38edo

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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 pions 7mus
0
1 31.57895 33.4737 40.42105 (28.6BCA16)
2 63.1579 66.9474 80.8421 (50.D79416)
3 94.7368 100.42105 121.2632 (79.435E16)
4 126.3157 133.8947 161.6843 (A1.AF2916)
5 157.8947 167.3684 202.1053 (CA.1AF316)
6 189.4737 200.8421 242.5263 (F2.86BD16)
7 221.0526 234.3157 282.9474 (11A.F28716)
8 252.6316 267.7895 323.3684 (143.5E5116)
9 284.2105 301.2632 365.7895 (16B.CA1B16)
10 315.7895 334.7368 404.2105 (194.35E516)
11 347.3684 368.2105 444.6316 (1BC.A1AF16)
12 378.9474 401.6843 485.0526 (1E5.0D7916)
13 410.5263 435.1579 525.4737 (20D.794316)
14 442.1053 468.6316 565.8947 (235.E50E16)
15 473.6843 502.1053 606.3157 (25E.50D816)
16 505.2632 535.57895 646.7368 (286.BCA216)
17 536.8421 569.0526 687.1579 (2AF.286C16)
18 568.42105 602.5263 727.57895 (2D7.943616)
19 600 636 768 (30016)
20 631.57895 669.4737 808.42105 (328.6BCA16)
21 663.1579 702.9474 848.8421 (350.D79416)
22 694.7368 736.42105 889.2632 (379.435E16)
23 726.3157 769.8947 929.6843 (3A1.AF2916)
24 757.8947 803.3684 970.1053 (3CA.1AF316)
25 789.4737 836.8421 1010.5263 (3F2.86BD16)
26 821.0526 870.3157 1050.9474 (41A.F28716)
27 852.6316 903.7895 1091.3684 (443.5E5116)
28 884.2105 937.2632 1131.7895 (46B.CA1B16)
29 915.7895 970.7368 1172.2105 (494.35E516)
30 947.3684 1004.2105 1212.6316 (4BC.A1AF16)
31 978.9474 1037.6843 1253.0526 (4E5.0D7916)
32 1010.5263 1071.1579 1293.4737 (50D.794316)
33 1042.1053 1104.6316 1333.8947 (535.E50E16)
34 1073.6843 1138.1053 1374.3157 (55E.50D816)
35 1105.2632 1171.57895 1414.7368 (586.BCA216)
36 1136.8421 1205.0526 1455.1579 (5AF.286C16)
37 1168.42105 1235.5263 1495.57895 (5D7.943616)
38 1200 1272 1536 (60016)