8edt

← 7edt

8edt

9edt →

Prime factorization	23
Step size	237.744¢
Octave	5\8edt (1188.72¢) (convergent)
Consistency limit	10
Distinct consistency limit	4

8 equal divisions of the tritave (8edt) is the nonoctave tuning system derived by dividing the tritave (3/1) into 13 equal steps of 237.744 cents each, or the eighth root of 3. As the double of 4edt, harmonically, it is the analog of 10edo for Lambda-based systems. However, the full 3:5:7 triad is already present in 4edt which is unlike the situation in 10edo where 4:5:6 gains a new better approximation than the sus4 triad in 5edo.

What it does introduce are flat pseudooctaves and sharp 3:2's, making it related to 5edo melodically.

Interval table

Steps	Cents	Approximate ratios
0	0	1/1, 33/32, 36/35, 40/39, 49/48, 55/54, 56/55, 64/63, 81/80
1	237.744	7/6, 8/7, 9/8, 10/9, 15/13, 32/27, 33/28, 39/35, 49/44, 52/45, 55/48, 55/49, 63/55, 64/55, 81/70
2	475.489	4/3, 9/7, 13/10, 14/11, 21/16, 27/20, 35/26, 35/27, 49/36, 50/39, 55/42, 64/49, 66/49, 72/55
3	713.233	3/2, 14/9, 20/13, 32/21, 39/25, 40/27, 49/32, 49/33, 52/35, 54/35, 55/36, 72/49, 81/52, 81/55
4	950.978	7/4, 12/7, 16/9, 26/15, 27/16, 45/26, 55/32, 56/33
5	1188.72	2/1, 25/13, 27/14, 35/18, 39/20, 49/24, 52/27, 55/27, 55/28, 63/32, 64/33, 80/39, 81/40
6	1426.47	7/3, 9/4, 16/7, 20/9, 30/13, 33/14, 49/22, 55/24, 78/35, 81/35
7	1664.21	8/3, 13/5, 18/7, 21/8, 27/10, 28/11, 35/13, 55/21, 70/27, 81/32
8	1901.96	3/1, 32/11, 35/12, 40/13, 49/16, 55/18, 64/21, 80/27

Prime harmonics

Approximation of prime harmonics in 8edt

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	absolute (¢)	-11	+0	+67	-40	-110	+77	+88	-105	+40	+114	-1
	relative (%)	-5	+0	+28	-17	-46	+32	+37	-44	+17	+48	-1
Steps (reduced)		5 (5)	8 (0)	12 (4)	14 (6)	17 (1)	19 (3)	21 (5)	21 (5)	23 (7)	25 (1)	25 (1)