26ed7/4

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26ed7/4

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Prime factorization	2 × 13
Step size	37.2625¢
Octave	32\26ed7/4 (1192.4¢) (→16\13ed7/4)
Twelfth	51\26ed7/4 (1900.39¢) (semiconvergent)
Consistency limit	4
Distinct consistency limit	3

26 equal divisions of 7/4 (abbreviated 26ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 26 equal parts of about 37.3 ¢ each. Each step represents a frequency ratio of (7/4)^1/26, or the 26th root of 7/4.

Intervals

Steps	Cents	Approximate ratios
0	0	1/1
1	37.3
2	74.5	21/20, 22/21
3	111.8
4	149.1	12/11, 13/12, 25/23
5	186.3	10/9, 19/17
6	223.6	8/7, 17/15
7	260.8	7/6
8	298.1	13/11
9	335.4	23/19
10	372.6	26/21
11	409.9	14/11, 19/15
12	447.2	13/10
13	484.4	25/19
14	521.7	23/17
15	558.9	11/8, 18/13
16	596.2
17	633.5	13/9
18	670.7	25/17
19	708	3/2
20	745.3	20/13, 23/15
21	782.5	11/7
22	819.8	21/13
23	857	18/11
24	894.3	5/3
25	931.6	12/7
26	968.8	7/4

Harmonics

Approximation of harmonics in 26ed7/4

Harmonic		2	3	4	5	6	7	8	9	10	11	12
Error	Absolute (¢)	-7.6	-1.6	-15.2	+8.4	-9.2	-15.2	+14.5	-3.1	+0.8	-15.2	-16.8
	Relative (%)	-20.4	-4.2	-40.8	+22.5	-24.6	-40.8	+38.8	-8.4	+2.1	-40.7	-45.0
Steps (reduced)		32 (6)	51 (25)	64 (12)	75 (23)	83 (5)	90 (12)	97 (19)	102 (24)	107 (3)	111 (7)	115 (11)

Approximation of harmonics in 26ed7/4

Harmonic		13	14	15	16	17	18	19	20	21	22	23
Error	Absolute (¢)	-6.3	+14.5	+6.8	+6.9	+13.7	-10.7	+7.5	-6.8	-16.8	+14.5	+12.1
	Relative (%)	-16.9	+38.8	+18.3	+18.4	+36.8	-28.8	+20.0	-18.3	-45.0	+38.9	+32.4
Steps (reduced)		119 (15)	123 (19)	126 (22)	129 (25)	132 (2)	134 (4)	137 (7)	139 (9)	141 (11)	144 (14)	146 (16)