9ed7/4

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← 8ed7/49ed7/410ed7/4 →
Prime factorization 32
Step size 107.647¢ 
Octave 11\9ed7/4 (1184.12¢)
(semiconvergent)
Twelfth 18\9ed7/4 (1937.65¢) (→2\1ed7/4)
Consistency limit 3
Distinct consistency limit 2

9 equal divisions of 7/4 (abbreviated 9ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 9 equal parts of about 108 ¢ each. Each step represents a frequency ratio of (7/4)1/9, or the 9th root of 7/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 107.647 13/12, 14/13, 18/17, 20/19, 21/20, 22/21
2 215.295 8/7, 17/15
3 322.942 6/5, 11/9, 16/13, 19/16
4 430.589 13/10, 22/17
5 538.237 15/11, 19/14
6 645.884 10/7, 19/13, 22/15
7 753.531 17/11, 20/13
8 861.179 5/3, 13/8, 18/11, 21/13
9 968.826 7/4, 12/7

Harmonics

Approximation of harmonics in 9ed7/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -15.9 +35.7 -31.8 +12.5 +19.8 -31.8 -47.6 -36.3 -3.4 +46.9 +3.9
Relative (%) -14.8 +33.2 -29.5 +11.6 +18.4 -29.5 -44.3 -33.7 -3.1 +43.6 +3.7
Steps
(reduced)
11
(2)
18
(0)
22
(4)
26
(8)
29
(2)
31
(4)
33
(6)
35
(8)
37
(1)
39
(3)
40
(4)
Approximation of harmonics in 9ed7/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -27.0 -47.6 +48.2 +44.1 +46.8 -52.1 -38.1 -19.2 +3.9 +31.0 -45.9
Relative (%) -25.1 -44.3 +44.8 +41.0 +43.5 -48.4 -35.4 -17.9 +3.7 +28.8 -42.6
Steps
(reduced)
41
(5)
42
(6)
44
(8)
45
(0)
46
(1)
46
(1)
47
(2)
48
(3)
49
(4)
50
(5)
50
(5)