4ed6

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4ed6

5ed6 →

Prime factorization	22
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
Special properties	Highly composite

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.

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

Harmonics

Approximation of harmonics in 4ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+351	-351	-74	+316	+0	-267	+277	+74	-109	-274	+351
	Relative (%)	+45.3	-45.3	-9.5	+40.7	+0.0	-34.4	+35.8	+9.5	-14.0	-35.3	+45.3
Steps (reduced)		2 (2)	2 (2)	3 (3)	4 (0)	4 (0)	4 (0)	5 (1)	5 (1)	5 (1)	5 (1)	6 (2)

Approximation of harmonics in 4ed6 (continued)

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	+212	+84	-35	-147	-252	-351	+331	+242	+158	+77	+0	-74
	Relative (%)	+27.4	+10.8	-4.6	-19.0	-32.5	-45.3	+42.7	+31.2	+20.3	+9.9	+0.0	-9.5
Steps (reduced)		6 (2)	6 (2)	6 (2)	6 (2)	6 (2)	6 (2)	7 (3)	7 (3)	7 (3)	7 (3)	7 (3)	7 (3)

Subsets and supersets

4ed6 is the first composite ed6, containing 2ed6 as the only nontrivial subset ed6.