31ed11/5

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← 30ed11/531ed11/532ed11/5 →
Prime factorization 31 (prime)
Step size 44.0324¢ 
Octave 27\31ed11/5 (1188.87¢)
Twelfth 43\31ed11/5 (1893.39¢)
Consistency limit 3
Distinct consistency limit 3

31 equal divisions of 11/5 (abbreviated 31ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 31 equal parts of about 44 ¢ each. Each step represents a frequency ratio of (11/5)1/31, or the 31st root of 11/5.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 44.032
2 88.065
3 132.097 14/13, 27/25
4 176.13 10/9, 21/19
5 220.162 17/15, 25/22, 26/23
6 264.194
7 308.227 6/5
8 352.259 11/9, 27/22
9 396.292
10 440.324 22/17
11 484.356
12 528.389 15/11, 19/14, 23/17, 27/20
13 572.421 25/18
14 616.454
15 660.486 19/13, 22/15, 25/17
16 704.518 3/2
17 748.551 17/11, 23/15
18 792.583 27/17
19 836.615 21/13
20 880.648 5/3
21 924.68 17/10
22 968.713
23 1012.745 9/5
24 1056.777 11/6
25 1100.81 17/9
26 1144.842
27 1188.875
28 1232.907
29 1276.939 23/11, 25/12
30 1320.972
31 1365.004 11/5

Harmonics

Approximation of harmonics in 31ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -11.1 -8.6 +21.8 -12.3 -19.7 +21.7 +10.7 -17.1 +20.6 -12.3 +13.2
Relative (%) -25.3 -19.4 +49.5 -27.9 -44.7 +49.2 +24.2 -38.9 +46.9 -27.9 +30.0
Steps
(reduced)
27
(27)
43
(12)
55
(24)
63
(1)
70
(8)
77
(15)
82
(20)
86
(24)
91
(29)
94
(1)
98
(5)
Approximation of harmonics in 31ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +6.7 +10.5 -20.8 -0.5 -17.4 +15.8 +10.2 +9.5 +13.1 +20.6 -12.3
Relative (%) +15.3 +23.9 -47.3 -1.1 -39.4 +35.8 +23.3 +21.6 +29.8 +46.9 -27.9
Steps
(reduced)
101
(8)
104
(11)
106
(13)
109
(16)
111
(18)
114
(21)
116
(23)
118
(25)
120
(27)
122
(29)
123
(30)