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	52.6	31/30, 34/33
2	105.2	33/31
3	157.7	23/21, 34/31
4	210.3	26/23
5	262.9	7/6
6	315.5	6/5
7	368	21/17, 26/21, 31/25
8	420.6	14/11, 23/18
9	473.2	25/19
10	525.8	19/14, 23/17
11	578.3	7/5
12	630.9
13	683.5
14	736.1	23/15, 26/17, 29/19
15	788.6	30/19
16	841.2
17	893.8
18	946.4	19/11
19	998.9
20	1051.5	11/6
21	1104.1	17/9
22	1156.7
23	1209.2
24	1261.8	27/13, 29/14
25	1314.4
26	1367	11/5
27	1419.5	25/11, 34/15
28	1472.1
29	1524.7	29/12
30	1577.3
31	1629.8
32	1682.4	29/11
33	1735	30/11
34	1787.6
35	1840.1	26/9, 29/10
36	1892.7
37	1945.3
38	1997.9	19/6
39	2050.4
40	2103
41	2155.6
42	2208.2	25/7
43	2260.7
44	2313.3	19/5
45	2365.9
46	2418.5
47	2471	25/6
48	2523.6	30/7
49	2576.2	31/7
50	2628.8
51	2681.4	33/7
52	2733.9	34/7
53	2786.5	5/1
54	2839.1	31/6
55	2891.7
56	2944.2
57	2996.8
58	3049.4
59	3102	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)