User:MisterShafXen/60ed8/3

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60ed8/3

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Prime factorization	22 × 3 × 5 (highly composite)
Step size	28.3007 ¢
Octave	42\60ed8/3 (1188.63 ¢) (→ 7\10ed8/3)
Twelfth	67\60ed8/3 (1896.15 ¢)
Consistency limit	3
Distinct consistency limit	3

60 equal divisions of 8/3 (abbreviated 60ed8/3) is a nonoctave tuning system that divides the interval of 8/3 into 60 equal parts of about 28.3 ¢ each. Each step represents a frequency ratio of (8/3)^1/60, or the 60th root of 8/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	28.3
2	56.6
3	84.9	22/21
4	113.2	31/29
5	141.5
6	169.8	21/19
7	198.1	28/25
8	226.4	33/29
9	254.7	22/19
10	283
11	311.3	6/5
12	339.6	17/14
13	367.9	21/17, 26/21
14	396.2	34/27
15	424.5
16	452.8	35/27
17	481.1	29/22
18	509.4
19	537.7
20	566	25/18
21	594.3	31/22
22	622.6	33/23
23	650.9
24	679.2
25	707.5
26	735.8	26/17, 29/19
27	764.1	14/9
28	792.4
29	820.7
30	849	31/19
31	877.3
32	905.6
33	933.9
34	962.2
35	990.5	23/13
36	1018.8	9/5
37	1047.1
38	1075.4	13/7
39	1103.7	17/9
40	1132
41	1160.3
42	1188.6
43	1216.9
44	1245.2
45	1273.5	23/11, 25/12
46	1301.8
47	1330.1
48	1358.4
49	1386.7	29/13
50	1415	34/15
51	1443.3
52	1471.6
53	1499.9
54	1528.2
55	1556.5
56	1584.8	5/2
57	1613.1	33/13
58	1641.4
59	1669.7
60	1698

Commas

This tuning tempers out 50/49 in the 7-limit, and 56/55 and 80/77 in the 11-limit.

Harmonics

Approximation of harmonics in 60ed8/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-11.4	-5.8	+5.6	-12.8	+11.1	-1.0	-5.8	-11.6	+4.1	+8.9	-0.2
	Relative (%)	-40.2	-20.5	+19.7	-45.4	+39.3	-3.7	-20.5	-41.0	+14.5	+31.4	-0.9
Steps (reduced)		42 (42)	67 (7)	85 (25)	98 (38)	110 (50)	119 (59)	127 (7)	134 (14)	141 (21)	147 (27)	152 (32)