60edo: Difference between revisions

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Line 7: Line 7:
| | degrees of 60edo
| | degrees of 60edo
| | cents value
| | cents value
|pions
|7mus
| | approximate ratios in the 2.3.5.13 subgroup
| | approximate ratios in the 2.3.5.13 subgroup
| | additional ratios of 7 and 11 (assuming flat values for primes)
| | additional ratios of 7 and 11 (assuming flat values for primes)
|-
|-
| | 0
| | 0
| | 0
| colspan="3"| 0
| |  
| |  
| |  
| |  
Line 17: Line 19:
| | 1
| | 1
| | 20
| | 20
|21.2
|25.6 (19.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 22: Line 26:
| | 2
| | 2
| | 40
| | 40
|42.4
|51.2 (33.3<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 27: Line 33:
| | 3
| | 3
| | 60
| | 60
|63.6
|76.8 (4C.D<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 32: Line 40:
| | 4
| | 4
| | 80
| | 80
|84.8
|102.4 (66.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 37: Line 47:
| | 5
| | 5
| | 100
| | 100
|106
|128 (80<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 42: Line 54:
| | 6
| | 6
| | 120
| | 120
|127.2
|153.6 (99.A<sub>16</sub>)
| | 16/15
| | 16/15
| |  
| |15/14
|-
|-
| | 7
| | 7
| | 140
| | 140
| |  
|148.4
|179.2 (B3.3<sub>16</sub>)
| |13/12
| |  
| |  
|-
|-
| | 8
| | 8
| | 160
| | 160
|169.6
|204.8 (CC.D<sub>16</sub>)
| |  
| |  
| | 12/11, 11/10
| | 12/11, 11/10
Line 57: Line 75:
| | 9
| | 9
| | 180
| | 180
|190.8
|230.4 (E6.6<sub>16</sub>)
| | 10/9
| | 10/9
| |  
| |  
Line 62: Line 82:
| | 10
| | 10
| | 200
| | 200
|212
|256 (100<sub>16</sub>)
| | 9/8
| | 9/8
| |  
| |  
Line 67: Line 89:
| | 11
| | 11
| | 220
| | 220
|233.2
|281.6 (119.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 72: Line 96:
| | 12
| | 12
| | 240
| | 240
|254.4
|307.2 (133.3<sub>16</sub>)
| | 15/13
| | 15/13
| | 8/7
| | 8/7
Line 77: Line 103:
| | 13
| | 13
| | 260
| | 260
|275.6
|332.8 (14C.D<sub>16</sub>)
| |  
| |  
| | 7/6
| | 7/6
Line 82: Line 110:
| | 14
| | 14
| | 280
| | 280
|296.8
|258.4 (166.6<sub>16</sub>)
| |  
| |  
| |  
| |13/11, 33/28
|-
|-
| | 15
| | 15
| | 300
| | 300
|318
|384 (180<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 92: Line 124:
| | 16
| | 16
| | 320
| | 320
|339.2
|409.6 (199.A<sub>16</sub>)
| |6/5
| |6/5
| |  
| |  
Line 97: Line 131:
| | 17
| | 17
| | 340
| | 340
|360.4
|435.2 (1B3.3<sub>16</sub>)
| |  
| |  
| | 11/9
| | 11/9
Line 102: Line 138:
| | 18
| | 18
| | 360
| | 360
|381.6
|460.8 (1CC.D<sub>16</sub>)
| | 16/13
| | 16/13
| |  
| |27/22
|-
|-
| | 19
| | 19
| | 380
| | 380
|402.8
|486.4 (1E6.6<sub>16</sub>)
| |5/4
| |5/4
| |  
| |  
Line 112: Line 152:
| | 20
| | 20
| | 400
| | 400
|424
|512 (200<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 117: Line 159:
| | 21
| | 21
| | 420
| | 420
|445.2
|537.6 (219.A<sub>16</sub>)
| |  
| |  
| | 14/11
| | 33/26, 14/11
|-
|-
| | 22
| | 22
| | 440
| | 440
|466.4
|563.2 (233.3<sub>16</sub>)
| |  
| |  
| | 9/7
| | 9/7
Line 127: Line 173:
| | 23
| | 23
| | 460
| | 460
|487.6
|588.8 (24C.D<sub>16</sub>)
| | 13/10
| | 13/10
| |  
| |  
Line 132: Line 180:
| | 24
| | 24
| | 480
| | 480
|508.8
|614.4 (266.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 137: Line 187:
| | 25
| | 25
| | 500
| | 500
|530
|640 (280<sub>16</sub>)
| | 4/3
| | 4/3
| |  
| |  
Line 142: Line 194:
| | 26
| | 26
| | 520
| | 520
|551.2
|665.6 (299.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 147: Line 201:
| | 27
| | 27
| | 540
| | 540
|572.4
|691.2 (2B3.3<sub>16</sub>)
| |  
| |  
| | 11/8, 15/11
| | 11/8, 15/11
Line 152: Line 208:
| | 28
| | 28
| | 560
| | 560
|593.6
|716.8 (2CC.D<sub>16</sub>)
| | 18/13
| | 18/13
| |  
| |  
Line 157: Line 215:
| | 29
| | 29
| | 580
| | 580
|614.8
|742.4 (2E6.6<sub>16</sub>)
| |  
| |  
| | 7/5
| | 7/5
Line 162: Line 222:
| | 30
| | 30
| | 600
| | 600
|636
|768 (300<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 167: Line 229:
| | 31
| | 31
| | 620
| | 620
|657.2
|793.6 (319.A<sub>16</sub>)
| |  
| |  
| | 10/7
| | 10/7
Line 172: Line 236:
| | 32
| | 32
| | 640
| | 640
|678.4
|819.2 (333.3<sub>16</sub>)
| | 13/9
| | 13/9
| |  
| |  
Line 177: Line 243:
| | 33
| | 33
| | 660
| | 660
|699.6
|844.8 (34C.D<sub>16</sub>)
| |  
| |  
| | 16/11, 22/15
| | 16/11, 22/15
Line 182: Line 250:
| | 34
| | 34
| | 680
| | 680
|720.8
|870.4 (366.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 187: Line 257:
| | 35
| | 35
| | 700
| | 700
|742
|896 (380<sub>16</sub>)
| | 3/2
| | 3/2
| |  
| |  
Line 192: Line 264:
| | 36
| | 36
| | 720
| | 720
|763.2
|921.6 (399.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 197: Line 271:
| | 37
| | 37
| | 740
| | 740
|784.4
|947.2 (3B3.3<sub>16</sub>)
| | 20/13
| | 20/13
| |  
| |  
Line 202: Line 278:
| | 38
| | 38
| | 760
| | 760
|805.6
|968.8 (3CC.D<sub>16</sub>)
| |  
| |  
| | 14/9
| | 14/9
Line 207: Line 285:
| | 39
| | 39
| | 780
| | 780
|826.8
|998.4 (3E6.6<sub>16</sub>)
| |  
| |  
| | 11/7
| | 52/33, 11/7
|-
|-
| | 40
| | 40
| | 800
| | 800
|848
|1024 (400<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 217: Line 299:
| | 41
| | 41
| | 820
| | 820
|869.2
|1049.6 (419.A<sub>16</sub>)
| |8/5
| |8/5
| |  
| |  
Line 222: Line 306:
| | 42
| | 42
| | 840
| | 840
|890.4
|1075.2 (433.3<sub>16</sub>)
| | 13/8
| | 13/8
| |  
| |  
Line 227: Line 313:
| | 43
| | 43
| | 860
| | 860
|911.6
|1100.8 (44C.D<sub>16</sub>)
| |  
| |  
| | 18/11
| | 18/11, 44/27
|-
|-
| | 44
| | 44
| | 880
| | 880
|932.8
|1126.4 (466.6<sub>16</sub>)
| |5/3
| |5/3
| |  
| |  
Line 237: Line 327:
| | 45
| | 45
| | 900
| | 900
|954
|1152 (480<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 242: Line 334:
| | 46
| | 46
| | 920
| | 920
|975.2
|1177.6 (499.A<sub>16</sub>)
| |  
| |  
| |  
| |22/13, 56/33
|-
|-
| | 47
| | 47
| | 940
| | 940
|996.4
|1203.2 (4B3.3<sub>16</sub>)
| |  
| |  
| | 12/7
| | 12/7
Line 252: Line 348:
| | 48
| | 48
| | 960
| | 960
|1017.6
|1228.8 (4CC.D<sub>16</sub>)
| | 26/15
| | 26/15
| | 7/4
| | 7/4
Line 257: Line 355:
| | 49
| | 49
| | 980
| | 980
|1038.8
|1254.4 (4E6.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 262: Line 362:
| | 50
| | 50
| | 1000
| | 1000
|1060
|1280 (500<sub>16</sub>)
| | 16/9
| | 16/9
| |  
| |  
Line 267: Line 369:
| | 51
| | 51
| | 1020
| | 1020
|1081.2
|1305.6 (519.A<sub>16</sub>)
| | 9/5
| | 9/5
| |  
| |  
Line 272: Line 376:
| | 52
| | 52
| | 1040
| | 1040
|1102.4
|1331.2 (533.3<sub>16</sub>)
| |  
| |  
| | 11/6, 20/11
| | 11/6, 20/11
Line 277: Line 383:
| | 53
| | 53
| | 1060
| | 1060
|1123.6
|1356.8 (54C.D<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 282: Line 390:
| | 54
| | 54
| | 1080
| | 1080
|1144.8
|1382.4 (566.6<sub>16</sub>)
| | 15/8
| | 15/8
| |  
| |28/15
|-
|-
| | 55
| | 55
| | 1100
| | 1100
|1166
|1408 (580<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 292: Line 404:
| | 56
| | 56
| | 1120
| | 1120
|1187.2
|1433.6 (599.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 297: Line 411:
| | 57
| | 57
| | 1140
| | 1140
|1208.4
|1459.2 (5B3.3<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 302: Line 418:
| | 58
| | 58
| | 1160
| | 1160
|1229.6
|1484.8 (5CC.D<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 307: Line 425:
| | 59
| | 59
| | 1180
| | 1180
|1250.8
|1510.4 (5E6.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 312: Line 432:
| | 60
| | 60
| | 1200
| | 1200
|1272
|1536 (600<sub>16</sub>)
| |  
| |  
| |  
| |  

Revision as of 21:35, 11 May 2019

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 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

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

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