60edt

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60edt

61edt →

Prime factorization	22 × 3 × 5
Step size	31.6993¢
Octave	38\60edt (1204.57¢) (→19\30edt)
Consistency limit	5
Distinct consistency limit	5
Special properties	Highly composite

60 equal divisions of the tritave, perfect twelfth, or 3rd harmonic (abbreviated 60edt or 60ed3), is a nonoctave tuning system that divides the interval of 3/1 into 60 equal parts of about 31.7⁠ ⁠¢ each. Each step represents a frequency ratio of 3^1/60, or the 60th root of 3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	31.7
2	63.4	26/25, 27/26, 28/27, 29/28
3	95.1	18/17, 19/18
4	126.8	14/13, 29/27
5	158.5	23/21, 34/31
6	190.2	19/17, 29/26
7	221.9	25/22, 33/29
8	253.6	22/19, 29/25
9	285.3	13/11, 20/17, 33/28
10	317	6/5
11	348.7	11/9
12	380.4
13	412.1	19/15, 33/26
14	443.8	22/17, 31/24
15	475.5	25/19, 29/22
16	507.2
17	538.9	15/11, 26/19
18	570.6	25/18
19	602.3	17/12
20	634	13/9
21	665.7	22/15, 25/17
22	697.4
23	729.1	29/19, 35/23
24	760.8	14/9, 31/20
25	792.5	19/12, 30/19
26	824.2	29/18
27	855.9	18/11, 23/14
28	887.6	5/3
29	919.3	17/10
30	951	26/15
31	982.7	30/17
32	1014.4	9/5
33	1046.1	11/6
34	1077.8	28/15
35	1109.5	19/10
36	1141.2	27/14, 29/15, 31/16
37	1172.9
38	1204.6
39	1236.3
40	1268	25/12, 27/13
41	1299.7
42	1331.4	28/13
43	1363.1	11/5
44	1394.8
45	1426.5
46	1458.2
47	1489.9	26/11
48	1521.6
49	1553.3	27/11
50	1585	5/2
51	1616.7	28/11, 33/13
52	1648.4
53	1680.1	29/11
54	1711.8	35/13
55	1743.5
56	1775.2
57	1806.9	17/6
58	1838.6	26/9
59	1870.3
60	1902	3/1

Harmonics

Approximation of harmonics in 60edt

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+4.6	+0.0	+9.1	+3.2	+4.6	-8.7	+13.7	+0.0	+7.8	+1.3	+9.1
	Relative (%)	+14.4	+0.0	+28.8	+10.2	+14.4	-27.5	+43.3	+0.0	+24.6	+4.0	+28.8
Steps (reduced)		38 (38)	60 (0)	76 (16)	88 (28)	98 (38)	106 (46)	114 (54)	120 (0)	126 (6)	131 (11)	136 (16)

Approximation of harmonics in 60edt

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-2.6	-4.1	+3.2	-13.4	+8.4	+4.6	+6.1	+12.4	-8.7	+5.9	-7.7
	Relative (%)	-8.3	-13.0	+10.2	-42.3	+26.6	+14.4	+19.1	+39.0	-27.5	+18.5	-24.3
Steps (reduced)		140 (20)	144 (24)	148 (28)	151 (31)	155 (35)	158 (38)	161 (41)	164 (44)	166 (46)	169 (49)	171 (51)