11ed5/2

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← 10ed5/211ed5/212ed5/2 →
Prime factorization 11 (prime)
Step size 144.21¢ 
Octave 8\11ed5/2 (1153.68¢)
Twelfth 13\11ed5/2 (1874.73¢)
(semiconvergent)
Consistency limit 3
Distinct consistency limit 3

11 equal divisions of 5/2 (abbreviated 11ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 11 equal parts of about 144 ¢ each. Each step represents a frequency ratio of (5/2)1/11, or the 11th root of 5/2.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 144.21 15/14, 21/19
2 288.421 6/5, 7/6, 13/11
3 432.631 9/7, 19/15, 22/17
4 576.841 7/5
5 721.052 3/2
6 865.262 5/3
7 1009.472 9/5
8 1153.683
9 1297.893 15/7, 19/9, 21/10
10 1442.103 7/3
11 1586.314 5/2

Harmonics

Approximation of harmonics in 11ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -46.3 -27.2 +51.6 -46.3 +70.7 -52.0 +5.3 -54.4 +51.6 +30.8 +24.4
Relative (%) -32.1 -18.9 +35.8 -32.1 +49.0 -36.1 +3.6 -37.8 +35.8 +21.3 +16.9
Steps
(reduced)
8
(8)
13
(2)
17
(6)
19
(8)
22
(0)
23
(1)
25
(3)
26
(4)
28
(6)
29
(7)
30
(8)
Approximation of harmonics in 11ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +30.0 +45.9 +70.7 -41.1 -1.8 +43.5 -50.2 +5.3 +65.0 -15.5 +51.7
Relative (%) +20.8 +31.8 +49.0 -28.5 -1.3 +30.1 -34.8 +3.6 +45.1 -10.8 +35.9
Steps
(reduced)
31
(9)
32
(10)
33
(0)
33
(0)
34
(1)
35
(2)
35
(2)
36
(3)
37
(4)
37
(4)
38
(5)