20ed5/4

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20ed5/4

21ed5/4 →

Prime factorization	22 × 5
Step size	19.3157¢
Octave	62\20ed5/4 (1197.57¢) (→31\10ed5/4)
Twelfth	98\20ed5/4 (1892.94¢) (→49\10ed5/4)
Consistency limit	4
Distinct consistency limit	2

20 equal divisions of 5/4 (abbreviated 20ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 20 equal parts of about 19.3 ¢ each. Each step represents a frequency ratio of (5/4)^1/20, or the 20th root of 5/4.

Intervals

Steps	Cents	Approximate Ratios
0	0	1/1
1	19.316
2	38.631
3	57.947	24/23
4	77.263	20/19, 21/20, 23/22, 25/24
5	96.578
6	115.894	14/13, 15/14, 16/15, 17/16
7	135.21	12/11, 25/23
8	154.525	13/12
9	173.841	11/10
10	193.157	9/8, 10/9, 19/17
11	212.473	25/22
12	231.788	8/7, 15/13, 17/15
13	251.104	22/19, 23/20
14	270.42	7/6, 20/17
15	289.735	13/11
16	309.051	6/5, 19/16, 25/21
17	328.367	23/19
18	347.682	16/13, 17/14
19	366.998
20	386.314	5/4

Harmonics

Approximation of harmonics in 20ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-2.43	-9.02	-4.85	-4.85	+7.87	-7.90	-7.28	+1.28	-7.28	+1.55	+5.44
	Relative (%)	-12.6	-46.7	-25.1	-25.1	+40.7	-40.9	-37.7	+6.6	-37.7	+8.0	+28.2
Steps (reduced)		62 (2)	98 (18)	124 (4)	144 (4)	161 (1)	174 (14)	186 (6)	197 (17)	206 (6)	215 (15)	223 (3)

Approximation of harmonics in 20ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	+8.99	+5.44	+9.61	+1.23	-1.15	+1.83	+9.61	+2.40	-0.87	-0.57
	Relative (%)	+10.8	+46.6	+28.2	+49.7	+6.4	-5.9	+9.5	+49.7	+12.4	-4.5	-2.9
Steps (reduced)		230 (10)	237 (17)	243 (3)	249 (9)	254 (14)	259 (19)	264 (4)	269 (9)	273 (13)	277 (17)	281 (1)