60edo

The 60 equal division divides the octave into 60 parts of exactly 20 cents each.

Theory

Since 60 = 5×12, 60edo belongs to the family of edos which contain 12edo, and like the other small edos of this kind, it tempers out the Pythagorean comma, 531441/524288 = [-19 12⟩. In the 5-limit, it tempers out both the magic comma, 3125/3072, and the amity comma, 1600000/1594323, and supplies the optimal patent val for 5-limit magic, tempering out 3125/3072. In the 7-limit it tempers out 875/864, 245/243, 225/224 and 10976/10935, and supports magic, compton and tritonic temperaments. In the 11-limit, the 60e val scores lower in badness than the patent val, and makes for an excellent tritonic tuning. It tempers out 121/120 and 441/440, whereas the patent val tempers out 100/99, 385/384 and 540/539. The tuning of 13 is superb at half a cent flat, and the 60e val also works excellently for 13-limit tritonic. As a no-fives val, it is also excellent for the 2.3.7.11.13 bleu temperament.

Intervals

Degrees	Cents	Approximate Ratios in the 2.3.5.13 subgroup	Additional Ratios of 7 and 11 (tending flat, i.e. 60e val)
0	0
1	20
2	40
3	60
4	80
5	100
6	120	16/15	15/14
7	140	13/12
8	160		12/11, 11/10
9	180	10/9
10	200	9/8
11	220
12	240	15/13	8/7
13	260		7/6
14	280		13/11, 33/28
15	300
16	320	6/5
17	340		11/9
18	360	16/13	27/22
19	380	5/4
20	400
21	420		33/26, 14/11
22	440		9/7
23	460	13/10
24	480
25	500	4/3
26	520
27	540		11/8, 15/11
28	560	18/13
29	580		7/5
30	600
31	620		10/7
32	640	13/9
33	660		16/11, 22/15
34	680
35	700	3/2
36	720
37	740	20/13
38	760		14/9
39	780		52/33, 11/7
40	800
41	820	8/5
42	840	13/8
43	860		18/11, 44/27
44	880	5/3
45	900
46	920		22/13, 56/33
47	940		12/7
48	960	26/15	7/4
49	980
50	1000	16/9
51	1020	9/5
52	1040		11/6, 20/11
53	1060
54	1080	15/8	28/15
55	1100
56	1120
57	1140
58	1160
59	1180
60	1200