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 2.3.5.13.17 subgroup	Additional Ratios of 7 and 11 (tending flat, i.e. 60e val)
0	0	1/1
1	20	81/80	49/48
2	40		50/49, 64/63, 33/32
3	60	25/24	28/27, 36/35
4	80
5	100	17/16, 18/17
6	120	16/15	15/14, 14/13
7	140	13/12
8	160		12/11, 11/10
9	180	10/9
10	200	9/8
11	220	17/15
12	240	15/13	8/7
13	260		7/6
14	280	20/17	13/11, 33/28
15	300	32/27
16	320	6/5
17	340	39/32	11/9, 17/14
18	360	16/13	27/22, 21/17
19	380	5/4
20	400	81/64
21	420		33/26, 14/11
22	440		9/7, 22/17
23	460	13/10, 17/13	21/16
24	480
25	500	4/3
26	520
27	540		11/8, 15/11
28	560	18/13
29	580		7/5
30	600	17/12, 24/17
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, 26/17	32/21
38	760		14/9, 17/11
39	780		52/33, 11/7
40	800	160/81
41	820	8/5
42	840	13/8	44/27, 34/21
43	860	64/39	18/11, 28/17
44	880	5/3
45	900	27/16
46	920	17/10	22/13, 56/33
47	940		12/7
48	960	26/15	7/4
49	980	30/17
50	1000	16/9
51	1020	9/5
52	1040		11/6, 20/11
53	1060
54	1080	15/8	28/15, 13/7
55	1100	17/9, 32/17
56	1120
57	1140	48/25	27/14, 35/18
58	1160		49/25, 63/32, 64/33
59	1180	160/81	96/49
60	1200	2/1

Compositions

Rojqoq (So-Called Peace) play by William Sethares

Skating On Thin Ice play

My Mother Said So play

Black Salt - White Pepper play

NGC 300play

all by Robin Perry

Dingshi and

Gene's Jitterbug (ogg) Gene's Jitterbug (mp3) Score

by Graham Breed

Images

Robin Perry guitar