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	Hekts	Approximate ratios
0	0	0	1/1
1	31.7	21.7
2	63.4	43.3	26/25, 27/26, 28/27, 29/28
3	95.1	65	18/17, 19/18
4	126.8	86.7	14/13, 29/27
5	158.5	108.3	23/21, 34/31
6	190.2	130	19/17, 29/26
7	221.9	151.7	25/22, 33/29
8	253.6	173.3	22/19, 29/25
9	285.3	195	13/11, 20/17, 33/28
10	317	216.7	6/5
11	348.7	238.3	11/9
12	380.4	260
13	412.1	281.7	19/15, 33/26
14	443.8	303.3	22/17, 31/24
15	475.5	325	25/19, 29/22
16	507.2	346.7
17	538.9	368.3	15/11, 26/19
18	570.6	390	25/18
19	602.3	411.7	17/12
20	634	433.3	13/9
21	665.7	455	22/15, 25/17
22	697.4	476.7
23	729.1	498.3	29/19, 35/23
24	760.8	520	14/9, 31/20
25	792.5	541.7	19/12, 30/19
26	824.2	563.3	29/18
27	855.9	585	18/11, 23/14
28	887.6	606.7	5/3
29	919.3	628.3	17/10
30	951	650	26/15
31	982.7	671.7	30/17
32	1014.4	693.3	9/5
33	1046.1	715	11/6
34	1077.8	736.7	28/15
35	1109.5	758.3	19/10
36	1141.2	780	27/14, 29/15, 31/16
37	1172.9	801.7
38	1204.6	823.3
39	1236.3	845
40	1268	866.7	25/12, 27/13
41	1299.7	888.3
42	1331.4	910	28/13
43	1363.1	931.7	11/5
44	1394.8	953.3
45	1426.5	975
46	1458.2	996.7
47	1489.9	1018.3	26/11
48	1521.6	1040
49	1553.3	1061.7	27/11
50	1585	1083.3	5/2
51	1616.7	1105	28/11, 33/13
52	1648.4	1126.7
53	1680.1	1148.3	29/11
54	1711.8	1170	35/13
55	1743.5	1191.7
56	1775.2	1213.3
57	1806.9	1235	17/6
58	1838.6	1256.7	26/9
59	1870.3	1278.3
60	1902	1300	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)