4edf

← 3edf

4edf

5edf →

Prime factorization	22 (highly composite)
Step size	175.489 ¢
Octave	7\4edf (1228.42 ¢) (semiconvergent)
Twelfth	11\4edf (1930.38 ¢) (semiconvergent)
Consistency limit	6
Distinct consistency limit	5

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

• Repetitions 1 – play | YouTube