4ed6

← 3ed6

4ed6

5ed6 →

Prime factorization	22 (highly composite)
Step size	775.489 ¢
Octave	2\4ed6 (1550.98 ¢) (→ 1\2ed6)
Twelfth	2\4ed6 (1550.98 ¢) (→ 1\2ed6)
Consistency limit	2
Distinct consistency limit	2

4 equal divisions of the 6th harmonic (abbreviated 4ed6) is a nonoctave tuning system that divides the interval of 6/1 into 4 equal parts of about 775 ¢ each. Each step represents a frequency ratio of 6^1/4, or the 4th root of 6.

Harmonics

4ed6, notably, approximates the 23rd harmonic with incredible accuracy, less than 0.15 cents off.

Approximation of harmonics in 4ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12	13	14	15	16
Error	Absolute (¢)	+351	-351	-74	+316	+0	-267	+277	+74	-109	-274	+351	+212	+84	-35	-147
	Relative (%)	+45.3	-45.3	-9.5	+40.7	+0.0	-34.4	+35.8	+9.5	-14.0	-35.3	+45.3	+27.4	+10.8	-4.6	-19.0
Steps (reduced)		2 (2)	2 (2)	3 (3)	4 (0)	4 (0)	4 (0)	5 (1)	5 (1)	5 (1)	5 (1)	6 (2)	6 (2)	6 (2)	6 (2)	6 (2)

Approximation of prime harmonics in 4ed6

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+351.0	-351.0	+315.6	-266.9	-273.9	+212.4	-252.0	+330.9	+0.1	+374.3	+258.9
	Relative (%)	+45.3	-45.3	+40.7	-34.4	-35.3	+27.4	-32.5	+42.7	+0.0	+48.3	+33.4
Steps (reduced)		2 (2)	2 (2)	4 (0)	4 (0)	5 (1)	6 (2)	6 (2)	7 (3)	7 (3)	8 (0)	8 (0)

This page is a stub. You can help the Xenharmonic Wiki by expanding it.