60edo: Difference between revisions

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→Intervals: Removed 7mus column
Line 7: Line 7:
| | degrees of 60edo
| | degrees of 60edo
| | cents value
| | cents value
|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
|0
|0
| |  
| |  
Line 19: Line 17:
| | 1
| | 1
| | 20
| | 20
|25.6 (19.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 25: Line 22:
| | 2
| | 2
| | 40
| | 40
|51.2 (33.3<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 31: Line 27:
| | 3
| | 3
| | 60
| | 60
|76.8 (4C.D<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 37: Line 32:
| | 4
| | 4
| | 80
| | 80
|102.4 (66.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 43: Line 37:
| | 5
| | 5
| | 100
| | 100
|128 (80<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 49: Line 42:
| | 6
| | 6
| | 120
| | 120
|153.6 (99.A<sub>16</sub>)
| | 16/15
| | 16/15
| |15/14
| |15/14
Line 55: Line 47:
| | 7
| | 7
| | 140
| | 140
|179.2 (B3.3<sub>16</sub>)
| |13/12
| |13/12
| |  
| |  
Line 61: Line 52:
| | 8
| | 8
| | 160
| | 160
|204.8 (CC.D<sub>16</sub>)
| |  
| |  
| | 12/11, 11/10
| | 12/11, 11/10
Line 67: Line 57:
| | 9
| | 9
| | 180
| | 180
|230.4 (E6.6<sub>16</sub>)
| | 10/9
| | 10/9
| |  
| |  
Line 73: Line 62:
| | 10
| | 10
| | 200
| | 200
|256 (100<sub>16</sub>)
| | 9/8
| | 9/8
| |  
| |  
Line 79: Line 67:
| | 11
| | 11
| | 220
| | 220
|281.6 (119.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 85: Line 72:
| | 12
| | 12
| | 240
| | 240
|307.2 (133.3<sub>16</sub>)
| | 15/13
| | 15/13
| | 8/7
| | 8/7
Line 91: Line 77:
| | 13
| | 13
| | 260
| | 260
|332.8 (14C.D<sub>16</sub>)
| |  
| |  
| | 7/6
| | 7/6
Line 97: Line 82:
| | 14
| | 14
| | 280
| | 280
|258.4 (166.6<sub>16</sub>)
| |  
| |  
| |13/11, 33/28
| |13/11, 33/28
Line 103: Line 87:
| | 15
| | 15
| | 300
| | 300
|384 (180<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 109: Line 92:
| | 16
| | 16
| | 320
| | 320
|409.6 (199.A<sub>16</sub>)
| |6/5
| |6/5
| |  
| |  
Line 115: Line 97:
| | 17
| | 17
| | 340
| | 340
|435.2 (1B3.3<sub>16</sub>)
| |  
| |  
| | 11/9
| | 11/9
Line 121: Line 102:
| | 18
| | 18
| | 360
| | 360
|460.8 (1CC.D<sub>16</sub>)
| | 16/13
| | 16/13
| |27/22
| |27/22
Line 127: Line 107:
| | 19
| | 19
| | 380
| | 380
|486.4 (1E6.6<sub>16</sub>)
| |5/4
| |5/4
| |  
| |  
Line 133: Line 112:
| | 20
| | 20
| | 400
| | 400
|512 (200<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 139: Line 117:
| | 21
| | 21
| | 420
| | 420
|537.6 (219.A<sub>16</sub>)
| |  
| |  
| | 33/26, 14/11
| | 33/26, 14/11
Line 145: Line 122:
| | 22
| | 22
| | 440
| | 440
|563.2 (233.3<sub>16</sub>)
| |  
| |  
| | 9/7
| | 9/7
Line 151: Line 127:
| | 23
| | 23
| | 460
| | 460
|588.8 (24C.D<sub>16</sub>)
| | 13/10
| | 13/10
| |  
| |  
Line 157: Line 132:
| | 24
| | 24
| | 480
| | 480
|614.4 (266.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 163: Line 137:
| | 25
| | 25
| | 500
| | 500
|640 (280<sub>16</sub>)
| | 4/3
| | 4/3
| |  
| |  
Line 169: Line 142:
| | 26
| | 26
| | 520
| | 520
|665.6 (299.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 175: Line 147:
| | 27
| | 27
| | 540
| | 540
|691.2 (2B3.3<sub>16</sub>)
| |  
| |  
| | 11/8, 15/11
| | 11/8, 15/11
Line 181: Line 152:
| | 28
| | 28
| | 560
| | 560
|716.8 (2CC.D<sub>16</sub>)
| | 18/13
| | 18/13
| |  
| |  
Line 187: Line 157:
| | 29
| | 29
| | 580
| | 580
|742.4 (2E6.6<sub>16</sub>)
| |  
| |  
| | 7/5
| | 7/5
Line 193: Line 162:
| | 30
| | 30
| | 600
| | 600
|768 (300<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 199: Line 167:
| | 31
| | 31
| | 620
| | 620
|793.6 (319.A<sub>16</sub>)
| |  
| |  
| | 10/7
| | 10/7
Line 205: Line 172:
| | 32
| | 32
| | 640
| | 640
|819.2 (333.3<sub>16</sub>)
| | 13/9
| | 13/9
| |  
| |  
Line 211: Line 177:
| | 33
| | 33
| | 660
| | 660
|844.8 (34C.D<sub>16</sub>)
| |  
| |  
| | 16/11, 22/15
| | 16/11, 22/15
Line 217: Line 182:
| | 34
| | 34
| | 680
| | 680
|870.4 (366.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 223: Line 187:
| | 35
| | 35
| | 700
| | 700
|896 (380<sub>16</sub>)
| | 3/2
| | 3/2
| |  
| |  
Line 229: Line 192:
| | 36
| | 36
| | 720
| | 720
|921.6 (399.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 235: Line 197:
| | 37
| | 37
| | 740
| | 740
|947.2 (3B3.3<sub>16</sub>)
| | 20/13
| | 20/13
| |  
| |  
Line 241: Line 202:
| | 38
| | 38
| | 760
| | 760
|968.8 (3CC.D<sub>16</sub>)
| |  
| |  
| | 14/9
| | 14/9
Line 247: Line 207:
| | 39
| | 39
| | 780
| | 780
|998.4 (3E6.6<sub>16</sub>)
| |  
| |  
| | 52/33, 11/7
| | 52/33, 11/7
Line 253: Line 212:
| | 40
| | 40
| | 800
| | 800
|1024 (400<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 259: Line 217:
| | 41
| | 41
| | 820
| | 820
|1049.6 (419.A<sub>16</sub>)
| |8/5
| |8/5
| |  
| |  
Line 265: Line 222:
| | 42
| | 42
| | 840
| | 840
|1075.2 (433.3<sub>16</sub>)
| | 13/8
| | 13/8
| |  
| |  
Line 271: Line 227:
| | 43
| | 43
| | 860
| | 860
|1100.8 (44C.D<sub>16</sub>)
| |  
| |  
| | 18/11, 44/27
| | 18/11, 44/27
Line 277: Line 232:
| | 44
| | 44
| | 880
| | 880
|1126.4 (466.6<sub>16</sub>)
| |5/3
| |5/3
| |  
| |  
Line 283: Line 237:
| | 45
| | 45
| | 900
| | 900
|1152 (480<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 289: Line 242:
| | 46
| | 46
| | 920
| | 920
|1177.6 (499.A<sub>16</sub>)
| |  
| |  
| |22/13, 56/33
| |22/13, 56/33
Line 295: Line 247:
| | 47
| | 47
| | 940
| | 940
|1203.2 (4B3.3<sub>16</sub>)
| |  
| |  
| | 12/7
| | 12/7
Line 301: Line 252:
| | 48
| | 48
| | 960
| | 960
|1228.8 (4CC.D<sub>16</sub>)
| | 26/15
| | 26/15
| | 7/4
| | 7/4
Line 307: Line 257:
| | 49
| | 49
| | 980
| | 980
|1254.4 (4E6.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 313: Line 262:
| | 50
| | 50
| | 1000
| | 1000
|1280 (500<sub>16</sub>)
| | 16/9
| | 16/9
| |  
| |  
Line 319: Line 267:
| | 51
| | 51
| | 1020
| | 1020
|1305.6 (519.A<sub>16</sub>)
| | 9/5
| | 9/5
| |  
| |  
Line 325: Line 272:
| | 52
| | 52
| | 1040
| | 1040
|1331.2 (533.3<sub>16</sub>)
| |  
| |  
| | 11/6, 20/11
| | 11/6, 20/11
Line 331: Line 277:
| | 53
| | 53
| | 1060
| | 1060
|1356.8 (54C.D<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 337: Line 282:
| | 54
| | 54
| | 1080
| | 1080
|1382.4 (566.6<sub>16</sub>)
| | 15/8
| | 15/8
| |28/15
| |28/15
Line 343: Line 287:
| | 55
| | 55
| | 1100
| | 1100
|1408 (580<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 349: Line 292:
| | 56
| | 56
| | 1120
| | 1120
|1433.6 (599.A<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 355: Line 297:
| | 57
| | 57
| | 1140
| | 1140
|1459.2 (5B3.3<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 361: Line 302:
| | 58
| | 58
| | 1160
| | 1160
|1484.8 (5CC.D<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 367: Line 307:
| | 59
| | 59
| | 1180
| | 1180
|1510.4 (5E6.6<sub>16</sub>)
| |  
| |  
| |  
| |  
Line 373: Line 312:
| | 60
| | 60
| | 1200
| | 1200
|1536 (600<sub>16</sub>)
| |  
| |  
| |  
| |  

Revision as of 15:56, 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 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 15/14
7 140 13/12
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 13/11, 33/28
15 300
16 320 6/5
17 340 11/9
18 360 16/13 27/22
19 380 5/4
20 400
21 420 33/26, 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 13/9
33 660 16/11, 22/15
34 680
35 700 3/2
36 720
37 740 20/13
38 760 14/9
39 780 52/33, 11/7
40 800
41 820 8/5
42 840 13/8
43 860 18/11, 44/27
44 880 5/3
45 900
46 920 22/13, 56/33
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 28/15
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

Retrieved from "https://en.xen.wiki/index.php?title=60edo&oldid=42730"