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	40.7
2	81.4	21/20, 22/21
3	122
4	162.7	11/10
5	203.4
6	244.1	15/13
7	284.7	13/11, 20/17
8	325.4
9	366.1	21/17, 26/21
10	406.8	19/15
11	447.5	22/17
12	488.1
13	528.8
14	569.5
15	610.2
16	650.8
17	691.5
18	732.2	26/17, 29/19
19	772.9
20	813.6
21	854.2
22	894.9
23	935.6
24	976.3
25	1016.9
26	1057.6
27	1098.3	17/9
28	1139	27/14, 29/15
29	1179.7
30	1220.3
31	1261	31/15
32	1301.7
33	1342.4
34	1383.1	20/9
35	1423.7
36	1464.4	7/3
37	1505.1	31/13
38	1545.8	22/9
39	1586.4
40	1627.1
41	1667.8
42	1708.5
43	1749.2
44	1789.8	31/11
45	1830.5
46	1871.2
47	1911.9
48	1952.5
49	1993.2
50	2033.9
51	2074.6
52	2115.3
53	2155.9
54	2196.6
55	2237.3
56	2278
57	2318.6
58	2359.3
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)