9ed9/5

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.
← 8ed9/59ed9/510ed9/5 →
Prime factorization 32
Step size 113.066¢ 
Octave 11\9ed9/5 (1243.73¢)
Twelfth 17\9ed9/5 (1922.13¢)
Consistency limit 3
Distinct consistency limit 3

9 equal divisions of 9/5 (abbreviated 9ed9/5) is a nonoctave tuning system that divides the interval of 9/5 into 9 equal parts of about 113 ¢ each. Each step represents a frequency ratio of (9/5)1/9, or the 9th root of 9/5.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 113.066 15/14, 22/21
2 226.133 19/17
3 339.199 6/5, 11/9
4 452.265 9/7, 14/11, 17/13
5 565.331 7/5, 15/11
6 678.398 3/2, 19/13, 22/15
7 791.464 11/7, 14/9
8 904.53 5/3
9 1017.596 9/5, 11/6

Harmonics

Approximation of harmonics in 9ed9/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +43.7 +20.2 -25.6 +40.3 -49.2 +23.2 +18.1 +40.3 -29.0 +32.1 -5.4
Relative (%) +38.7 +17.8 -22.6 +35.7 -43.5 +20.5 +16.0 +35.7 -25.6 +28.4 -4.8
Steps
(reduced)
11
(2)
17
(8)
21
(3)
25
(7)
27
(0)
30
(3)
32
(5)
34
(7)
35
(8)
37
(1)
38
(2)
Approximation of harmonics in 9ed9/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -30.9 -46.2 -52.6 -51.2 -43.1 -29.0 -9.5 +14.7 +43.3 -37.2 -1.1
Relative (%) -27.4 -40.8 -46.5 -45.3 -38.1 -25.6 -8.4 +13.0 +38.3 -32.9 -1.0
Steps
(reduced)
39
(3)
40
(4)
41
(5)
42
(6)
43
(7)
44
(8)
45
(0)
46
(1)
47
(2)
47
(2)
48
(3)