5ed4

← 3ed4

5ed4

7ed4 →

Prime factorization	5 (prime)
Step size	480 ¢
Octave	3\5ed4 (1440 ¢)
Twelfth	4\5ed4 (1920 ¢) (convergent)
Consistency limit	1
Distinct consistency limit	1

5 equal divisions of the 4th harmonic (abbreviated 5ed4) is a nonoctave tuning system that divides the interval of 4/1 into 5 equal parts of exactly 480 ¢ each. Each step represents a frequency ratio of 4^1/5, or the 5th root of 4.

Relation to 5edo

This tuning inherits all the following intervals from 5edo:

4/3 (-18.045¢/3.76%)

7/4 (-8.826¢/1.84%)

147/64 (+0.393¢/0.08%)

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	480	9/7, 14/11, 15/11, 17/13, 19/14, 19/15
2	960	9/5, 19/11
3	1440	7/3
4	1920	3/1
5	2400

Harmonics

Approximation of harmonics in 5ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+240	+18	+0	+94	-222	-9	+240	+36	-146	+169	+18
	Relative (%)	+50.0	+3.8	+0.0	+19.5	-46.2	-1.8	+50.0	+7.5	-30.5	+35.1	+3.8
Steps (reduced)		3 (3)	4 (4)	5 (0)	6 (1)	6 (1)	7 (2)	8 (3)	8 (3)	8 (3)	9 (4)	9 (4)

Approximation of harmonics in 5ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-121	+231	+112	+0	-105	-204	+182	+94	+9	-71	-148
	Relative (%)	-25.1	+48.2	+23.3	+0.0	-21.9	-42.5	+38.0	+19.5	+1.9	-14.9	-30.9
Steps (reduced)		9 (4)	10 (0)	10 (0)	10 (0)	10 (0)	10 (0)	11 (1)	11 (1)	11 (1)	11 (1)	11 (1)