60ed7/3

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60ed7/3

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Prime factorization	22 × 3 × 5
Step size	24.4478¢
Octave	49\60ed7/3 (1197.94¢) (semiconvergent)
Twelfth	78\60ed7/3 (1906.93¢) (→13\10ed7/3)
Consistency limit	8
Distinct consistency limit	6
Special properties	Highly composite

60 equal divisions of 7/3 (abbreviated 60ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 60 equal parts of about 24.4⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/60, or the 60th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	24.4
2	48.9	34/33, 35/34
3	73.3	23/22, 24/23, 25/24
4	97.8	18/17, 19/18, 35/33
5	122.2	15/14
6	146.7	12/11, 25/23
7	171.1	21/19, 32/29
8	195.6	19/17, 28/25
9	220	17/15, 25/22
10	244.5	15/13, 23/20
11	268.9	7/6
12	293.4	13/11
13	317.8	6/5
14	342.3	28/23
15	366.7	21/17, 26/21
16	391.2
17	415.6	14/11, 33/26
18	440.1	31/24
19	464.5	17/13
20	489
21	513.4	31/23, 35/26
22	537.9	15/11
23	562.3	18/13
24	586.7	7/5
25	611.2	27/19
26	635.6	13/9
27	660.1	19/13, 22/15
28	684.5
29	709
30	733.4	26/17
31	757.9	17/11, 31/20
32	782.3	11/7
33	806.8	35/22
34	831.2	21/13, 34/21
35	855.7	18/11, 23/14
36	880.1	5/3
37	904.6
38	929	12/7
39	953.5	26/15, 33/19
40	977.9
41	1002.4	25/14
42	1026.8	29/16
43	1051.3	11/6
44	1075.7	13/7
45	1100.2	17/9
46	1124.6	23/12
47	1149	31/16, 33/17, 35/18
48	1173.5
49	1197.9	2/1
50	1222.4
51	1246.8	35/17
52	1271.3	25/12
53	1295.7	19/9
54	1320.2	15/7
55	1344.6
56	1369.1	11/5
57	1393.5
58	1418	25/11, 34/15
59	1442.4	23/10
60	1466.9	7/3

Harmonics

Approximation of harmonics in 60ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.1	+5.0	-4.1	+0.7	+2.9	+5.0	-6.2	+10.0	-1.3	+4.8	+0.9
	Relative (%)	-8.4	+20.4	-16.8	+3.0	+12.0	+20.4	-25.2	+40.7	-5.4	+19.7	+3.5
Steps (reduced)		49 (49)	78 (18)	98 (38)	114 (54)	127 (7)	138 (18)	147 (27)	156 (36)	163 (43)	170 (50)	176 (56)

Approximation of harmonics in 60ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+9.0	+2.9	+5.7	-8.2	+9.1	+7.9	+12.1	-3.4	+10.0	+2.8	-0.9
	Relative (%)	+36.7	+12.0	+23.4	-33.6	+37.1	+32.3	+49.4	-13.8	+40.7	+11.3	-3.5
Steps (reduced)		182 (2)	187 (7)	192 (12)	196 (16)	201 (21)	205 (25)	209 (29)	212 (32)	216 (36)	219 (39)	222 (42)