15ed9/4

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.
← 13ed9/415ed9/417ed9/4 →
Prime factorization 3 × 5
Step size 93.594¢ 
Octave 13\15ed9/4 (1216.72¢)
Twelfth 20\15ed9/4 (1871.88¢) (→4\3ed9/4)
Consistency limit 2
Distinct consistency limit 2

15 equal divisions of 9/4 (abbreviated 15ed9/4) is a nonoctave tuning system that divides the interval of 9/4 into 15 equal parts of about 93.6 ¢ each. Each step represents a frequency ratio of (9/4)1/15, or the 15th root of 9/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 93.594 18/17, 19/18, 22/21, 23/22
2 187.188 19/17, 21/19
3 280.782 7/6, 13/11
4 374.376 5/4, 21/17
5 467.97 17/13, 22/17
6 561.564 7/5, 18/13
7 655.158 13/9, 19/13, 22/15
8 748.752 17/11, 23/15
9 842.346 18/11, 21/13, 23/14
10 935.94 12/7, 19/11
11 1029.534 11/6
12 1123.128 17/9, 21/11, 23/12
13 1216.722 2/1
14 1310.316 15/7, 19/9
15 1403.91

Harmonics

Approximation of harmonics in 15ed9/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +16.7 -30.1 +33.4 +21.5 -13.4 +0.6 -43.4 +33.4 +38.2 -33.2 +3.4
Relative (%) +17.9 -32.1 +35.7 +23.0 -14.3 +0.6 -46.4 +35.7 +40.8 -35.5 +3.6
Steps
(reduced)
13
(13)
20
(5)
26
(11)
30
(0)
33
(3)
36
(6)
38
(8)
41
(11)
43
(13)
44
(14)
46
(1)
Approximation of harmonics in 15ed9/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -41.6 +17.3 -8.6 -26.7 -38.1 -43.4 -43.4 -38.6 -29.5 -16.5 +0.2
Relative (%) -44.5 +18.5 -9.2 -28.5 -40.7 -46.4 -46.4 -41.3 -31.5 -17.6 +0.2
Steps
(reduced)
47
(2)
49
(4)
50
(5)
51
(6)
52
(7)
53
(8)
54
(9)
55
(10)
56
(11)
57
(12)
58
(13)