25ed5/4

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25ed5/4

26ed5/4 →

Prime factorization	52
Step size	15.4525¢
Octave	78\25ed5/4 (1205.3¢)
Twelfth	123\25ed5/4 (1900.66¢)
Consistency limit	3
Distinct consistency limit	3

25 equal divisions of 5/4 (abbreviated 25ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 25 equal parts of about 15.5 ¢ each. Each step represents a frequency ratio of (5/4)^1/25, or the 25th root of 5/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	15.5
2	30.9
3	46.4
4	61.8
5	77.3	21/20, 26/25
6	92.7	19/18, 20/19, 22/21
7	108.2	15/14, 18/17
8	123.6
9	139.1	14/13, 25/23
10	154.5	12/11, 23/21
11	170	11/10, 21/19
12	185.4	10/9
13	200.9	19/17
14	216.3	17/15, 26/23
15	231.8	23/20
16	247.2	15/13
17	262.7	7/6, 22/19
18	278.1	13/11
19	293.6	20/17, 25/21
20	309.1
21	324.5	6/5, 17/14, 23/19
22	340
23	355.4	11/9
24	370.9	21/17, 26/21
25	386.3

Harmonics

Approximation of harmonics in 25ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+5.30	-1.29	-4.85	-4.85	+4.01	-0.17	+0.44	-2.58	+0.44	+5.42	-6.15
	Relative (%)	+34.3	-8.4	-31.4	-31.4	+25.9	-1.1	+2.9	-16.7	+2.9	+35.1	-39.8
Steps (reduced)		78 (3)	123 (23)	155 (5)	180 (5)	201 (1)	218 (18)	233 (8)	246 (21)	258 (8)	269 (19)	278 (3)

Approximation of harmonics in 25ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-5.65	+5.13	-6.15	+5.74	-6.50	+2.72	+1.83	+5.74	-1.46	-4.74	-4.43
	Relative (%)	-36.5	+33.2	-39.8	+37.2	-42.0	+17.6	+11.8	+37.2	-9.5	-30.6	-28.7
Steps (reduced)		287 (12)	296 (21)	303 (3)	311 (11)	317 (17)	324 (24)	330 (5)	336 (11)	341 (16)	346 (21)	351 (1)