36ed11/5

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← 35ed11/5 36ed11/5 37ed11/5 →
Prime factorization 22 × 32
Step size 37.9168¢ 
Octave 32\36ed11/5 (1213.34¢) (→8\9ed11/5)
Twelfth 50\36ed11/5 (1895.84¢) (→25\18ed11/5)
Consistency limit 2
Distinct consistency limit 2
Special properties

36 equal divisions of 11/5 (abbreviated 36ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 36 equal parts of about 37.9 ¢ each. Each step represents a frequency ratio of (11/5)1/36, or the 36th root of 11/5.

Intervals

Steps Cents Approximate ratios
0 0 1/1
1 37.917
2 75.834 22/21, 23/22
3 113.75
4 151.667 23/21
5 189.584 10/9, 19/17, 29/26
6 227.501
7 265.417 7/6
8 303.334
9 341.251 11/9
10 379.168
11 417.085 19/15, 23/18
12 455.001 13/10
13 492.918
14 530.835 15/11, 23/17
15 568.752 18/13
16 606.669 27/19
17 644.585 13/9, 29/20
18 682.502
19 720.419
20 758.336 17/11
21 796.252 27/17
22 834.169 21/13
23 872.086
24 910.003 22/13
25 947.92 19/11
26 985.836 23/13
27 1023.753 9/5
28 1061.67
29 1099.587 17/9
30 1137.504
31 1175.42
32 1213.337
33 1251.254
34 1289.171 19/9, 21/10
35 1327.087
36 1365.004 11/5

Harmonics

Approximation of harmonics in 36ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +13.3 -6.1 -11.2 -18.4 +7.2 +5.8 +2.1 -12.2 -5.1 -18.4 -17.4
Relative (%) +35.2 -16.1 -29.7 -48.5 +19.0 +15.2 +5.5 -32.3 -13.3 -48.5 -45.8
Steps
(reduced)
32
(32)
50
(14)
63
(27)
73
(1)
82
(10)
89
(17)
95
(23)
100
(28)
105
(33)
109
(1)
113
(5)
Approximation of harmonics in 36ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -4.3 -18.8 +13.4 +15.4 -13.7 +1.1 -16.7 +8.3 -0.3 -5.1 -6.2
Relative (%) -11.2 -49.6 +35.4 +40.7 -36.1 +2.9 -43.9 +21.9 -0.9 -13.3 -16.3
Steps
(reduced)
117
(9)
120
(12)
124
(16)
127
(19)
129
(21)
132
(24)
134
(26)
137
(29)
139
(31)
141
(33)
143
(35)