13ed4

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← 11ed413ed415ed4 →
Prime factorization 13 (prime)
Step size 184.615¢ 
Octave 7\13ed4 (1292.31¢)
Twelfth 10\13ed4 (1846.15¢)
Consistency limit 1
Distinct consistency limit 1

13 equal divisions of the 4th harmonic (abbreviated 13ed4) is a nonoctave tuning system that divides the interval of 4/1 into 13 equal parts of about 185 ¢ each. Each step represents a frequency ratio of 41/13, or the 13th root of 4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 184.615 19/17
2 369.231 11/9
3 553.846 15/11, 18/13, 19/14
4 738.462 23/15
5 923.077 17/10, 22/13
6 1107.692 19/10, 21/11
7 1292.308 23/11
8 1476.923 7/3
9 1661.538 13/5
10 1846.154
11 2030.769
12 2215.385 18/5
13 2400

Harmonics

Approximation of harmonics in 13ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +92.3 -55.8 +0.0 -17.1 +36.5 -45.7 +92.3 +73.0 +75.2 -89.8 -55.8
Relative (%) +50.0 -30.2 +0.0 -9.3 +19.8 -24.8 +50.0 +39.5 +40.7 -48.6 -30.2
Steps
(reduced)
7
(7)
10
(10)
13
(0)
15
(2)
17
(4)
18
(5)
20
(7)
21
(8)
22
(9)
22
(9)
23
(10)
Approximation of harmonics in 13ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -9.8 +46.6 -72.9 +0.0 +79.7 -19.3 +71.7 -17.1 +83.1 +2.5 -74.4
Relative (%) -5.3 +25.2 -39.5 +0.0 +43.1 -10.5 +38.8 -9.3 +45.0 +1.4 -40.3
Steps
(reduced)
24
(11)
25
(12)
25
(12)
26
(0)
27
(1)
27
(1)
28
(2)
28
(2)
29
(3)
29
(3)
29
(3)