32ed7/3

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← 31ed7/332ed7/333ed7/3 →
Prime factorization 25
Step size 45.8397¢ 
Octave 26\32ed7/3 (1191.83¢) (→13\16ed7/3)
Twelfth 41\32ed7/3 (1879.43¢)
Consistency limit 4
Distinct consistency limit 4

32 equal divisions of 7/3 (abbreviated 32ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 32 equal parts of about 45.8 ¢ each. Each step represents a frequency ratio of (7/3)1/32, or the 32nd root of 7/3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 45.84
2 91.679 20/19
3 137.519
4 183.359 19/17
5 229.199 8/7, 25/22
6 275.038 7/6, 20/17
7 320.878
8 366.718
9 412.557 19/15
10 458.397 13/10, 17/13
11 504.237 4/3
12 550.077 26/19
13 595.916
14 641.756
15 687.596
16 733.435 23/15, 26/17
17 779.275
18 825.115
19 870.955
20 916.794 17/10, 22/13
21 962.634 7/4
22 1008.474
23 1054.313
24 1100.153
25 1145.993
26 1191.833 2/1
27 1237.672
28 1283.512
29 1329.352
30 1375.191
31 1421.031 25/11
32 1466.871 7/3

Harmonics

Approximation of harmonics in 32ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) -8.2 -22.5 -16.3 +9.9 +15.1 -22.5 +21.3 +0.8 +1.7 +20.1 +7.0
Relative (%) -17.8 -49.1 -35.6 +21.6 +33.0 -49.1 +46.5 +1.7 +3.8 +43.8 +15.2
Steps
(reduced)
26
(26)
41
(9)
52
(20)
61
(29)
68
(4)
73
(9)
79
(15)
83
(19)
87
(23)
91
(27)
94
(30)
Approximation of harmonics in 32ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +5.9 +15.1 -12.6 +13.2 -0.1 -7.4 -9.3 -6.4 +0.8 +11.9 -19.2
Relative (%) +12.9 +33.0 -27.5 +28.7 -0.2 -16.1 -20.3 -14.0 +1.7 +26.0 -41.9
Steps
(reduced)
97
(1)
100
(4)
102
(6)
105
(9)
107
(11)
109
(13)
111
(15)
113
(17)
115
(19)
117
(21)
118
(22)