14ed6

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14ed6

15ed6 →

Prime factorization	2 × 7
Step size	221.568 ¢
Octave	5\14ed6 (1107.84 ¢)
Twelfth	9\14ed6 (1994.11 ¢)
Consistency limit	2
Distinct consistency limit	2

14 equal divisions of the 6th harmonic (abbreviated 14ed6) is a nonoctave tuning system that divides the interval of 6/1 into 14 equal parts of about 222 ¢ each. Each step represents a frequency ratio of 6^1/14, or the 14th root of 6.

Theory

14ed6 corresponds to 5.4159…edo. It is the generator chain for the hemisensi temperament.

Harmonics

Approximation of harmonics in 14ed6

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-92.2	+92.2	+37.3	+94.1	+0.0	-45.3	-54.9	-37.3	+1.9	+58.5	-92.2
	Relative (%)	-41.6	+41.6	+16.8	+42.5	+0.0	-20.4	-24.8	-16.8	+0.9	+26.4	-41.6
Steps (reduced)		5 (5)	9 (9)	11 (11)	13 (13)	14 (0)	15 (1)	16 (2)	17 (3)	18 (4)	19 (5)	19 (5)

Approximation of harmonics in 14ed6

Harmonic		13	14	15	16	17	18	19	20	21	22	23	24
Error	Absolute (¢)	-9.2	+84.1	-35.3	+74.5	-30.5	+92.2	-1.4	-90.2	+46.9	-33.7	-110.6	+37.3
	Relative (%)	-4.1	+38.0	-15.9	+33.6	-13.7	+41.6	-0.7	-40.7	+21.1	-15.2	-49.9	+16.8
Steps (reduced)		20 (6)	21 (7)	21 (7)	22 (8)	22 (8)	23 (9)	23 (9)	23 (9)	24 (10)	24 (10)	24 (10)	25 (11)

Subsets and supersets

Since 14 factors into primes as 2 × 7, 14ed6 contains 2ed6 and 7ed6 as subset ed6's.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	221.6	23/20
2	443.1	13/10, 17/13, 22/17
3	664.7	19/13
4	886.3	5/3
5	1107.8	19/10, 21/11, 23/12
6	1329.4	13/6
7	1551	17/7
8	1772.5
9	1994.1	19/6, 22/7
10	2215.7	18/5
11	2437.3
12	2658.8
13	2880.4
14	3102	6/1