4edf

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← 3edf4edf5edf →
Prime factorization 22
Step size 175.489¢ 
Octave 7\4edf (1228.42¢)
(semiconvergent)
Twelfth 11\4edf (1930.38¢)
(semiconvergent)
Consistency limit 6
Distinct consistency limit 2
Special properties

4 equal divisions of the perfect fifth (abbreviated 4edf or 4ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 4 equal parts of about 175 ¢ each. Each step represents a frequency ratio of (3/2)1/4, or the 4th root of 3/2. It corresponds to 6.8380edo.

Theory

4edf is related to the tetracot temperament, which tempers out 20000/19683 in the 5-limit.

Harmonics

Approximation of harmonics in 4edf
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +28.4 +28.4 +56.8 +21.5 +56.8 -34.5 +85.3 +56.8 +49.9 +60.4 +85.3
Relative (%) +16.2 +16.2 +32.4 +12.3 +32.4 -19.7 +48.6 +32.4 +28.5 +34.4 +48.6
Steps
(reduced)
7
(3)
11
(3)
14
(2)
16
(0)
18
(2)
19
(3)
21
(1)
22
(2)
23
(3)
24
(0)
25
(1)

Intervals

# Cents Tetratonic
Notation
0 0.0 C
1 175.5 D
2 351.0 E
3 526.5 F
4 702.0 C
5 877.4 D
6 1052.9 E
7 1228.4 F
8 1403.9 C
9 1579.4 D
10 1754.9 E
11 1930.4 F
12 2105.9 C
13 2281.4 D
14 2456.8 E

Music

Carlo Serafini