13ed9/4

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← 11ed9/413ed9/415ed9/4 →
Prime factorization 13 (prime)
Step size 107.993¢ 
Octave 11\13ed9/4 (1187.92¢)
(semiconvergent)
Twelfth 18\13ed9/4 (1943.88¢)
Consistency limit 2
Distinct consistency limit 2

13 equal divisions of 9/4 (abbreviated 13ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 13 equal parts of about 108 ¢ each. Each step represents a frequency ratio of (9/4)1/13, or the 13th root of 9/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 107.993 14/13, 17/16, 20/19, 21/20
2 215.986 8/7, 19/17, 23/20
3 323.979 6/5, 17/14, 23/19
4 431.972 13/10, 14/11, 22/17
5 539.965 11/8, 19/14, 23/17
6 647.958 16/11, 19/13, 23/16
7 755.952 17/11, 20/13
8 863.945 5/3, 13/8, 23/14
9 971.938 7/4, 19/11, 23/13
10 1079.931 13/7
11 1187.924 2/1
12 1295.917 17/8, 21/10, 23/11
13 1403.91

Harmonics

Approximation of harmonics in 13ed9/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -12.1 +41.9 -24.2 +21.5 +29.8 -21.0 -36.2 -24.2 +9.4 -47.6 +17.8
Relative (%) -11.2 +38.8 -22.4 +19.9 +27.6 -19.5 -33.5 -22.4 +8.7 -44.1 +16.5
Steps
(reduced)
11
(11)
18
(5)
22
(9)
26
(0)
29
(3)
31
(5)
33
(7)
35
(9)
37
(11)
38
(12)
40
(1)
Approximation of harmonics in 13ed9/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -12.8 -33.1 -44.6 -48.3 -45.3 -36.2 -21.8 -2.6 +20.9 +48.3 -28.6
Relative (%) -11.9 -30.7 -41.3 -44.7 -41.9 -33.5 -20.2 -2.5 +19.3 +44.8 -26.5
Steps
(reduced)
41
(2)
42
(3)
43
(4)
44
(5)
45
(6)
46
(7)
47
(8)
48
(9)
49
(10)
50
(11)
50
(11)