Augene

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Augene is a regular temperament of the augmented family, which means that 128/125 is tempered out and three 5/4's 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 mos scales are 3L 3s, 3L 6s, 3L 9s, 12L 3s, … and the first edos that reasonably support augene are 12edo, 15edo, and especially 27edo.

Interval chain

In the following table, odd harmonics 1–11 are in bold.

# Period 0 Period 1 Period 2
Cents* Approx. Ratios Cents* Approx. Ratios Cents* Approx. Ratios
0 0.0 1/1 400.0 5/4, 14/11 800.0 8/5, 11/7
1 1113.1 15/8, 40/21 313.1 6/5 713.1 3/2
2 1026.3 9/5, 20/11 226.3 8/7, 9/8 626.3 10/7, 16/11
3 939.4 12/7 139.4 12/11, 15/14 539.4 15/11
4 852.6 18/11 52.6 45/44 452.6 9/7
5 765.7 54/35 1165.7 27/14, 96/49 365.7 27/22

* in 11-odd-limit minimax tuning

Tuning spectrum

Edo
Generator
Eigenmonzo
(Unchanged-interval)
*
Fifth (¢) Comments
13/7 671.702
15/8 688.269
13/11 689.210
7\12 700.000
3/2 701.955
30\51 705.882
15/14 706.481
23\39 707.692
7/5 708.744
9/7 708.771
9/5 708.798 9-odd-limit minimax
39\66 709.091
7/6 711.043
16\27 711.111
15/11 712.317
57\96 712.500
11/9 713.148 11-odd-limit minimax
25\42 714.286
7/4 715.587 7-, 13- and 15-odd-limit minimax
5/3 715.641 5-odd-limit minimax
34\57 715.789
25\72 716.667
11/6 716.879
11/10 717.498
9\15 720.000
13/9 721.127
15/13 723.871
11/8 724.341
13/12 730.714
13/10 745.786
13/8 759.472

* besides the octave

Music

Igliashon Jones
Joel Grant Taylor