7ed4

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7 equal divisions of the 4th harmonic (abbreviated 7ed4) is a nonoctave tuning system that divides the interval of 4/1 into 7 equal parts of about 343 ¢ each. Each step represents a frequency ratio of 4^1/7, or the 7th root of 4.

← 5ed4

7ed4

9ed4 →

Prime factorization	7 (prime)
Step size	342.857 ¢
Octave	4\7ed4 (1371.43 ¢)
Twelfth	6\7ed4 (2057.14 ¢)
Consistency limit	1
Distinct consistency limit	1

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	342.9
2	685.7	3/2, 19/13
3	1028.6	13/7
4	1371.4	9/4, 11/5, 20/9
5	1714.3	19/7
6	2057.1	10/3
7	2400

Harmonics

Approximation of harmonics in 7ed4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+171	+155	+0	-43	-16	+60	+171	-32	+128	-37	+155
	Relative (%)	+50.0	+45.3	+0.0	-12.7	-4.7	+17.4	+50.0	-9.5	+37.3	-10.8	+45.3
Steps (reduced)		4 (4)	6 (6)	7 (0)	8 (1)	9 (2)	10 (3)	11 (4)	11 (4)	12 (5)	12 (5)	13 (6)

Approximation of harmonics in 7ed4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+17	-112	+112	+0	-105	+139	+45	-43	-128	+134	+57
	Relative (%)	+4.8	-32.6	+32.6	+0.0	-30.6	+40.5	+13.2	-12.7	-37.3	+39.2	+16.8
Steps (reduced)		13 (6)	13 (6)	14 (0)	14 (0)	14 (0)	15 (1)	15 (1)	15 (1)	15 (1)	16 (2)	16 (2)