Augene: Difference between revisions
Jump to navigation
Jump to search
Cmloegcmluin (talk | contribs) unchanged interval → unchanged-interval |
Fix typo MOS sequence -> optimal ET sequence. Add link. |
||
| Line 1: | Line 1: | ||
Augene is a regular temperament of the [[Augmented_family#x-Augene|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|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 | Augene is a regular temperament of the [[Augmented_family#x-Augene|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|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 [[optimal ET 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 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]]. | ||
Revision as of 09:31, 13 May 2024
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 optimal ET 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.
11-limit interval chain
| Gen. | Period 1 | Period 2 | Period 3 (0) |
|---|---|---|---|
| 0 | 400.000 | 800.000 | 1200.000 |
| 1 | 313.148 | 713.148 | 1113.148 |
| 2 | 226.296 | 626.296 | 1026.296 |
| 3 | 139.444 | 539.444 | 939.444 |
| 4 | 52.592 | 452.592 | 852.592 |
| 5 | 1165.740 | 365.740 | 765.740 |
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