2ed7

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2ed7

3ed7 →

Prime factorization	2 (prime)
Step size	1684.41¢
Octave	1\2ed7 (1684.41¢) (convergent)
Twelfth	1\2ed7 (1684.41¢) (convergent)
Consistency limit	3
Distinct consistency limit	1
Special properties	Highly composite

2 equal divisions of the 7th harmonic (abbreviated 2ed7) is a nonoctave tuning system that divides the interval of 7/1 into 2 equal parts of about 1680⁠ ⁠¢ each. Each step represents a frequency ratio of 7^1/2, or the 2nd root of 7.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1, 13/12, 14/13, 15/14, 17/15, 18/17, 19/17, 19/18
1	1684.4	3/1, 5/2, 7/3, 12/5, 13/5, 14/5, 17/6, 17/7, 18/7, 19/7
2	3368.8	7/1, 13/2, 15/2, 19/3

Harmonics

Approximation of prime harmonics in 2ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+484	-218	+583	+0	-782	+613	+148	-44	-375	-776	+793
	Relative (%)	+28.8	-12.9	+34.6	+0.0	-46.5	+36.4	+8.8	-2.6	-22.3	-46.1	+47.1
Steps (reduced)		1 (1)	1 (1)	2 (0)	2 (0)	2 (0)	3 (1)	3 (1)	3 (1)	3 (1)	3 (1)	4 (0)

Approximation of prime harmonics in 2ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+486	+309	+226	+72	-136	-322	-379	-542	-642	-690	-827
	Relative (%)	+28.9	+18.3	+13.4	+4.3	-8.1	-19.1	-22.5	-32.2	-38.1	-41.0	-49.1
Steps (reduced)		4 (0)	4 (0)	4 (0)	4 (0)	4 (0)	4 (0)	4 (0)	4 (0)	4 (0)	4 (0)	4 (0)

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