15ed5/3

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.
← 14ed5/3 15ed5/3 16ed5/3 →
Prime factorization 3 × 5
Step size 58.9572¢ 
Octave 20\15ed5/3 (1179.14¢) (→4\3ed5/3)
Twelfth 32\15ed5/3 (1886.63¢)
Consistency limit 3
Distinct consistency limit 3

15 equal divisions of 5/3 (abbreviated 15ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 15 equal parts of about 59 ¢ each. Each step represents a frequency ratio of (5/3)1/15, or the 15th root of 5/3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 58.957 22/21
2 117.914 14/13, 15/14
3 176.872 10/9, 11/10, 19/17, 21/19, 23/21
4 235.829 15/13, 17/15, 22/19
5 294.786 6/5, 13/11
6 353.743 11/9, 17/14, 21/17
7 412.701 14/11, 19/15
8 471.658 13/10, 17/13
9 530.615 15/11, 19/14, 23/17
10 589.572 7/5
11 648.53 13/9, 19/13, 22/15
12 707.487 3/2
13 766.444 11/7, 14/9, 17/11
14 825.401 21/13
15 884.359 5/3

Harmonics

Approximation of harmonics in 15ed5/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -20.9 -15.3 +17.2 -15.3 +22.8 -8.3 -3.6 +28.3 +22.8 -24.3 +1.9
Relative (%) -35.4 -26.0 +29.3 -26.0 +38.6 -14.0 -6.1 +48.0 +38.6 -41.2 +3.3
Steps
(reduced)
20
(5)
32
(2)
41
(11)
47
(2)
53
(8)
57
(12)
61
(1)
65
(5)
68
(8)
70
(10)
73
(13)
Approximation of harmonics in 15ed5/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -18.7 -29.1 +28.3 -24.5 -11.5 +7.5 -27.2 +1.9 -23.6 +13.8 -4.2
Relative (%) -31.8 -49.4 +48.0 -41.5 -19.5 +12.6 -46.1 +3.3 -40.0 +23.4 -7.1
Steps
(reduced)
75
(0)
77
(2)
80
(5)
81
(6)
83
(8)
85
(10)
86
(11)
88
(13)
89
(14)
91
(1)
92
(2)