8ed7/4

From Xenharmonic Wiki
Jump to navigation Jump to search
Icon-Stub.png This page is a stub. You can help the Xenharmonic Wiki by expanding it.
← 7ed7/48ed7/49ed7/4 →
Prime factorization 23
Step size 121.103¢ 
Octave 10\8ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth 16\8ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit 8
Distinct consistency limit 2

8 equal divisions of 7/4 (abbreviated 8ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 8 equal parts of about 121 ¢ each. Each step represents a frequency ratio of (7/4)1/8, or the 8th root of 7/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 121.103 11/10, 13/12, 14/13, 15/14, 16/15, 17/16, 18/17, 20/19, 21/20
2 242.206 7/6, 8/7, 9/8, 15/13, 17/15, 20/17, 22/19
3 363.31 5/4, 16/13, 17/14, 21/17
4 484.413 4/3, 13/10, 17/13, 19/14, 21/16
5 605.516 7/5, 10/7, 13/9, 17/12, 18/13
6 726.619 3/2, 14/9, 20/13
7 847.723 5/3, 8/5, 13/8, 21/13
8 968.826 7/4, 12/7, 16/9, 19/11

Harmonics

Approximation of harmonics in 8ed7/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +11.0 +35.7 +22.1 -0.9 +46.7 +22.1 +33.1 -49.7 +10.1 -33.8 +57.8
Relative (%) +9.1 +29.5 +18.2 -0.8 +38.6 +18.2 +27.3 -41.0 +8.3 -27.9 +47.7
Steps
(reduced)
10
(2)
16
(0)
20
(4)
23
(7)
26
(2)
28
(4)
30
(6)
31
(7)
33
(1)
34
(2)
36
(4)
Approximation of harmonics in 8ed7/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +40.3 +33.1 +34.8 +44.1 +60.3 -38.7 -11.2 +21.1 +57.8 -22.8 +21.4
Relative (%) +33.3 +27.3 +28.7 +36.4 +49.8 -31.9 -9.2 +17.4 +47.7 -18.8 +17.6
Steps
(reduced)
37
(5)
38
(6)
39
(7)
40
(0)
41
(1)
41
(1)
42
(2)
43
(3)
44
(4)
44
(4)
45
(5)