Augene
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
Gencom: [2 7/6; 99/98 121/120 176/175 275/273]
Gencom map: [<1 0 3 1 3 8|, <0 7 -3 8 2 -19|]
| ET generator |
eigenmonzo (unchanged interval) |
subminor third (¢) |
comments |
|---|---|---|---|
| 7/6 | 266.871 | ||
| 15/11 | 268.475 | ||
| 14/11 | 269.585 | ||
| 12/11 | 270.127 | ||
| 15/14 | 270.139 | ||
| 7\31 | 270.968 | ||
| 11/9 | 271.049 | ||
| 8/7 | 271.103 | ||
| 7/5 | 271.137 | ||
| 5/4 | 271.229 | ||
| 1361367/1000000 | 271.326 | 7 limit least squares | |
| 14/13 | 271.418 | 13 and 15 limit minimax | |
| 19\84 | 271.429 | ||
| [0 119 -46 20 -16⟩ | 271.445 | 11 limit least squares | |
| [math]\displaystyle{ x^{10} + 2x^3 = 8 }[/math] | 271.508 | equal beating | |
| 16/13 | 271.551 | ||
| [0 90 -41 14⟩ | 271.561 | 9 limit least squares | |
| 6/5 | 271.564 | 5 limit minimax | |
| [0 -211 30 -47 -5 142⟩ | 271.567 | 13 limit least squares | |
| [0 -236 5 -51 -3 165⟩ | 271.570 | 15 limit least squares | |
| 1220703125/1033121304 | 271.590 | 5 limit least squares | |
| 13/12 | 271.593 | ||
| 13/10 | 271.612 | ||
| 18/13 | 271.618 | ||
| 10/9 | 271.623 | 9 limit minimax | |
| 15/13 | 271.641 | ||
| 12\53 | 271.698 | ||
| 4/3 | 271.708 | ||
| 13/11 | 271.942 | ||
| 16/15 | 272.067 | ||
| 9/7 | 272.514 | ||
| 5\22 | 272.727 | ||
| 11/10 | 273.001 | ||
| 11/8 | 275.659 |
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