26ed5/4

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26ed5/4

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Prime factorization	2 × 13
Step size	14.8582¢
Octave	81\26ed5/4 (1203.52¢)
Twelfth	128\26ed5/4 (1901.85¢) (→64\13ed5/4)
Consistency limit	7
Distinct consistency limit	6

26 equal divisions of 5/4 (abbreviated 26ed5/4) is a nonoctave tuning system that divides the interval of 5/4 into 26 equal parts of about 14.9⁠ ⁠¢ each. Each step represents a frequency ratio of (5/4)^1/26, or the 26th root of 5/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	14.9
2	29.7
3	44.6
4	59.4	26/25
5	74.3	21/20, 22/21, 23/22, 25/24
6	89.1	19/18
7	104	18/17
8	118.9	15/14, 16/15
9	133.7	13/12, 14/13
10	148.6	23/21
11	163.4
12	178.3	21/19
13	193.2	9/8, 10/9, 19/17
14	208	17/15
15	222.9	26/23
16	237.7	8/7
17	252.6	15/13, 22/19
18	267.4	7/6
19	282.3
20	297.2	13/11
21	312	6/5, 25/21
22	326.9	17/14, 23/19
23	341.7	11/9
24	356.6
25	371.5	21/17, 26/21
26	386.3	5/4

Harmonics

Approximation of harmonics in 26ed5/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+3.52	-0.10	+7.03	+7.03	+3.41	+3.99	-4.31	-0.21	-4.31	-5.87	+6.93
	Relative (%)	+23.7	-0.7	+47.3	+47.3	+23.0	+26.9	-29.0	-1.4	-29.0	-39.5	+46.6
Steps (reduced)		81 (3)	128 (24)	162 (6)	188 (6)	209 (1)	227 (19)	242 (8)	256 (22)	268 (8)	279 (19)	290 (4)

Approximation of harmonics in 26ed5/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+2.08	-7.35	+6.93	-0.80	-1.74	+3.31	-1.14	-0.80	+3.89	-2.36	-5.02
	Relative (%)	+14.0	-49.5	+46.6	-5.4	-11.7	+22.3	-7.7	-5.4	+26.2	-15.9	-33.8
Steps (reduced)		299 (13)	307 (21)	316 (4)	323 (11)	330 (18)	337 (25)	343 (5)	349 (11)	355 (17)	360 (22)	365 (1)