9ed5/4

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Prime factorization 32
Step size 42.9237¢ 
Octave 28\9ed5/4 (1201.86¢)
(convergent)
Twelfth 44\9ed5/4 (1888.64¢)
(semiconvergent)
Consistency limit 6
Distinct consistency limit 2

9 equal divisions of 5/4 (abbreviated 9ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 9 equal parts of about 42.9 ¢ each. Each step represents a frequency ratio of (5/4)1/9, or the 9th root of 5/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 42.924
2 85.847 17/16, 18/17, 20/19
3 128.771 12/11, 13/12, 14/13, 15/14, 16/15, 19/18
4 171.695 9/8, 11/10
5 214.619 10/9, 17/15, 19/17
6 257.542 7/6, 8/7, 13/11, 15/13, 22/19
7 300.466 6/5, 19/16, 20/17
8 343.39 17/14, 21/17
9 386.314 5/4, 11/9, 14/11, 16/13

Harmonics

Approximation of harmonics in 9ed5/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.9 -13.3 +3.7 +3.7 -11.4 -20.8 +5.6 +16.3 +5.6 +12.3 -9.6
Relative (%) +4.3 -31.0 +8.7 +8.7 -26.7 -48.4 +13.0 +38.0 +13.0 +28.6 -22.3
Steps
(reduced)
28
(1)
44
(8)
56
(2)
65
(2)
72
(0)
78
(6)
84
(3)
89
(8)
93
(3)
97
(7)
100
(1)
Approximation of harmonics in 9ed5/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -19.4 -18.9 -9.6 +7.5 -11.6 +18.2 +10.4 +7.5 +8.8 +14.2 -19.9
Relative (%) -45.2 -44.1 -22.3 +17.4 -27.1 +42.3 +24.3 +17.4 +20.6 +33.0 -46.3
Steps
(reduced)
103
(4)
106
(7)
109
(1)
112
(4)
114
(6)
117
(0)
119
(2)
121
(4)
123
(6)
125
(8)
126
(0)