25ed4

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Icon-Todo.png Todo: review
See if there’s a better way to reword the theory section’s contents, they’re a bit confusing & unclear
← 23ed425ed427ed4 →
Prime factorization 52
Step size 96¢ 
Octave 13\25ed4 (1248¢)
Twelfth 20\25ed4 (1920¢) (→4\5ed4)
Consistency limit 1
Distinct consistency limit 1

25ed4 is the equal division of the double octave into 25 parts of exactly 96 cents each (every second step of 25edo). It corresponds to 12.5edo and is notable as a type of compressed 12edo.

Theory

We could have 12edo with a quarter note, like with 1.5edo, where the 2nd note is the same as the 3rd in 4edo or we could squish the notes and fit in something else.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 96
2 192 10/9, 19/17
3 288 13/11
4 384
5 480 25/19
6 576 7/5
7 672 22/15, 25/17
8 768 14/9
9 864 23/14
10 960 26/15
11 1056
12 1152
13 1248
14 1344
15 1440 23/10
16 1536 17/7, 22/9
17 1632 23/9
18 1728 19/7
19 1824
20 1920
21 2016
22 2112 17/5
23 2208 25/7
24 2304 19/5
25 2400

Harmonics

Approximation of harmonics in 25ed4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +48.0 +18.0 +0.0 -2.3 -30.0 -8.8 +48.0 +36.1 +45.7 -23.3 +18.0
Relative (%) +50.0 +18.8 +0.0 -2.4 -31.2 -9.2 +50.0 +37.6 +47.6 -24.3 +18.8
Steps
(reduced)
13
(13)
20
(20)
25
(0)
29
(4)
32
(7)
35
(10)
38
(13)
40
(15)
42
(17)
43
(18)
45
(20)
Approximation of harmonics in 25ed4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -24.5 +39.2 +15.7 +0.0 -9.0 -11.9 -9.5 -2.3 +9.2 +24.7 +43.7
Relative (%) -25.5 +40.8 +16.4 +0.0 -9.3 -12.4 -9.9 -2.4 +9.6 +25.7 +45.5
Steps
(reduced)
46
(21)
48
(23)
49
(24)
50
(0)
51
(1)
52
(2)
53
(3)
54
(4)
55
(5)
56
(6)
57
(7)
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