14ed7

← 13ed7

14ed7

15ed7 →

Prime factorization	2 × 7
Step size	240.63¢
Octave	5\14ed7 (1203.15¢) (convergent)
Twelfth	8\14ed7 (1925.04¢) (→4\7ed7)
Consistency limit	10
Distinct consistency limit	4

14 equal divisions of the 7th harmonic (abbreviated 14ed7) is a nonoctave tuning system that divides the interval of 7/1 into 14 equal parts of about 241⁠ ⁠¢ each. Each step represents a frequency ratio of 7^1/14, or the 14th root of 7. It is closely related to 5edo.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	240.6	8/7, 22/19, 23/20
2	481.3	4/3, 17/13, 21/16
3	721.9	3/2, 23/15
4	962.5	7/4, 19/11
5	1203.2	2/1
6	1443.8	7/3, 16/7, 23/10
7	1684.4	8/3, 21/8
8	1925	3/1
9	2165.7	7/2
10	2406.3	4/1
11	2646.9	14/3, 23/5
12	2887.6	16/3, 21/4
13	3128.2
14	3368.8	7/1

Harmonics

Approximation of prime harmonics in 14ed7

Harmonic		2	3	5	7	11	13	17	19	23	29	31
Error	Absolute (¢)	+3	+23	+101	+0	-61	-109	-92	-44	+106	-54	+71
	Relative (%)	+1.3	+9.6	+42.1	+0.0	-25.2	-45.4	-38.4	-18.4	+44.1	-22.6	+29.4
Steps (reduced)		5 (5)	8 (8)	12 (12)	14 (0)	17 (3)	18 (4)	20 (6)	21 (7)	23 (9)	24 (10)	25 (11)

Approximation of prime harmonics in 14ed7

Harmonic		37	41	43	47	53	59	61	67	71	73	79
Error	Absolute (¢)	+5	+68	-14	+72	+105	-81	+102	-60	+80	+32	-105
	Relative (%)	+2.1	+28.2	-6.0	+30.0	+43.5	-33.6	+42.4	-25.1	+33.2	+13.2	-43.6
Steps (reduced)		26 (12)	27 (13)	27 (13)	28 (0)	29 (1)	29 (1)	30 (2)	30 (2)	31 (3)	31 (3)	31 (3)

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