19ed5/2

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19ed5/2

20ed5/2 →

Prime factorization	19 (prime)
Step size	83.4902¢
Octave	14\19ed5/2 (1168.86¢)
Twelfth	23\19ed5/2 (1920.27¢)
Consistency limit	2
Distinct consistency limit	2

19 equal divisions of 5/2 (abbreviated 19ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 19 equal parts of about 83.5 ¢ each. Each step represents a frequency ratio of (5/2)^1/19, or the 19th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	83.49	18/17, 19/18, 22/21, 23/22
2	166.98	21/19, 23/21
3	250.471	7/6, 15/13, 22/19
4	333.961	11/9, 23/19
5	417.451	19/15, 23/18
6	500.941
7	584.431	7/5
8	667.922	19/13, 22/15
9	751.412	17/11, 23/15
10	834.902	21/13
11	918.392	12/7, 22/13
12	1001.882	23/13
13	1085.373	13/7, 17/9
14	1168.863
15	1252.353
16	1335.843	13/6, 15/7
17	1419.333
18	1502.824	12/5
19	1586.314	5/2

Harmonics

Approximation of harmonics in 19ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-31.1	+18.3	+21.2	-31.1	-12.8	-29.2	-9.9	+36.6	+21.2	+23.2	+39.5
	Relative (%)	-37.3	+21.9	+25.4	-37.3	-15.4	-35.0	-11.9	+43.9	+25.4	+27.8	+47.4
Steps (reduced)		14 (14)	23 (4)	29 (10)	33 (14)	37 (18)	40 (2)	43 (5)	46 (8)	48 (10)	50 (12)	52 (14)

Approximation of harmonics in 19ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-15.5	+23.1	-12.8	-41.1	+21.0	+5.5	-4.6	-9.9	-10.9	-7.9	-1.4
	Relative (%)	-18.6	+27.7	-15.4	-49.2	+25.1	+6.6	-5.5	-11.9	-13.1	-9.5	-1.7
Steps (reduced)		53 (15)	55 (17)	56 (18)	57 (0)	59 (2)	60 (3)	61 (4)	62 (5)	63 (6)	64 (7)	65 (8)