59edt

← 58edt

59edt

60edt →

Prime factorization	59 (prime)
Step size	32.2365¢
Octave	37\59edt (1192.75¢)
Consistency limit	5
Distinct consistency limit	5

59EDT is the equal division of the third harmonic into 59 parts of 32.2365 cents each, corresponding to 37.2249 edo. It is related to the regular temperament which tempers out |413 -347 59> in the 5-limit, which is supported by 335, 1489, 1824, 2159, 2494, 2829, and 3164 EDOs.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	32.237
2	64.473	27/26, 28/27, 29/28
3	96.71	18/17, 19/18
4	128.946	14/13
5	161.183	34/31
6	193.419	19/17, 29/26
7	225.656	33/29
8	257.892	22/19
9	290.129	13/11
10	322.365
11	354.602	27/22
12	386.838	5/4
13	419.075	14/11
14	451.311
15	483.548
16	515.784	31/23
17	548.021
18	580.257
19	612.494	27/19
20	644.731
21	676.967	34/23
22	709.204
23	741.44	23/15
24	773.677	25/16
25	805.913
26	838.15
27	870.386
28	902.623
29	934.859
30	967.096
31	999.332
32	1031.569
33	1063.805
34	1096.042
35	1128.278	23/12
36	1160.515
37	1192.751
38	1224.988
39	1257.224	29/14, 31/15
40	1289.461	19/9
41	1321.698
42	1353.934
43	1386.171	29/13
44	1418.407	34/15
45	1450.644
46	1482.88	33/14
47	1515.117	12/5
48	1547.353	22/9
49	1579.59
50	1611.826	33/13
51	1644.063	31/12
52	1676.299	29/11
53	1708.536
54	1740.772
55	1773.009
56	1805.245	17/6
57	1837.482	26/9
58	1869.718
59	1901.955	3/1

Prime harmonics

Approximation of prime harmonics in 59edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-7.2	+0.0	-14.0	+16.0	+7.2	+8.1	-5.0	-4.1	-12.5	+5.2	-13.5
	Relative (%)	-22.5	+0.0	-43.3	+49.7	+22.3	+25.2	-15.5	-12.8	-38.9	+16.2	-41.9
Steps (reduced)		37 (37)	59 (0)	86 (27)	105 (46)	129 (11)	138 (20)	152 (34)	158 (40)	168 (50)	181 (4)	184 (7)

Approximation of prime harmonics in 59edt

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+2.5	-14.0	+0.3	+7.5	-7.1	+0.6	+7.4	+6.1	+2.5	-13.4	+11.0
	Relative (%)	+7.9	-43.4	+0.8	+23.1	-22.1	+1.9	+22.9	+19.1	+7.7	-41.5	+34.3
Steps (reduced)		194 (17)	199 (22)	202 (25)	207 (30)	213 (36)	219 (42)	221 (44)	226 (49)	229 (52)	230 (53)	235 (58)

Related regular temperaments

149&186 temperament

5-limit

Comma: |118 12 -59>

POTE generator: ~3125/3072 = 32.2390

Map: [<1 0 2|, <0 59 12|]

EDOs: 37, 149, 186, 335, 484, 521

7-limit 149&186

Commas: 3136/3125, 49433168575/48922361856

POTE generator: ~49/48 = 32.2368

Map: [<1 0 2 2|, <0 59 12 30|]

EDOs: 37, 149, 186, 335

7-limit 149d&186

Commas: 1280000000/1275989841, 8589934592/8544921875

POTE generator: ~3125/3072 = 32.2456

Map: [<1 0 2 7|, <0 59 12 -156|]

EDOs: 149d, 186, 335d, 521, 707

7-limit 149&186d

Commas: 29360128/29296875, 1937102445/1927561216

POTE generator: ~3125/3072 = 32.2308

Map: [<1 0 2 -2|, <0 59 12 179|]

EDOs: 149, 186d, 335d, 484, 633

335&2159 temperament

5-limit

Comma: |413 -347 59>

POTE generator: ~|-119 100 -17> = 32.2373

Map: [<1 0 -7|, <0 59 347|]

EDOs: 335, 1489, 1824, 2159, 2494, 2829, 3164