# 60edo

(Redirected from 60-edo)

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 pions 7mus approximate ratios in the 2.3.5.13 subgroup additional ratios of 7 and 11 (assuming flat values for primes) 0 1 20 21.2 25.6 (19.A16) 2 40 42.4 51.2 (33.316) 3 60 63.6 76.8 (4C.D16) 4 80 84.8 102.4 (66.616) 5 100 106 128 (8016) 6 120 127.2 153.6 (99.A16) 16/15 15/14 7 140 148.4 179.2 (B3.316) 13/12 8 160 169.6 204.8 (CC.D16) 12/11, 11/10 9 180 190.8 230.4 (E6.616) 10/9 10 200 212 256 (10016) 9/8 11 220 233.2 281.6 (119.A16) 12 240 254.4 307.2 (133.316) 15/13 8/7 13 260 275.6 332.8 (14C.D16) 7/6 14 280 296.8 258.4 (166.616) 13/11, 33/28 15 300 318 384 (18016) 16 320 339.2 409.6 (199.A16) 6/5 17 340 360.4 435.2 (1B3.316) 11/9 18 360 381.6 460.8 (1CC.D16) 16/13 27/22 19 380 402.8 486.4 (1E6.616) 5/4 20 400 424 512 (20016) 21 420 445.2 537.6 (219.A16) 33/26, 14/11 22 440 466.4 563.2 (233.316) 9/7 23 460 487.6 588.8 (24C.D16) 13/10 24 480 508.8 614.4 (266.616) 25 500 530 640 (28016) 4/3 26 520 551.2 665.6 (299.A16) 27 540 572.4 691.2 (2B3.316) 11/8, 15/11 28 560 593.6 716.8 (2CC.D16) 18/13 29 580 614.8 742.4 (2E6.616) 7/5 30 600 636 768 (30016) 31 620 657.2 793.6 (319.A16) 10/7 32 640 678.4 819.2 (333.316) 13/9 33 660 699.6 844.8 (34C.D16) 16/11, 22/15 34 680 720.8 870.4 (366.616) 35 700 742 896 (38016) 3/2 36 720 763.2 921.6 (399.A16) 37 740 784.4 947.2 (3B3.316) 20/13 38 760 805.6 968.8 (3CC.D16) 14/9 39 780 826.8 998.4 (3E6.616) 52/33, 11/7 40 800 848 1024 (40016) 41 820 869.2 1049.6 (419.A16) 8/5 42 840 890.4 1075.2 (433.316) 13/8 43 860 911.6 1100.8 (44C.D16) 18/11, 44/27 44 880 932.8 1126.4 (466.616) 5/3 45 900 954 1152 (48016) 46 920 975.2 1177.6 (499.A16) 22/13, 56/33 47 940 996.4 1203.2 (4B3.316) 12/7 48 960 1017.6 1228.8 (4CC.D16) 26/15 7/4 49 980 1038.8 1254.4 (4E6.616) 50 1000 1060 1280 (50016) 16/9 51 1020 1081.2 1305.6 (519.A16) 9/5 52 1040 1102.4 1331.2 (533.316) 11/6, 20/11 53 1060 1123.6 1356.8 (54C.D16) 54 1080 1144.8 1382.4 (566.616) 15/8 28/15 55 1100 1166 1408 (58016) 56 1120 1187.2 1433.6 (599.A16) 57 1140 1208.4 1459.2 (5B3.316) 58 1160 1229.6 1484.8 (5CC.D16) 59 1180 1250.8 1510.4 (5E6.616) 60 1200 1272 1536 (60016)

# Compositions

Rojqoq (So-Called Peace) play by William Sethares

all by Robin Perry

Dingshi and

by Graham Breed

# Images

Robin Perry guitar