33ed5/2

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← 32ed5/233ed5/234ed5/2 →
Prime factorization 3 × 11
Step size 48.0701¢ 
Octave 25\33ed5/2 (1201.75¢)
(semiconvergent)
Twelfth 40\33ed5/2 (1922.8¢)
Consistency limit 6
Distinct consistency limit 6

33 equal divisions of 5/2 (abbreviated 33ed5/2) is a nonoctave tuning system that divides the interval of 5/2 into 33 equal parts of about 48.1 ¢ each. Each step represents a frequency ratio of (5/2)1/33, or the 33rd root of 5/2.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 48.07
2 96.14 17/16, 20/19
3 144.21 25/23
4 192.28 19/17, 28/25
5 240.351 23/20
6 288.421 13/11, 20/17
7 336.491 17/14, 23/19, 28/23
8 384.561 5/4
9 432.631
10 480.701 25/19
11 528.771 19/14, 23/17
12 576.841 7/5
13 624.911 10/7, 23/16
14 672.982 25/17, 28/19
15 721.052
16 769.122 25/16
17 817.192 8/5
18 865.262 23/14, 28/17
19 913.332 17/10, 22/13
20 961.402 7/4
21 1009.472 25/14
22 1057.542
23 1105.613 19/10
24 1153.683
25 1201.753 2/1
26 1249.823
27 1297.893 17/8
28 1345.963
29 1394.033
30 1442.103 23/10
31 1490.173 19/8, 26/11
32 1538.244 17/7
33 1586.314 5/2

Harmonics

Approximation of harmonics in 33ed5/2
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +1.8 +20.8 +3.5 +1.8 +22.6 -3.9 +5.3 -6.4 +3.5 -17.3 -23.7
Relative (%) +3.6 +43.4 +7.3 +3.6 +47.0 -8.2 +10.9 -13.3 +7.3 -36.0 -49.3
Steps
(reduced)
25
(25)
40
(7)
50
(17)
58
(25)
65
(32)
70
(4)
75
(9)
79
(13)
83
(17)
86
(20)
89
(23)
Approximation of harmonics in 33ed5/2
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -18.1 -2.2 +22.6 +7.0 -1.8 -4.6 -2.1 +5.3 +16.9 -15.5 +3.6
Relative (%) -37.6 -4.5 +47.0 +14.6 -3.8 -9.6 -4.3 +10.9 +35.2 -32.3 +7.6
Steps
(reduced)
92
(26)
95
(29)
98
(32)
100
(1)
102
(3)
104
(5)
106
(7)
108
(9)
110
(11)
111
(12)
113
(14)