59ed6

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59ed6

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Prime factorization	59 (prime)
Step size	52.5755¢
Octave	23\59ed6 (1209.24¢)
Twelfth	36\59ed6 (1892.72¢)
Consistency limit	3
Distinct consistency limit	3

59 equal divisions of the 6th harmonic (abbreviated 59ed6) is a nonoctave tuning system that divides the interval of 6/1 into 59 equal parts of about 52.6 ¢ each. Each step represents a frequency ratio of 6^1/59, or the 59th root of 6. It is a stretched version of 23edo, corresponding to ‘22.8243edo’.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	52.576	31/30, 34/33
2	105.151	33/31
3	157.727	23/21, 34/31
4	210.302	26/23
5	262.878	7/6
6	315.453	6/5
7	368.029	21/17, 26/21, 31/25
8	420.604	14/11, 23/18
9	473.18	25/19
10	525.755	19/14, 23/17
11	578.331	7/5
12	630.906
13	683.482
14	736.057	23/15, 26/17, 29/19
15	788.633	30/19
16	841.208
17	893.784
18	946.359	19/11
19	998.935
20	1051.51	11/6
21	1104.086	17/9
22	1156.661
23	1209.237
24	1261.812	27/13, 29/14
25	1314.388
26	1366.963	11/5
27	1419.539	25/11, 34/15
28	1472.114
29	1524.69	29/12
30	1577.265
31	1629.841
32	1682.416	29/11
33	1734.992	30/11
34	1787.567
35	1840.143	26/9, 29/10
36	1892.718
37	1945.294
38	1997.869	19/6
39	2050.445
40	2103.02
41	2155.596
42	2208.171	25/7
43	2260.747
44	2313.322	19/5
45	2365.898
46	2418.473
47	2471.049	25/6
48	2523.624	30/7
49	2576.2	31/7
50	2628.775
51	2681.351	33/7
52	2733.926	34/7
53	2786.502	5/1
54	2839.077	31/6
55	2891.653
56	2944.228
57	2996.804
58	3049.379
59	3101.955	6/1

Harmonics

Approximation of harmonics in 59ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+9.2	-9.2	+18.5	+0.2	+0.0	-4.0	-24.9	-18.5	+9.4	+2.1	+9.2
	Relative (%)	+17.6	-17.6	+35.1	+0.4	+0.0	-7.6	-47.3	-35.1	+17.9	+4.1	+17.6
Steps (reduced)		23 (23)	36 (36)	46 (46)	53 (53)	59 (0)	64 (5)	68 (9)	72 (13)	76 (17)	79 (20)	82 (23)

Approximation of harmonics in 59ed6

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-24.2	+5.2	-9.0	-15.6	-15.4	-9.2	+2.3	+18.7	-13.2	+11.4	-13.0
	Relative (%)	-46.0	+10.0	-17.2	-29.7	-29.4	-17.6	+4.4	+35.5	-25.2	+21.7	-24.7
Steps (reduced)		84 (25)	87 (28)	89 (30)	91 (32)	93 (34)	95 (36)	97 (38)	99 (40)	100 (41)	102 (43)	103 (44)