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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
0
0
1
31.579
2
63.158
3
94.737
4
126.316
5
157.895
6
189.474
7
221.053
8
252.632
9
284.211
10
315.789
11
347.368
12
378.947
13
410.526
14
442.105
15
473.684
16
505.263
17
536.842
18
568.421
19
600
20
631.579
21
663.158
22
694.737
23
726.316
24
757.895
25
789.474
26
821.053
27
852.632
28
884.211
29
915.789
30
947.368
31
978.947
32
1010.526
33
1042.105
34
1073.684
35
1105.263
36
1136.842
37
1168.421