14ed5/3

This page is a stub. You can help the Xenharmonic Wiki by expanding it.

← 13ed5/3

14ed5/3

15ed5/3 →

Prime factorization	2 × 7
Step size	63.1685¢
Octave	19\14ed5/3 (1200.2¢) (convergent)
Twelfth	30\14ed5/3 (1895.05¢) (→15\7ed5/3)
Consistency limit	10
Distinct consistency limit	4

14 equal divisions of 5/3 (abbreviated 14ed5/3) is a nonoctave tuning system that divides the interval of 5/3 into 14 equal parts of about 63.2 ¢ each. Each step represents a frequency ratio of (5/3)^1/14, or the 14th root of 5/3.

It is extremely close to 19edo, with a mere 0.2 cents of octave stretching, but with the 5/3 being just rather than the 2/1.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	63.2	21/20, 23/22
2	126.3	13/12, 14/13, 15/14, 16/15, 17/16
3	189.5	9/8, 10/9, 19/17
4	252.7	7/6, 8/7, 15/13, 22/19, 23/20
5	315.8	6/5, 19/16, 23/19
6	379	5/4, 16/13
7	442.2	9/7, 13/10, 22/17, 23/18
8	505.3	4/3, 23/17
9	568.5	7/5, 11/8, 18/13
10	631.7	10/7, 13/9, 16/11, 23/16
11	694.9	3/2
12	758	14/9, 17/11, 20/13, 23/15
13	821.2	8/5, 13/8, 21/13
14	884.4	5/3

Harmonics

Approximation of harmonics in 14ed5/3

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+0.2	-6.9	+0.4	-6.9	-6.7	-20.9	+0.6	-13.8	-6.7	+17.8	-6.5
	Relative (%)	+0.3	-10.9	+0.6	-10.9	-10.6	-33.1	+1.0	-21.8	-10.6	+28.2	-10.3
Steps (reduced)		19 (5)	30 (2)	38 (10)	44 (2)	49 (7)	53 (11)	57 (1)	60 (4)	63 (7)	66 (10)	68 (12)

Approximation of harmonics in 14ed5/3

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-18.7	-20.7	-13.8	+0.8	+22.2	-13.6	+19.1	-6.5	-27.8	+18.0	+4.2
	Relative (%)	-29.7	-32.8	-21.8	+1.3	+35.1	-21.5	+30.3	-10.3	-44.0	+28.5	+6.7
Steps (reduced)		70 (0)	72 (2)	74 (4)	76 (6)	78 (8)	79 (9)	81 (11)	82 (12)	83 (13)	85 (1)	86 (2)