59ed7/3

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59ed7/3

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Prime factorization	59 (prime)
Step size	24.8622¢
Octave	48\59ed7/3 (1193.39¢)
Twelfth	76\59ed7/3 (1889.53¢)
Consistency limit	3
Distinct consistency limit	3

59 equal divisions of 7/3 (abbreviated 59ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 59 equal parts of about 24.9⁠ ⁠¢ each. Each step represents a frequency ratio of (7/3)^1/59, or the 59th root of 7/3.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	24.9
2	49.7	34/33
3	74.6	23/22
4	99.4
5	124.3
6	149.2
7	174
8	198.9
9	223.8	25/22, 33/29
10	248.6
11	273.5	34/29
12	298.3	32/27
13	323.2
14	348.1
15	372.9	31/25
16	397.8	29/23
17	422.7
18	447.5	22/17
19	472.4	21/16, 25/19
20	497.2	4/3
21	522.1	23/17
22	547	26/19
23	571.8
24	596.7	31/22
25	621.6	10/7, 33/23
26	646.4	29/20
27	671.3	25/17
28	696.1
29	721
30	745.9
31	770.7
32	795.6
33	820.5
34	845.3	31/19
35	870.2	33/20
36	895
37	919.9	17/10
38	944.8	19/11
39	969.6	7/4
40	994.5	16/9
41	1019.4
42	1044.2	31/17
43	1069.1
44	1093.9
45	1118.8
46	1143.7	29/15
47	1168.5
48	1193.4
49	1218.2
50	1243.1
51	1268
52	1292.8
53	1317.7	15/7
54	1342.6
55	1367.4	11/5
56	1392.3
57	1417.1	25/11, 34/15
58	1442	23/10
59	1466.9	7/3

Harmonics

Approximation of harmonics in 59ed7/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-6.6	-12.4	+11.6	-1.7	+5.8	-12.4	+5.0	+0.0	-8.4	+0.7	-0.8
	Relative (%)	-26.6	-50.0	+46.8	-7.0	+23.4	-50.0	+20.2	+0.0	-33.6	+2.7	-3.2
Steps (reduced)		48 (48)	76 (17)	97 (38)	112 (53)	125 (7)	135 (17)	145 (27)	153 (35)	160 (42)	167 (49)	173 (55)

Approximation of harmonics in 59ed7/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+9.8	+5.8	+10.7	-1.6	-7.1	-6.6	-0.8	+9.9	+0.0	-5.9	-8.3
	Relative (%)	+39.5	+23.4	+43.0	-6.4	-28.6	-26.6	-3.0	+39.8	+0.0	-23.9	-33.4
Steps (reduced)		179 (2)	184 (7)	189 (12)	193 (16)	197 (20)	201 (24)	205 (28)	209 (32)	212 (35)	215 (38)	218 (41)