38edf

← 37edf

38edf

39edf →

Prime factorization	2 × 19
Step size	18.4725¢
Octave	65\38edf (1200.71¢)
Twelfth	103\38edf (1902.67¢)
Consistency limit	6
Distinct consistency limit	6

Division of the just perfect fifth into 38 equal parts (38EDF) is related to 65edo, but with the 3/2 rather than the 2/1 being just. The octave is stretched by about 0.7125 cents and the step size is about 18.4725 cents.

Lookalikes: 65edo, 103edt

Harmonics

Approximation of prime harmonics in 38edf

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+0.71	+0.71	+3.03	-6.83	+4.99	-7.13	+8.73	+0.90	+2.64	+7.73	+3.11
	Relative (%)	+3.9	+3.9	+16.4	-37.0	+27.0	-38.6	+47.3	+4.9	+14.3	+41.9	+16.8
Steps (reduced)		65 (27)	103 (27)	151 (37)	182 (30)	225 (35)	240 (12)	266 (0)	276 (10)	294 (28)	316 (12)	322 (18)

Intervals

Intervals of 38edf

Step number	Cents value
1	18.4725
2	36.945
3	55.4175
4	73.89
5	92.3625
6	110.835
7	129.3075
8	147.78
9	166.2525
10	184.725
11	203.1975
12	221.67
13	240.1425
14	258.615
15	277.0875
16	295.56
17	314.0325
18	332.505
19	350.9775
20	369.45
21	387.9225
22	406.395
23	424.8675
24	443.34
25	461.8125
26	480.285
27	498.7575
28	517.23
29	535.7025
30	553.175
31	572.6475
32	591.12
33	609.5925
34	628.065
35	646.5375
36	664.01
37	683.4825
38	701.955
39	720.4275
40	738.9
41	757.3725
42	775.845
43	794.3175
44	812.79
45	831.2625
46	849.735
47	868.2075
48	886.605
49	905.1525
50	923.625
51	942.0975
52	960.57
53	979.0425
54	997.515
55	1015.9875
56	1034.46
57	1052.9235
58	1071.405
59	1089.8775
60	1108.35
61	1126.8225
62	1145.295
63	1163.7675
64	1182.24
65	1200.7125
66	1219.185
67	1237.6575
68	1256.13
69	1274.6025
70	1293.075
71	1311.5775
72	1330.02
73	1348.4925
74	1366.965
75	1385.4375
76	1403.91

Todo: complete table Add a third column that comments on the intervals, either what JI they approximate, what they are named, or how they can be used musically.