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	31.699
2	63.399	26/25, 27/26, 28/27, 29/28
3	95.098	18/17, 19/18
4	126.797	14/13, 29/27
5	158.496	23/21, 34/31
6	190.196	19/17, 29/26
7	221.895	25/22, 33/29
8	253.594	22/19, 29/25
9	285.293	13/11, 20/17, 33/28
10	316.993	6/5
11	348.692	11/9
12	380.391
13	412.09	19/15, 33/26
14	443.79	22/17, 31/24
15	475.489	25/19, 29/22
16	507.188
17	538.887	15/11, 26/19
18	570.587	25/18
19	602.286	17/12
20	633.985	13/9
21	665.684	22/15, 25/17
22	697.384
23	729.083	29/19, 35/23
24	760.782	14/9, 31/20
25	792.481	19/12, 30/19
26	824.181	29/18
27	855.88	18/11, 23/14
28	887.579	5/3
29	919.278	17/10
30	950.978	26/15
31	982.677	30/17
32	1014.376	9/5
33	1046.075	11/6
34	1077.775	28/15
35	1109.474	19/10
36	1141.173	27/14, 29/15, 31/16
37	1172.872
38	1204.572
39	1236.271
40	1267.97	25/12, 27/13
41	1299.669
42	1331.369	28/13
43	1363.068	11/5
44	1394.767
45	1426.466
46	1458.166
47	1489.865	26/11
48	1521.564
49	1553.263	27/11
50	1584.963	5/2
51	1616.662	28/11, 33/13
52	1648.361
53	1680.06	29/11
54	1711.76	35/13
55	1743.459
56	1775.158
57	1806.857	17/6
58	1838.557	26/9
59	1870.256
60	1901.955	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)