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	Hekts	Approximate ratios
0	0	0	1/1
1	32.2	22
2	64.5	44.1	27/26, 28/27, 29/28
3	96.7	66.1	18/17, 19/18
4	128.9	88.1	14/13
5	161.2	110.2	34/31
6	193.4	132.2	19/17, 29/26
7	225.7	154.2	33/29
8	257.9	176.3	22/19
9	290.1	198.3	13/11
10	322.4	220.3
11	354.6	242.4	27/22
12	386.8	264.4	5/4
13	419.1	286.4	14/11
14	451.3	308.5
15	483.5	330.5
16	515.8	352.5	31/23
17	548	374.6
18	580.3	396.6
19	612.5	418.6	27/19
20	644.7	440.7
21	677	462.7	34/23
22	709.2	484.7
23	741.4	506.8	23/15
24	773.7	528.8	25/16
25	805.9	550.8
26	838.1	572.9
27	870.4	594.9
28	902.6	616.9
29	934.9	639
30	967.1	661
31	999.3	683.1
32	1031.6	705.1
33	1063.8	727.1
34	1096	749.2
35	1128.3	771.2	23/12
36	1160.5	793.2
37	1192.8	815.3
38	1225	837.3
39	1257.2	859.3	29/14, 31/15
40	1289.5	881.4	19/9
41	1321.7	903.4
42	1353.9	925.4
43	1386.2	947.5	29/13
44	1418.4	969.5	34/15
45	1450.6	991.5
46	1482.9	1013.6	33/14
47	1515.1	1035.6	12/5
48	1547.4	1057.6	22/9
49	1579.6	1079.7
50	1611.8	1101.7	33/13
51	1644.1	1123.7	31/12
52	1676.3	1145.8	29/11
53	1708.5	1167.8
54	1740.8	1189.8
55	1773	1211.9
56	1805.2	1233.9	17/6
57	1837.5	1255.9	26/9
58	1869.7	1278
59	1902	1300	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