26ed5/2

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26ed5/2

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Prime factorization	2 × 13
Step size	61.0121¢
Octave	20\26ed5/2 (1220.24¢) (→10\13ed5/2)
Twelfth	31\26ed5/2 (1891.37¢) (semiconvergent)
Consistency limit	2
Distinct consistency limit	2

26 equal divisions of 5/2 (abbreviated 26ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 26 equal parts of about 61 ¢ each. Each step represents a frequency ratio of (5/2)^1/26, or the 26th root of 5/2.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	61	25/24, 26/25
2	122	14/13, 15/14
3	183
4	244	15/13, 22/19
5	305.1	6/5
6	366.1	21/17
7	427.1	9/7, 14/11, 23/18
8	488.1
9	549.1	26/19
10	610.1
11	671.1	22/15
12	732.1	23/15
13	793.2	11/7, 19/12
14	854.2	18/11, 23/14
15	915.2	22/13
16	976.2	23/13
17	1037.2
18	1098.2	17/9
19	1159.2
20	1220.2
21	1281.3	23/11, 25/12
22	1342.3	13/6
23	1403.3
24	1464.3	7/3
25	1525.3	12/5, 17/7
26	1586.3	5/2

Harmonics

Approximation of harmonics in 26ed5/2

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+20.2	-10.6	-20.5	+20.2	+9.7	-13.2	-0.3	-21.2	-20.5	-2.5	+29.9
	Relative (%)	+33.2	-17.3	-33.6	+33.2	+15.8	-21.6	-0.5	-34.7	-33.6	-4.1	+49.0
Steps (reduced)		20 (20)	31 (5)	39 (13)	46 (20)	51 (25)	55 (3)	59 (7)	62 (10)	65 (13)	68 (16)	71 (19)

Approximation of harmonics in 26ed5/2

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+13.4	+7.1	+9.7	+20.0	-24.0	-0.9	+27.5	-0.3	-23.7	+17.7	+1.8
	Relative (%)	+21.9	+11.6	+15.8	+32.7	-39.3	-1.5	+45.1	-0.5	-38.9	+29.1	+2.9
Steps (reduced)		73 (21)	75 (23)	77 (25)	79 (1)	80 (2)	82 (4)	84 (6)	85 (7)	86 (8)	88 (10)	89 (11)