3ed7

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3ed7

4ed7 →

Prime factorization	3 (prime)
Step size	1122.94¢
Octave	1\3ed7 (1122.94¢) (convergent)
Twelfth	2\3ed7 (2245.88¢) (semiconvergent)
Consistency limit	4
Distinct consistency limit	2

3 equal divisions of the 7th harmonic (abbreviated 3ed7) is a nonoctave tuning system that divides the interval of 7/1 into 3 equal parts of about 1120⁠ ⁠¢ each. Each step represents a frequency ratio of 7^1/3, or the 3rd root of 7.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1, 14/13, 15/14, 16/15, 17/16, 19/18
1	1122.9	2/1, 11/6, 13/7, 15/8
2	2245.9	7/2, 11/3, 15/4, 17/5
3	3368.8	7/1, 13/2, 15/2

Harmonics

Approximation of prime harmonics in 3ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	-77	+344	-540	+0	+340	+51	-413	+517	+186	-215	-330
	Relative (%)	-6.9	+30.6	-48.1	+0.0	+30.3	+4.6	-36.8	+46.1	+16.6	-19.1	-29.4
Steps (reduced)		1 (1)	2 (2)	2 (2)	3 (0)	4 (1)	4 (1)	4 (1)	5 (2)	5 (2)	5 (2)	5 (2)

Approximation of prime harmonics in 3ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+486	+309	+226	+72	-136	-322	-379	-542	+481	+433	+296
	Relative (%)	+43.3	+27.5	+20.1	+6.4	-12.1	-28.6	-33.8	-48.2	+42.8	+38.5	+26.4
Steps (reduced)		6 (0)	6 (0)	6 (0)	6 (0)	6 (0)	6 (0)	6 (0)	6 (0)	7 (1)	7 (1)	7 (1)

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