60edo: Difference between revisions

From Xenharmonic Wiki
Jump to navigation Jump to search
← Older editNewer edit →
VisualWikitext
Jkarimak (talk | contribs)
191 edits
→Intervals: Removed pions column
Line 7: Line 7:
| | degrees of 60edo
| | degrees of 60edo
| | cents value
| | cents value
|pions
|7mus
|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)
|-
|-
| colspan="4"| 0
| colspan="3" | 0
| |  
| |  
| |  
| |  
Line 18: Line 17:
| | 1
| | 1
| | 20
| | 20
|21.2
|25.6 (19.A<sub>16</sub>)
|25.6 (19.A<sub>16</sub>)
| |  
| |  
Line 25: Line 23:
| | 2
| | 2
| | 40
| | 40
|42.4
|51.2 (33.3<sub>16</sub>)
|51.2 (33.3<sub>16</sub>)
| |  
| |  
Line 32: Line 29:
| | 3
| | 3
| | 60
| | 60
|63.6
|76.8 (4C.D<sub>16</sub>)
|76.8 (4C.D<sub>16</sub>)
| |  
| |  
Line 39: Line 35:
| | 4
| | 4
| | 80
| | 80
|84.8
|102.4 (66.6<sub>16</sub>)
|102.4 (66.6<sub>16</sub>)
| |  
| |  
Line 46: Line 41:
| | 5
| | 5
| | 100
| | 100
|106
|128 (80<sub>16</sub>)
|128 (80<sub>16</sub>)
| |  
| |  
Line 53: Line 47:
| | 6
| | 6
| | 120
| | 120
|127.2
|153.6 (99.A<sub>16</sub>)
|153.6 (99.A<sub>16</sub>)
| | 16/15
| | 16/15
Line 60: Line 53:
| | 7
| | 7
| | 140
| | 140
|148.4
|179.2 (B3.3<sub>16</sub>)
|179.2 (B3.3<sub>16</sub>)
| |13/12
| |13/12
Line 67: Line 59:
| | 8
| | 8
| | 160
| | 160
|169.6
|204.8 (CC.D<sub>16</sub>)
|204.8 (CC.D<sub>16</sub>)
| |  
| |  
Line 74: Line 65:
| | 9
| | 9
| | 180
| | 180
|190.8
|230.4 (E6.6<sub>16</sub>)
|230.4 (E6.6<sub>16</sub>)
| | 10/9
| | 10/9
Line 81: Line 71:
| | 10
| | 10
| | 200
| | 200
|212
|256 (100<sub>16</sub>)
|256 (100<sub>16</sub>)
| | 9/8
| | 9/8
Line 88: Line 77:
| | 11
| | 11
| | 220
| | 220
|233.2
|281.6 (119.A<sub>16</sub>)
|281.6 (119.A<sub>16</sub>)
| |  
| |  
Line 95: Line 83:
| | 12
| | 12
| | 240
| | 240
|254.4
|307.2 (133.3<sub>16</sub>)
|307.2 (133.3<sub>16</sub>)
| | 15/13
| | 15/13
Line 102: Line 89:
| | 13
| | 13
| | 260
| | 260
|275.6
|332.8 (14C.D<sub>16</sub>)
|332.8 (14C.D<sub>16</sub>)
| |  
| |  
Line 109: Line 95:
| | 14
| | 14
| | 280
| | 280
|296.8
|258.4 (166.6<sub>16</sub>)
|258.4 (166.6<sub>16</sub>)
| |  
| |  
Line 116: Line 101:
| | 15
| | 15
| | 300
| | 300
|318
|384 (180<sub>16</sub>)
|384 (180<sub>16</sub>)
| |  
| |  
Line 123: Line 107:
| | 16
| | 16
| | 320
| | 320
|339.2
|409.6 (199.A<sub>16</sub>)
|409.6 (199.A<sub>16</sub>)
| |6/5
| |6/5
Line 130: Line 113:
| | 17
| | 17
| | 340
| | 340
|360.4
|435.2 (1B3.3<sub>16</sub>)
|435.2 (1B3.3<sub>16</sub>)
| |  
| |  
Line 137: Line 119:
| | 18
| | 18
| | 360
| | 360
|381.6
|460.8 (1CC.D<sub>16</sub>)
|460.8 (1CC.D<sub>16</sub>)
| | 16/13
| | 16/13
Line 144: Line 125:
| | 19
| | 19
| | 380
| | 380
|402.8
|486.4 (1E6.6<sub>16</sub>)
|486.4 (1E6.6<sub>16</sub>)
| |5/4
| |5/4
Line 151: Line 131:
| | 20
| | 20
| | 400
| | 400
|424
|512 (200<sub>16</sub>)
|512 (200<sub>16</sub>)
| |  
| |  
Line 158: Line 137:
| | 21
| | 21
| | 420
| | 420
|445.2
|537.6 (219.A<sub>16</sub>)
|537.6 (219.A<sub>16</sub>)
| |  
| |  
Line 165: Line 143:
| | 22
| | 22
| | 440
| | 440
|466.4
|563.2 (233.3<sub>16</sub>)
|563.2 (233.3<sub>16</sub>)
| |  
| |  
Line 172: Line 149:
| | 23
| | 23
| | 460
| | 460
|487.6
|588.8 (24C.D<sub>16</sub>)
|588.8 (24C.D<sub>16</sub>)
| | 13/10
| | 13/10
Line 179: Line 155:
| | 24
| | 24
| | 480
| | 480
|508.8
|614.4 (266.6<sub>16</sub>)
|614.4 (266.6<sub>16</sub>)
| |  
| |  
Line 186: Line 161:
| | 25
| | 25
| | 500
| | 500
|530
|640 (280<sub>16</sub>)
|640 (280<sub>16</sub>)
| | 4/3
| | 4/3
Line 193: Line 167:
| | 26
| | 26
| | 520
| | 520
|551.2
|665.6 (299.A<sub>16</sub>)
|665.6 (299.A<sub>16</sub>)
| |  
| |  
Line 200: Line 173:
| | 27
| | 27
| | 540
| | 540
|572.4
|691.2 (2B3.3<sub>16</sub>)
|691.2 (2B3.3<sub>16</sub>)
| |  
| |  
Line 207: Line 179:
| | 28
| | 28
| | 560
| | 560
|593.6
|716.8 (2CC.D<sub>16</sub>)
|716.8 (2CC.D<sub>16</sub>)
| | 18/13
| | 18/13
Line 214: Line 185:
| | 29
| | 29
| | 580
| | 580
|614.8
|742.4 (2E6.6<sub>16</sub>)
|742.4 (2E6.6<sub>16</sub>)
| |  
| |  
Line 221: Line 191:
| | 30
| | 30
| | 600
| | 600
|636
|768 (300<sub>16</sub>)
|768 (300<sub>16</sub>)
| |  
| |  
Line 228: Line 197:
| | 31
| | 31
| | 620
| | 620
|657.2
|793.6 (319.A<sub>16</sub>)
|793.6 (319.A<sub>16</sub>)
| |  
| |  
Line 235: Line 203:
| | 32
| | 32
| | 640
| | 640
|678.4
|819.2 (333.3<sub>16</sub>)
|819.2 (333.3<sub>16</sub>)
| | 13/9
| | 13/9
Line 242: Line 209:
| | 33
| | 33
| | 660
| | 660
|699.6
|844.8 (34C.D<sub>16</sub>)
|844.8 (34C.D<sub>16</sub>)
| |  
| |  
Line 249: Line 215:
| | 34
| | 34
| | 680
| | 680
|720.8
|870.4 (366.6<sub>16</sub>)
|870.4 (366.6<sub>16</sub>)
| |  
| |  
Line 256: Line 221:
| | 35
| | 35
| | 700
| | 700
|742
|896 (380<sub>16</sub>)
|896 (380<sub>16</sub>)
| | 3/2
| | 3/2
Line 263: Line 227:
| | 36
| | 36
| | 720
| | 720
|763.2
|921.6 (399.A<sub>16</sub>)
|921.6 (399.A<sub>16</sub>)
| |  
| |  
Line 270: Line 233:
| | 37
| | 37
| | 740
| | 740
|784.4
|947.2 (3B3.3<sub>16</sub>)
|947.2 (3B3.3<sub>16</sub>)
| | 20/13
| | 20/13
Line 277: Line 239:
| | 38
| | 38
| | 760
| | 760
|805.6
|968.8 (3CC.D<sub>16</sub>)
|968.8 (3CC.D<sub>16</sub>)
| |  
| |  
Line 284: Line 245:
| | 39
| | 39
| | 780
| | 780
|826.8
|998.4 (3E6.6<sub>16</sub>)
|998.4 (3E6.6<sub>16</sub>)
| |  
| |  
Line 291: Line 251:
| | 40
| | 40
| | 800
| | 800
|848
|1024 (400<sub>16</sub>)
|1024 (400<sub>16</sub>)
| |  
| |  
Line 298: Line 257:
| | 41
| | 41
| | 820
| | 820
|869.2
|1049.6 (419.A<sub>16</sub>)
|1049.6 (419.A<sub>16</sub>)
| |8/5
| |8/5
Line 305: Line 263:
| | 42
| | 42
| | 840
| | 840
|890.4
|1075.2 (433.3<sub>16</sub>)
|1075.2 (433.3<sub>16</sub>)
| | 13/8
| | 13/8
Line 312: Line 269:
| | 43
| | 43
| | 860
| | 860
|911.6
|1100.8 (44C.D<sub>16</sub>)
|1100.8 (44C.D<sub>16</sub>)
| |  
| |  
Line 319: Line 275:
| | 44
| | 44
| | 880
| | 880
|932.8
|1126.4 (466.6<sub>16</sub>)
|1126.4 (466.6<sub>16</sub>)
| |5/3
| |5/3
Line 326: Line 281:
| | 45
| | 45
| | 900
| | 900
|954
|1152 (480<sub>16</sub>)
|1152 (480<sub>16</sub>)
| |  
| |  
Line 333: Line 287:
| | 46
| | 46
| | 920
| | 920
|975.2
|1177.6 (499.A<sub>16</sub>)
|1177.6 (499.A<sub>16</sub>)
| |  
| |  
Line 340: Line 293:
| | 47
| | 47
| | 940
| | 940
|996.4
|1203.2 (4B3.3<sub>16</sub>)
|1203.2 (4B3.3<sub>16</sub>)
| |  
| |  
Line 347: Line 299:
| | 48
| | 48
| | 960
| | 960
|1017.6
|1228.8 (4CC.D<sub>16</sub>)
|1228.8 (4CC.D<sub>16</sub>)
| | 26/15
| | 26/15
Line 354: Line 305:
| | 49
| | 49
| | 980
| | 980
|1038.8
|1254.4 (4E6.6<sub>16</sub>)
|1254.4 (4E6.6<sub>16</sub>)
| |  
| |  
Line 361: Line 311:
| | 50
| | 50
| | 1000
| | 1000
|1060
|1280 (500<sub>16</sub>)
|1280 (500<sub>16</sub>)
| | 16/9
| | 16/9
Line 368: Line 317:
| | 51
| | 51
| | 1020
| | 1020
|1081.2
|1305.6 (519.A<sub>16</sub>)
|1305.6 (519.A<sub>16</sub>)
| | 9/5
| | 9/5
Line 375: Line 323:
| | 52
| | 52
| | 1040
| | 1040
|1102.4
|1331.2 (533.3<sub>16</sub>)
|1331.2 (533.3<sub>16</sub>)
| |  
| |  
Line 382: Line 329:
| | 53
| | 53
| | 1060
| | 1060
|1123.6
|1356.8 (54C.D<sub>16</sub>)
|1356.8 (54C.D<sub>16</sub>)
| |  
| |  
Line 389: Line 335:
| | 54
| | 54
| | 1080
| | 1080
|1144.8
|1382.4 (566.6<sub>16</sub>)
|1382.4 (566.6<sub>16</sub>)
| | 15/8
| | 15/8
Line 396: Line 341:
| | 55
| | 55
| | 1100
| | 1100
|1166
|1408 (580<sub>16</sub>)
|1408 (580<sub>16</sub>)
| |  
| |  
Line 403: Line 347:
| | 56
| | 56
| | 1120
| | 1120
|1187.2
|1433.6 (599.A<sub>16</sub>)
|1433.6 (599.A<sub>16</sub>)
| |  
| |  
Line 410: Line 353:
| | 57
| | 57
| | 1140
| | 1140
|1208.4
|1459.2 (5B3.3<sub>16</sub>)
|1459.2 (5B3.3<sub>16</sub>)
| |  
| |  
Line 417: Line 359:
| | 58
| | 58
| | 1160
| | 1160
|1229.6
|1484.8 (5CC.D<sub>16</sub>)
|1484.8 (5CC.D<sub>16</sub>)
| |  
| |  
Line 424: Line 365:
| | 59
| | 59
| | 1180
| | 1180
|1250.8
|1510.4 (5E6.6<sub>16</sub>)
|1510.4 (5E6.6<sub>16</sub>)
| |  
| |  
Line 431: Line 371:
| | 60
| | 60
| | 1200
| | 1200
|1272
|1536 (600<sub>16</sub>)
|1536 (600<sub>16</sub>)
| |  
| |  

Revision as of 13:16, 12 December 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 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

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

Retrieved from "https://en.xen.wiki/index.php?title=60edo&oldid=42614"