37edf

← 36edf

37edf

38edf →

Prime factorization	37 (prime)
Step size	18.9718¢
Octave	63\37edf (1195.22¢)
Twelfth	100\37edf (1897.18¢)
Consistency limit	2
Distinct consistency limit	2

37 equal divisions of the perfect fifth (abbreviated 37edf or 37ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 37 equal parts of about 19⁠ ⁠¢ each. Each step represents a frequency ratio of (3/2)^1/37, or the 37th root of 3/2.

Theory

37edf corresponds to 63.2519edo, similar to every fourth step of 253edo. It is related to the regular temperament which tempers out 385/384, 12005/11979, and 820125/819896 in the 11-limit, which is supported by 63edo, 190edo, and 253edo among others.

Harmonics

Approximation of harmonics in 37edf

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-4.78	-4.78	+9.41	+2.53	+9.41	+8.15	+4.63	+9.41	-2.24	+3.50	+4.63
	Relative (%)	-25.2	-25.2	+49.6	+13.4	+49.6	+42.9	+24.4	+49.6	-11.8	+18.4	+24.4
Steps (reduced)		63 (26)	100 (26)	127 (16)	147 (36)	164 (16)	178 (30)	190 (5)	201 (16)	210 (25)	219 (34)	227 (5)

Approximation of harmonics in 37edf

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-1.14	+3.37	-2.24	-0.15	+8.73	+4.63	+5.89	-7.02	+3.37	-1.28	-2.35
	Relative (%)	-6.0	+17.7	-11.8	-0.8	+46.0	+24.4	+31.0	-37.0	+17.7	-6.8	-12.4
Steps (reduced)		234 (12)	241 (19)	247 (25)	253 (31)	259 (0)	264 (5)	269 (10)	273 (14)	278 (19)	282 (23)	286 (27)

Intervals

Intervals of 37edf

degree	cents value	corresponding JI intervals	comments
0		exact 1/1
1	18.9718
2	37.9435	45/44
3	56.9153
4	75.887	25/24
5	94.8588
6	113.8305	16/15
7	132.8023
8	151.7741	12/11
9	170.7458
10	189.7176	10/9
11	208.6893	9/8
12	227.6611	8/7
13	246.6328	15/13
14	265.6046	7/6
15	284.5764	33/28
16	303.5481	25/21
17	322.5199	6/5
18	341.4916	11/9
19	360.4634	27/22
20	379.4351	5/4
21	398.4069	34/27
22	417.3786	14/11
23	436.3504	9/7
24	455.3222	13/10
25	474.2939
26	493.2657	4/3
27	512.2374
28	531.2092	15/11
29	550.1809	11/8	pseudo-25/18
30	569.1527		real 25/18
31	588.1245	45/32, 7/5
32	607.0962	64/45, 10/7
33	626.068		real 36/25
34	645.0397	16/11	pseudo-36/25
35	664.0115	22/15
36	682.9832	40/27
37	701.955	exact 3/2	just perfect fifth
38	720.9268
39	739.8985	135/88
40	758.8703
41	777.842	25/16
42	796.8138
43	815.7855	8/5
44	834.7573
45	853.7291	18/11
46	872.7008
47	891.6726	5/3
48	910.6443	27/16
49	929.6161	12/7
50	948.5978	45/26
51	967.5596	7/4
52	986.5314	99/56
53	1005.5031	25/14
54	1024.4749	9/5
55	1043.4466
56	1062.4184
57	1081.3901	15/8
58	1100.3619	17/9
59	1119.3336	21/11
60	1138.3054	27/14
61	1157.2772	39/20
62	1176.2489
63	1195.2007	2/1
64	1214.1924
65	1233.1642	45/22
66	1252.1359	33/16	pseudo-25/12
67	1271.1077		real 25/12
68	1290.0795	135/64, 21/10
69	1309.0512	32/15, 15/7
70	1328.023		real 54/25
71	1347.9947	24/11	pseudo-54/25
72	1365.9668	11/5
73	1385.9382	20/9
74	1403.91	exact 9/4

Related regular temperaments

7-limit 63&190

Commas: 2460375/2458624, 514714375/509607936

POTE generator: ~1728/1715 = 18.957

Mapping: [<1 1 3 2|, <0 37 -43 51|]

EDOs: 63, 190, 253

11-limit 63&190

Commas: 385/384, 12005/11979, 820125/819896

POTE generator: ~99/98 = 18.957

Mapping: [<1 1 3 2 3|, <0 37 -43 51 29|]

EDOs: 63, 190, 253

13-limit 63&190

Commas: 385/384, 1575/1573, 2200/2197, 4459/4455

POTE generator: ~99/98 = 18.959

Mapping: [<1 1 3 2 3 4|, <0 37 -43 51 29 -19|]

EDOs: 63, 190, 253