Augene

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, ….

It is also the unique 7-limit regular temperament that tempers out the essential tempering commas of the 5 (128/125)- and 7-limit (64/63, 126/125).

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

• Sad Like Winter Leaves – in Augene[12] tuned to 27edo

Joel Grant Taylor

• Galticeran Sonatina – in Augene[12] tuned to 27edo