Eigenmonzos: improve and standardize tuning spectra tables |
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The first few augene MOSes are [[3L_3s|3L 3s]], [[3L_6s|3L 6s]], [[3L_9s|3L 9s]], [[12L_3s|12L 3s]]... and the first EDOs that reasonably support augene are [[12edo|12edo]], [[15edo|15edo]], and especially [[27edo|27edo]]. | The first few augene MOSes are [[3L_3s|3L 3s]], [[3L_6s|3L 6s]], [[3L_9s|3L 9s]], [[12L_3s|12L 3s]]... and the first EDOs that reasonably support augene are [[12edo|12edo]], [[15edo|15edo]], and especially [[27edo|27edo]]. | ||
= | == Tuning spectrum == | ||
{| class="wikitable" | {| class="wikitable center-all" | ||
|- | |- | ||
! | | ! | ET<br>generator | ||
! | | ! | [[eigenmonzo|eigenmonzo<br>(unchanged interval]]) | ||
! | fifth<br>(¢) | |||
! | comments | |||
|- | |- | ||
| | | |||
| | 14/13 | | | 14/13 | ||
| | 671.702 | | | 671.702 | ||
| | | |||
|- | |- | ||
| | 12\28 | | | 12\28 | ||
| | | |||
| | 685.714 | | | 685.714 | ||
| | | |||
|- | |- | ||
| | | |||
| | 16/15 | | | 16/15 | ||
| | 688.269 | | | 688.269 | ||
| | | |||
|- | |- | ||
| | | |||
| | 13/11 | | | 13/11 | ||
| | 689.210 | | | 689.210 | ||
| | | |||
|- | |- | ||
| | 7\12 | | | 7\12 | ||
| | | |||
| | 700.000 | | | 700.000 | ||
| | | |||
|- | |- | ||
| | 31\53 | | | 31\53 | ||
| | | |||
| | 701.887 | | | 701.887 | ||
| | | |||
|- | |- | ||
| | | |||
| | 4/3 | | | 4/3 | ||
| | 701.955 | | | 701.955 | ||
| | | |||
|- | |- | ||
| | 30\51 | | | 30\51 | ||
| | | |||
| | 705.882 | | | 705.882 | ||
| | | |||
|- | |- | ||
| | | |||
| | 15/14 | | | 15/14 | ||
| | 706.481 | | | 706.481 | ||
| | | |||
|- | |- | ||
| | 23\39 | | | 23\39 | ||
| | | |||
| | 707.692 | | | 707.692 | ||
| | | |||
|- | |- | ||
| | | |||
| | 7/5 | | | 7/5 | ||
| | 708.744 | | | 708.744 | ||
| | | |||
|- | |- | ||
| | | |||
| | 9/7 | | | 9/7 | ||
| | 708.771 | | | 708.771 | ||
| | | |||
|- | |- | ||
| | | |||
| | 10/9 | | | 10/9 | ||
| | 708.798 | | | 708.798 | ||
| | 9 limit minimax | |||
|- | |- | ||
| | 39\66 | | | 39\66 | ||
| | | |||
| | 709.091 | | | 709.091 | ||
| | | |||
|- | |- | ||
| | | |||
| | 7/6 | | | 7/6 | ||
| | 711.043 | | | 711.043 | ||
| | | |||
|- | |- | ||
| | 16\27 | | | 16\27 | ||
| | | |||
| | 711.111 | | | 711.111 | ||
| | | |||
|- | |- | ||
| | | |||
| | 15/11 | | | 15/11 | ||
| | 712.317 | | | 712.317 | ||
| | | |||
|- | |- | ||
| | 57\96 | | | 57\96 | ||
| | | |||
| | 712.5 | | | 712.5 | ||
| | | |||
|- | |- | ||
| | | |||
| | 11/9 | | | 11/9 | ||
| | 713.148 | | | 713.148 | ||
| | 11 limit minimax | |||
|- | |- | ||
| | 25\42 | | | 25\42 | ||
| | | |||
| | 714.286 | | | 714.286 | ||
| | | |||
|- | |- | ||
| | | |||
| | 8/7 | | | 8/7 | ||
| | 715.587 | | | 715.587 | ||
| | 7, 13 and 15 limit minimax | |||
|- | |- | ||
| | | |||
| | 6/5 | | | 6/5 | ||
| | 715.641 | | | 715.641 | ||
| | 5 limit minimax | |||
|- | |- | ||
| | 34\57 | | | 34\57 | ||
| | | |||
| | 715.789 | | | 715.789 | ||
| | | |||
|- | |- | ||
| | 25\72 | | | 25\72 | ||
| | | |||
| | 716.667 | | | 716.667 | ||
| | | |||
|- | |- | ||
| | | |||
| | 12/11 | | | 12/11 | ||
| | 716.879 | | | 716.879 | ||
| | | |||
|- | |- | ||
| | | |||
| | 11/10 | | | 11/10 | ||
| | 717.498 | | | 717.498 | ||
| | | |||
|- | |- | ||
| | 9\15 | | | 9\15 | ||
| | | |||
| | 720.000 | | | 720.000 | ||
| | | |||
|- | |- | ||
| | | |||
| | 18/13 | | | 18/13 | ||
| | 721.127 | | | 721.127 | ||
| | | |||
|- | |- | ||
| | | |||
| | 15/13 | | | 15/13 | ||
| | 723.871 | | | 723.871 | ||
| | | |||
|- | |- | ||
| | | |||
| | 11/8 | | | 11/8 | ||
| | 724.341 | | | 724.341 | ||
| | | |||
|- | |- | ||
| | | |||
| | 13/12 | | | 13/12 | ||
| | 730.714 | | | 730.714 | ||
| | | |||
|- | |- | ||
| | | |||
| | 13/10 | | | 13/10 | ||
| | 745.786 | | | 745.786 | ||
| | | |||
|- | |- | ||
| | | |||
| | 16/13 | | | 16/13 | ||
| | 759.472 | | | 759.472 | ||
| | | |||
|} | |} | ||
Revision as of 00:25, 30 September 2021
Augene is a regular temperament of the augmented family, which means that 128/125 is tempered out and three 5/4s make a 2/1. Augene is distinguished from its relative august by tempering out 64/63, which means that tunings in which the fifth is larger than 7\12 (700 cents) are optimal. Therefore the MOS sequence of augene goes 12, 15, 27... in constrast to august's which goes 9, 12, 21...
The first few augene MOSes are 3L 3s, 3L 6s, 3L 9s, 12L 3s... and the first EDOs that reasonably support augene are 12edo, 15edo, and especially 27edo.
Tuning spectrum
| ET generator |
eigenmonzo (unchanged interval) |
fifth (¢) |
comments |
|---|---|---|---|
| 14/13 | 671.702 | ||
| 12\28 | 685.714 | ||
| 16/15 | 688.269 | ||
| 13/11 | 689.210 | ||
| 7\12 | 700.000 | ||
| 31\53 | 701.887 | ||
| 4/3 | 701.955 | ||
| 30\51 | 705.882 | ||
| 15/14 | 706.481 | ||
| 23\39 | 707.692 | ||
| 7/5 | 708.744 | ||
| 9/7 | 708.771 | ||
| 10/9 | 708.798 | 9 limit minimax | |
| 39\66 | 709.091 | ||
| 7/6 | 711.043 | ||
| 16\27 | 711.111 | ||
| 15/11 | 712.317 | ||
| 57\96 | 712.5 | ||
| 11/9 | 713.148 | 11 limit minimax | |
| 25\42 | 714.286 | ||
| 8/7 | 715.587 | 7, 13 and 15 limit minimax | |
| 6/5 | 715.641 | 5 limit minimax | |
| 34\57 | 715.789 | ||
| 25\72 | 716.667 | ||
| 12/11 | 716.879 | ||
| 11/10 | 717.498 | ||
| 9\15 | 720.000 | ||
| 18/13 | 721.127 | ||
| 15/13 | 723.871 | ||
| 11/8 | 724.341 | ||
| 13/12 | 730.714 | ||
| 13/10 | 745.786 | ||
| 16/13 | 759.472 |
Music
Sad Like Winter Leaves by Igliashon Jones in Augene[12] tuned to 27edo
Galticeran Sonatina by Joel Grant Taylor in Augene[12] tuned to 27edo