38edo

← 37edo

38edo

39edo →

Prime factorization	2 x 19
Step size	31.5789 ¢
Fifth	22\38 (694.737 ¢) (→ 11\19)
Semitones (A1:m2)	2:4 (63.16 ¢ : 126.3 ¢)
Consistency limit	5
Distinct consistency limit	5

38edo divides the octave into 38 equal parts of 31.578947 cents. Since 38 = 2*19, it can be thought of as two parallel 19edos. It tempers out the same 5-limit commas as 19edo, 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.

Intervals

Step	Cents	Ups and Downs Notation*
0	0.0000	Perfect 1sn	P1	D
1	31.5789	Up 1sn	^1	^D
2	63.1579	Aug 1sn, dim 2nd	A1, d2	D#, Ebb
3	94.7368	Upaug 1sn, downminor 2nd	^A1, vm2	^D#, vEb
4	126.3157	Minor 2nd	m2	Eb
5	157.8947	Mid 2nd	~2	vE
6	189.4737	Major 2nd	M2	E
7	221.0526	Upmajor 2nd	^M2	^E
8	252.6316	Aug 2nd, Dim 3rd	A2, d3	E#, Fb
9	284.2105	Downminor 3rd	vm3	vF
10	315.7895	Minor 3rd	m3	F
11	347.3684	Mid 3rd	~3	^F
12	378.9474	Major 3rd	M3	F#
13	410.5263	Upmajor 3rd, Downdim 4th	^M3, vd4	^F#, vGb
14	442.1053	Aug 3rd, dim 4th	A3, d4	Fx, Gb
15	473.6843	Down 4th	v4	vG
16	505.2632	Perfect 4th	P4	G
17	536.8421	Up 4th	^4	^G
18	568.4211	Aug 4th	A4	G#
19	600.0000	Upaug 4th, downdim 5th	^A4, vd5	^G#, vAb
20	631.5789	Dim 5th	d5	Ab
21	663.1579	Down 5th	v5	vA
22	694.7368	Perfect 5th	P5	A
23	726.3157	Up 5th	^5	^A
24	757.8947	Aug 5th, dim 6th	A5, d6	A#, Bbb
25	789.4737	Upaug 5th, downminor 6th	^A5, vm6	^A#, vBb
26	821.0526	Minor 6th	m6	Bb
27	852.6316	Mid 6th	~6	vB
28	884.2105	Major 6th	M6	B
29	915.7895	Upmajor 6th	^M6	^B
30	947.3684	Aug 6th, dim 7th	A6, d7	B#, Cb
31	978.9474	Downminor 7th	vm7	vC
32	1010.5263	Minor 7th	m7	C
33	1042.1053	Mid 7th	~7	^C
34	1073.6843	Major 7th	M7	C#
35	1105.2632	Upmajor 7th, Downdim 8ve	^M7, vd8	^C#, vDb
36	1136.8421	Aug 7th, dim 8ve	A7, d8	Cx, Db
37	1168.4211	Down 8ve	v8	vD
38	1200.0000	Perfect 8ve	P8	D

* Ups and downs may be substituted with semi-sharps and semi-flats, respectively