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 harmonics in 14ed7

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3	+23	+6	+101	+26	+0	+9	+46	+104	-61	+29
	Relative (%)	+1.3	+9.6	+2.6	+42.1	+10.9	+0.0	+3.9	+19.2	+43.4	-25.2	+12.2
Steps (reduced)		5 (5)	8 (8)	10 (10)	12 (12)	13 (13)	14 (0)	15 (1)	16 (2)	17 (3)	17 (3)	18 (4)

Approximation of harmonics in 14ed7

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-109	+3	-116	+13	-92	+49	-44	+108	+23	-57	+106
	Relative (%)	-45.4	+1.3	-48.3	+5.2	-38.4	+20.5	-18.4	+44.7	+9.6	-23.9	+44.1
Steps (reduced)		18 (4)	19 (5)	19 (5)	20 (6)	20 (6)	21 (7)	21 (7)	22 (8)	22 (8)	22 (8)	23 (9)

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