38edo

38 tone equal temperament

38edo divides the octave into 38 equal parts of 31.579 cents. Since 38 = 2*19, it can be thought of as two parallel 19edos. It tempers out the same 5-limit commas as 19, namely 81/80, 3125/3072 and 15625/15552. In the 7-limit, we can add 50/49, and tempering out 81/80 and 50/49 gives injera temperament, for which 38 is the optimal patent val. In the 11-limit, we can add 121/120 and 176/175.

38-EDO Intervals:

Step	Size in
	Cents	7mus
0	0.0000	0
1	31.57895	40.42105 (28.6BCA16)
2	63.1579	80.8421 (50.D79416)
3	94.7368	121.2632 (79.435E16)
4	126.3157	161.6843 (A1.AF2916)
5	157.8947	202.1053 (CA.1AF316)
6	189.4737	242.5263 (F2.86BD16)
7	221.0526	282.9474 (11A.F28716)
8	252.6316	323.3684 (143.5E5116)
9	284.2105	365.7895 (16B.CA1B16)
10	315.7895	404.2105 (194.35E516)
11	347.3684	444.6316 (1BC.A1AF16)
12	378.9474	485.0526 (1E5.0D7916)
13	410.5263	525.4737 (20D.794316)
14	442.1053	565.8947 (235.E50E16)
15	473.6843	606.3157 (25E.50D816)
16	505.2632	646.7368 (286.BCA216)
17	536.8421	687.1579 (2AF.286C16)
18	568.42105	727.57895 (2D7.943616)
19	600	768 (30016)
20	631.57895	808.42105 (328.6BCA16)
21	663.1579	848.8421 (350.D79416)
22	694.7368	889.2632 (379.435E16)
23	726.3157	929.6843 (3A1.AF2916)
24	757.8947	970.1053 (3CA.1AF316)
25	789.4737	1010.5263 (3F2.86BD16)
26	821.0526	1050.9474 (41A.F28716)
27	852.6316	1091.3684 (443.5E5116)
28	884.2105	1131.7895 (46B.CA1B16)
29	915.7895	1172.2105 (494.35E516)
30	947.3684	1212.6316 (4BC.A1AF16)
31	978.9474	1253.0526 (4E5.0D7916)
32	1010.5263	1293.4737 (50D.794316)
33	1042.1053	1333.8947 (535.E50E16)
34	1073.6843	1374.3157 (55E.50D816)
35	1105.2632	1414.7368 (586.BCA216)
36	1136.8421	1455.1579 (5AF.286C16)
37	1168.42105	1495.57895 (5D7.943616)
38	1200	1536 (60016)