User:MisterShafXen/25ed7

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← 24ed7 25ed7 26ed7 →
Prime factorization 52
Step size 134.753 ¢ 
Octave 9\25ed7 (1212.78 ¢)
Twelfth 14\25ed7 (1886.54 ¢)
Consistency limit 8
Distinct consistency limit 6

25 equal divisions of the 7th harmonic (abbreviated 25ed7) is a nonoctave tuning system that divides the interval of 7/1 into 25 equal parts of about 135 ¢ each. Each step represents a frequency ratio of 71/25, or the 25th root of 7.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 134.8 13/12, 14/13
2 269.5 7/6
3 404.3 19/15, 24/19
4 539 11/8, 15/11, 19/14, 26/19
5 673.8 22/15
6 808.5 8/5
7 943.3 12/7, 19/11, 26/15
8 1078 13/7, 15/8
9 1212.8
10 1347.5 13/6, 24/11
11 1482.3 26/11
12 1617 23/9
13 1751.8 11/4
14 1886.5
15 2021.3 16/5
16 2156
17 2290.8 15/4
18 2425.6
19 2560.3 22/5
20 2695.1 19/4
21 2829.8
22 2964.6
23 3099.3 6/1
24 3234.1 13/2
25 3368.8 7/1

Harmonics

Approximation of prime harmonics in 25ed7
Harmonic 2 3 5 7 11 13 17 19 23 29 31
Error Absolute (¢) +12.8 -15.4 +43.5 +0.0 +26.0 +6.3 -53.8 +23.1 -38.2 -35.2 -15.9
Relative (%) +9.5 -11.4 +32.3 +0.0 +19.3 +4.7 -40.0 +17.1 -28.3 -26.1 -11.8
Steps
(reduced)
9
(9)
14
(14)
21
(21)
25
(0)
31
(6)
33
(8)
36
(11)
38
(13)
40
(15)
43
(18)
44
(19)

Theory