60edo
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 | 7mus | approximate ratios in the 2.3.5.13 subgroup | additional ratios of 7 and 11 (assuming flat values for primes) |
| 0 | ||||
| 1 | 20 | 25.6 (19.A16) | ||
| 2 | 40 | 51.2 (33.316) | ||
| 3 | 60 | 76.8 (4C.D16) | ||
| 4 | 80 | 102.4 (66.616) | ||
| 5 | 100 | 128 (8016) | ||
| 6 | 120 | 153.6 (99.A16) | 16/15 | 15/14 |
| 7 | 140 | 179.2 (B3.316) | 13/12 | |
| 8 | 160 | 204.8 (CC.D16) | 12/11, 11/10 | |
| 9 | 180 | 230.4 (E6.616) | 10/9 | |
| 10 | 200 | 256 (10016) | 9/8 | |
| 11 | 220 | 281.6 (119.A16) | ||
| 12 | 240 | 307.2 (133.316) | 15/13 | 8/7 |
| 13 | 260 | 332.8 (14C.D16) | 7/6 | |
| 14 | 280 | 258.4 (166.616) | 13/11, 33/28 | |
| 15 | 300 | 384 (18016) | ||
| 16 | 320 | 409.6 (199.A16) | 6/5 | |
| 17 | 340 | 435.2 (1B3.316) | 11/9 | |
| 18 | 360 | 460.8 (1CC.D16) | 16/13 | 27/22 |
| 19 | 380 | 486.4 (1E6.616) | 5/4 | |
| 20 | 400 | 512 (20016) | ||
| 21 | 420 | 537.6 (219.A16) | 33/26, 14/11 | |
| 22 | 440 | 563.2 (233.316) | 9/7 | |
| 23 | 460 | 588.8 (24C.D16) | 13/10 | |
| 24 | 480 | 614.4 (266.616) | ||
| 25 | 500 | 640 (28016) | 4/3 | |
| 26 | 520 | 665.6 (299.A16) | ||
| 27 | 540 | 691.2 (2B3.316) | 11/8, 15/11 | |
| 28 | 560 | 716.8 (2CC.D16) | 18/13 | |
| 29 | 580 | 742.4 (2E6.616) | 7/5 | |
| 30 | 600 | 768 (30016) | ||
| 31 | 620 | 793.6 (319.A16) | 10/7 | |
| 32 | 640 | 819.2 (333.316) | 13/9 | |
| 33 | 660 | 844.8 (34C.D16) | 16/11, 22/15 | |
| 34 | 680 | 870.4 (366.616) | ||
| 35 | 700 | 896 (38016) | 3/2 | |
| 36 | 720 | 921.6 (399.A16) | ||
| 37 | 740 | 947.2 (3B3.316) | 20/13 | |
| 38 | 760 | 968.8 (3CC.D16) | 14/9 | |
| 39 | 780 | 998.4 (3E6.616) | 52/33, 11/7 | |
| 40 | 800 | 1024 (40016) | ||
| 41 | 820 | 1049.6 (419.A16) | 8/5 | |
| 42 | 840 | 1075.2 (433.316) | 13/8 | |
| 43 | 860 | 1100.8 (44C.D16) | 18/11, 44/27 | |
| 44 | 880 | 1126.4 (466.616) | 5/3 | |
| 45 | 900 | 1152 (48016) | ||
| 46 | 920 | 1177.6 (499.A16) | 22/13, 56/33 | |
| 47 | 940 | 1203.2 (4B3.316) | 12/7 | |
| 48 | 960 | 1228.8 (4CC.D16) | 26/15 | 7/4 |
| 49 | 980 | 1254.4 (4E6.616) | ||
| 50 | 1000 | 1280 (50016) | 16/9 | |
| 51 | 1020 | 1305.6 (519.A16) | 9/5 | |
| 52 | 1040 | 1331.2 (533.316) | 11/6, 20/11 | |
| 53 | 1060 | 1356.8 (54C.D16) | ||
| 54 | 1080 | 1382.4 (566.616) | 15/8 | 28/15 |
| 55 | 1100 | 1408 (58016) | ||
| 56 | 1120 | 1433.6 (599.A16) | ||
| 57 | 1140 | 1459.2 (5B3.316) | ||
| 58 | 1160 | 1484.8 (5CC.D16) | ||
| 59 | 1180 | 1510.4 (5E6.616) | ||
| 60 | 1200 | 1536 (60016) | ||
Compositions
Rojqoq (So-Called Peace) play by William Sethares
Black Salt - White Pepper play
all by Robin Perry
Dingshi and
Gene's Jitterbug (ogg) Gene's Jitterbug (mp3) Score
by Graham Breed
Images
Robin Perry guitar