20ed7/4

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20ed7/4

21ed7/4 →

Prime factorization	22 × 5
Step size	48.4413¢
Octave	25\20ed7/4 (1211.03¢) (→5\4ed7/4)
Twelfth	39\20ed7/4 (1889.21¢) (semiconvergent)
Consistency limit	3
Distinct consistency limit	3

20 equal divisions of 7/4 (abbreviated 20ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 20 equal parts of about 48.4 ¢ each. Each step represents a frequency ratio of (7/4)^1/20, or the 20th root of 7/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	48.441
2	96.883	18/17, 19/18
3	145.324	12/11, 13/12, 23/21
4	193.765	19/17
5	242.206	8/7, 15/13
6	290.648	13/11
7	339.089	23/19
8	387.53	5/4
9	435.972	23/18
10	484.413
11	532.854	15/11, 23/17
12	581.296	7/5
13	629.737	10/7
14	678.178	22/15
15	726.619	23/15
16	775.061	11/7, 25/16
17	823.502	8/5, 21/13
18	871.943
19	920.385	12/7, 22/13
20	968.826	7/4

Harmonics

Approximation of harmonics in 20ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+11.0	-12.7	+22.1	+23.3	-1.7	+22.1	-15.3	+23.0	-14.1	+14.6	+9.3
	Relative (%)	+22.8	-26.3	+45.5	+48.1	-3.5	+45.5	-31.7	+47.4	-29.2	+30.2	+19.2
Steps (reduced)		25 (5)	39 (19)	50 (10)	58 (18)	64 (4)	70 (10)	74 (14)	79 (19)	82 (2)	86 (6)	89 (9)

Approximation of harmonics in 20ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+16.1	-15.3	+10.5	-4.3	-12.4	-14.5	-11.2	-3.1	+9.3	-22.8	-2.8
	Relative (%)	+33.2	-31.7	+21.8	-8.9	-25.6	-29.8	-23.1	-6.4	+19.2	-47.0	-5.9
Steps (reduced)		92 (12)	94 (14)	97 (17)	99 (19)	101 (1)	103 (3)	105 (5)	107 (7)	109 (9)	110 (10)	112 (12)