11ed7

This page presents a topic of primarily mathematical interest. While it is derived from sound mathematical principles, its applications in terms of utility for actual music may be limited, highly contrived, or as yet unknown.

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11ed7

12ed7 →

Prime factorization	11 (prime)
Step size	306.257 ¢
Octave	4\11ed7 (1225.03 ¢) (semiconvergent)
Twelfth	6\11ed7 (1837.54 ¢)
Consistency limit	8
Distinct consistency limit	3

11 equal divisions of the 7th harmonic (abbreviated 11ed7) is a nonoctave tuning system that divides the interval of 7/1 into 11 equal parts of about 306 ¢ each. Each step represents a frequency ratio of 7^1/11, or the 11th root of 7.

Harmonics

Approximation of harmonics in 11ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+25	-64	+50	-30	-39	+0	+75	-129	-5	+136	-14
	Relative (%)	+8.2	-21.0	+16.3	-9.8	-12.9	+0.0	+24.5	-42.1	-1.6	+44.5	-4.7
Steps (reduced)		4 (4)	6 (6)	8 (8)	9 (9)	10 (10)	11 (0)	12 (1)	12 (1)	13 (2)	14 (3)	14 (3)