59ed4

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59ed4

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Prime factorization	59 (prime)
Step size	40.678¢
Octave	30\59ed4 (1220.34¢)
Twelfth	47\59ed4 (1911.86¢)
Consistency limit	1
Distinct consistency limit	1

59 equal divisions of the 4th harmonic (abbreviated 59ed4) is a nonoctave tuning system that divides the interval of 4/1 into 59 equal parts of about 40.7 ¢ each. Each step represents a frequency ratio of 4^1/59, or the 59th root of 4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	40.678
2	81.356	21/20, 22/21
3	122.034
4	162.712	11/10
5	203.39
6	244.068	15/13
7	284.746	13/11, 20/17
8	325.424
9	366.102	21/17, 26/21
10	406.78	19/15
11	447.458	22/17
12	488.136
13	528.814
14	569.492
15	610.169
16	650.847
17	691.525
18	732.203	26/17, 29/19
19	772.881
20	813.559
21	854.237
22	894.915
23	935.593
24	976.271
25	1016.949
26	1057.627
27	1098.305	17/9
28	1138.983	27/14, 29/15
29	1179.661
30	1220.339
31	1261.017	31/15
32	1301.695
33	1342.373
34	1383.051	20/9
35	1423.729
36	1464.407	7/3
37	1505.085	31/13
38	1545.763	22/9
39	1586.441
40	1627.119
41	1667.797
42	1708.475
43	1749.153
44	1789.831	31/11
45	1830.508
46	1871.186
47	1911.864
48	1952.542
49	1993.22
50	2033.898
51	2074.576
52	2115.254
53	2155.932
54	2196.61
55	2237.288
56	2277.966
57	2318.644
58	2359.322
59	2400

Harmonics

Approximation of harmonics in 59ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+20.3	+9.9	+0.0	-20.2	-10.4	+7.4	+20.3	+19.8	+0.1	-2.2	+9.9
	Relative (%)	+50.0	+24.4	+0.0	-49.7	-25.6	+18.3	+50.0	+48.7	+0.3	-5.3	+24.4
Steps (reduced)		30 (30)	47 (47)	59 (0)	68 (9)	76 (17)	83 (24)	89 (30)	94 (35)	98 (39)	102 (43)	106 (47)

Approximation of harmonics in 59ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.6	-12.9	-10.3	+0.0	+17.1	-0.5	-12.8	-20.2	+17.4	+18.2	-18.1
	Relative (%)	-16.3	-31.7	-25.3	+0.0	+42.0	-1.3	-31.4	-49.7	+42.7	+44.7	-44.5
Steps (reduced)		109 (50)	112 (53)	115 (56)	118 (0)	121 (3)	123 (5)	125 (7)	127 (9)	130 (12)	132 (14)	133 (15)