61ed4

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61ed4

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Prime factorization	61 (prime)
Step size	39.3443¢
Octave	31\61ed4 (1219.67¢)
Twelfth	48\61ed4 (1888.52¢)
Consistency limit	1
Distinct consistency limit	1

61 equal divisions of the 4th harmonic (abbreviated 61ed4) is a nonoctave tuning system that divides the interval of 4/1 into 61 equal parts of about 39.3 ¢ each. Each step represents a frequency ratio of 4^1/61, or the 61st root of 4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	39.3
2	78.7
3	118	31/29
4	157.4	23/21
5	196.7	19/17
6	236.1
7	275.4
8	314.8	6/5
9	354.1
10	393.4
11	432.8
12	472.1	25/19
13	511.5	35/26
14	550.8
15	590.2
16	629.5
17	668.9	25/17
18	708.2
19	747.5
20	786.9	11/7, 30/19
21	826.2	21/13, 29/18
22	865.6
23	904.9
24	944.3	19/11, 31/18
25	983.6	23/13, 30/17
26	1023
27	1062.3
28	1101.6
29	1141	29/15
30	1180.3
31	1219.7
32	1259	31/15
33	1298.4
34	1337.7	13/6
35	1377
36	1416.4
37	1455.7
38	1495.1
39	1534.4	17/7
40	1573.8
41	1613.1	33/13
42	1652.5	13/5
43	1691.8
44	1731.1	19/7
45	1770.5
46	1809.8
47	1849.2	35/12
48	1888.5
49	1927.9
50	1967.2
51	2006.6	35/11
52	2045.9
53	2085.2
54	2124.6
55	2163.9
56	2203.3	25/7
57	2242.6
58	2282
59	2321.3
60	2360.7
61	2400

Harmonics

Approximation of harmonics in 61ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+19.7	-13.4	+0.0	+7.1	+6.2	+14.8	+19.7	+12.5	-12.5	+19.2	-13.4
	Relative (%)	+50.0	-34.1	+0.0	+18.1	+15.9	+37.6	+50.0	+31.7	-31.9	+48.7	-34.1
Steps (reduced)		31 (31)	48 (48)	61 (0)	71 (10)	79 (18)	86 (25)	92 (31)	97 (36)	101 (40)	106 (45)	109 (48)

Approximation of harmonics in 61ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+5.4	-4.9	-6.3	+0.0	+13.1	-7.2	+17.2	+7.1	+1.4	-0.5	+1.2
	Relative (%)	+13.7	-12.4	-16.0	+0.0	+33.2	-18.3	+43.8	+18.1	+3.4	-1.3	+3.1
Steps (reduced)		113 (52)	116 (55)	119 (58)	122 (0)	125 (3)	127 (5)	130 (8)	132 (10)	134 (12)	136 (14)	138 (16)