8edt

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← 7edt8edt9edt →
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, 49/48, 55/54, 56/55, 64/63, 81/80
1 237.744 7/6, 8/7, 9/8, 15/13, 52/45, 55/48, 55/49, 63/55, 64/55, 81/70
2 475.489 4/3, 13/10, 21/16, 35/26, 35/27, 55/42, 64/49, 72/55
3 713.233 3/2, 20/13, 32/21, 40/27, 49/32, 49/33, 52/35, 54/35, 55/36
4 950.978 7/4, 12/7, 26/15, 45/26, 55/32, 56/33
5 1188.72 2/1, 35/18, 39/20, 55/28, 63/32, 81/40
6 1426.47 9/4, 16/7, 30/13, 55/24, 78/35, 81/35
7 1664.21 8/3, 13/5, 18/7, 21/8, 55/21, 70/27
8 1901.96 3/1, 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)