60edo

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The 60 equal division divides the octave into 60 parts of exactly 20 cents each. Since 60 = 5 * 12, it 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 of 60edo cents value approximate ratios in the 2.3.5.13 subgroup additional ratios of 7 and 11 (assuming flat values for primes)
0 0
1 20
2 40
3 60
4 80
5 100
6 120 16/15
7 140
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
15 300
16 320
17 340 11/9
18 360 16/13
19 380
20 400
21 420 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 13/8
33 660 16/11, 22/15
34 680
35 700 3/2
36 720
37 740 20/13
38 760 14/9
39 780 11/7
40 800
41 820
42 840 13/8
43 860 18/11
44 880
45 900
46 920
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
55 1100
56 1120
57 1140
58 1160
59 1180
60 1200

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

60edo wheel with cents values.png

blue_60edo.png

60edoguitar.jpg

Robin Perry guitar