19ed7/4

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19ed7/4

20ed7/4 →

Prime factorization	19 (prime)
Step size	50.9908¢
Octave	24\19ed7/4 (1223.78¢)
Twelfth	37\19ed7/4 (1886.66¢) (semiconvergent)
Consistency limit	2
Distinct consistency limit	2

19 equal divisions of 7/4 (abbreviated 19ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 19 equal parts of about 51 ¢ each. Each step represents a frequency ratio of (7/4)^1/19, or the 19th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	50.991
2	101.982	18/17, 19/18
3	152.973	23/21
4	203.963	17/15, 19/17
5	254.954	7/6, 15/13, 22/19
6	305.945	6/5, 13/11
7	356.936	11/9, 21/17
8	407.927	19/15, 23/18
9	458.918	17/13, 22/17
10	509.908	23/17
11	560.899	18/13
12	611.89
13	662.881	19/13, 22/15
14	713.872
15	764.863	17/11
16	815.853	21/13
17	866.844	18/11
18	917.835	22/13
19	968.826

Harmonics

Approximation of harmonics in 19ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+23.8	-15.3	-3.4	+18.2	+8.5	-3.4	+20.3	+20.4	-9.0	-21.1	-18.7
	Relative (%)	+46.6	-30.0	-6.7	+35.7	+16.6	-6.7	+39.9	+40.0	-17.7	-41.3	-36.7
Steps (reduced)		24 (5)	37 (18)	47 (9)	55 (17)	61 (4)	66 (9)	71 (14)	75 (18)	78 (2)	81 (5)	84 (8)

Approximation of harmonics in 19ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-4.3	+20.3	+2.9	-6.9	-9.8	-6.8	+1.6	+14.8	-18.7	+2.7	-23.2
	Relative (%)	-8.5	+39.9	+5.7	-13.5	-19.3	-13.4	+3.1	+28.9	-36.7	+5.3	-45.6
Steps (reduced)		87 (11)	90 (14)	92 (16)	94 (18)	96 (1)	98 (3)	100 (5)	102 (7)	103 (8)	105 (10)	106 (11)