26ed11/5

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26ed11/5

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Prime factorization	2 × 13
Step size	52.5002¢
Octave	23\26ed11/5 (1207.5¢)
Twelfth	36\26ed11/5 (1890.01¢) (→18\13ed11/5)
Consistency limit	3
Distinct consistency limit	2

26 equal divisions of 11/5 (abbreviated 26ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 26 equal parts of about 52.5 ¢ each. Each step represents a frequency ratio of (11/5)^1/26, or the 26th root of 11/5.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	52.5
2	105	18/17, 19/18
3	157.5	11/10, 12/11, 23/21
4	210.001	17/15, 25/22
5	262.501	7/6, 22/19
6	315.001	6/5
7	367.501	16/13, 21/17
8	420.001	14/11, 19/15, 23/18
9	472.501	25/19
10	525.002	19/14, 23/17
11	577.502	7/5, 25/18
12	630.002
13	682.502
14	735.002	20/13, 23/15
15	787.502	11/7, 19/12
16	840.003	13/8
17	892.503	5/3
18	945.003	12/7, 19/11
19	997.503	25/14
20	1050.003	11/6, 24/13
21	1102.503	17/9, 19/10
22	1155.004
23	1207.504	2/1
24	1260.004	25/12
25	1312.504	15/7
26	1365.004	11/5

Harmonics

Approximation of harmonics in 26ed11/5

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	+7.5	-11.9	+15.0	-3.8	-4.4	-8.8	+22.5	-23.9	+3.7	-3.8	+3.1
	Relative (%)	+14.3	-22.8	+28.6	-7.2	-8.5	-16.8	+42.9	-45.5	+7.0	-7.2	+5.8
Steps (reduced)		23 (23)	36 (10)	46 (20)	53 (1)	59 (7)	64 (12)	69 (17)	72 (20)	76 (24)	79 (1)	82 (4)

Approximation of harmonics in 26ed11/5

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	+22.0	-1.3	-15.8	-22.5	-22.4	-16.4	-5.0	+11.2	-20.8	+3.7	-20.8
	Relative (%)	+41.9	-2.5	-30.0	-42.8	-42.7	-31.2	-9.5	+21.3	-39.6	+7.0	-39.5
Steps (reduced)		85 (7)	87 (9)	89 (11)	91 (13)	93 (15)	95 (17)	97 (19)	99 (21)	100 (22)	102 (24)	103 (25)