26ed7/3

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← 25ed7/326ed7/327ed7/3 →
Prime factorization 2 × 13
Step size 56.4181¢ 
Octave 21\26ed7/3 (1184.78¢)
Twelfth 34\26ed7/3 (1918.22¢) (→17\13ed7/3)
Consistency limit 2
Distinct consistency limit 2

26 equal divisions of 7/3 (abbreviated 26ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 26 equal parts of about 56.4 ¢ each. Each step represents a frequency ratio of (7/3)1/26, or the 26th root of 7/3. It corresponds to 21.2698edo.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 56.418
2 112.836 15/14
3 169.254
4 225.672 17/15
5 282.091 13/11
6 338.509 11/9, 17/14, 23/19
7 394.927 5/4, 24/19
8 451.345 22/17
9 507.763
10 564.181 18/13
11 620.599
12 677.017
13 733.435 23/15, 26/17
14 789.854 11/7, 19/12
15 846.272 18/11
16 902.69 22/13
17 959.108 26/15
18 1015.526
19 1071.944 13/7
20 1128.362 21/11, 23/12
21 1184.78
22 1241.198
23 1297.617
24 1354.035
25 1410.453
26 1466.871 7/3

Harmonics

Approximation of harmonics in 26ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -15.2 +16.3 +26.0 -21.8 +1.0 +16.3 +10.8 -23.9 +19.4 +23.6 -14.2
Relative (%) -27.0 +28.8 +46.0 -38.7 +1.8 +28.8 +19.1 -42.4 +34.3 +41.9 -25.1
Steps
(reduced)
21
(21)
34
(8)
43
(17)
49
(23)
55
(3)
60
(8)
64
(12)
67
(15)
71
(19)
74
(22)
76
(24)
Approximation of harmonics in 26ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +16.5 +1.0 -5.6 -4.5 +3.4 +17.3 -19.9 +4.2 -23.9 +8.4 -12.1
Relative (%) +29.3 +1.8 -9.9 -7.9 +6.1 +30.7 -35.2 +7.4 -42.4 +14.9 -21.5
Steps
(reduced)
79
(1)
81
(3)
83
(5)
85
(7)
87
(9)
89
(11)
90
(12)
92
(14)
93
(15)
95
(17)
96
(18)

Music

birdshite stalactite