33ed7/4

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← 32ed7/433ed7/434ed7/4 →
Prime factorization 3 × 11
Step size 29.3584¢ 
Octave 41\33ed7/4 (1203.69¢)
Twelfth 65\33ed7/4 (1908.29¢)
Consistency limit 10
Distinct consistency limit 3

33 equal divisions of 7/4 (abbreviated 33ed7/4) is a nonoctave tuning system that divides the interval of 7/4 into 33 equal parts of about 29.4 ¢ each. Each step represents a frequency ratio of (7/4)1/33, or the 33rd root of 7/4.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 29.358
2 58.717 28/27
3 88.075 19/18, 20/19, 21/20
4 117.433 15/14, 16/15
5 146.792 25/23
6 176.15 10/9, 21/19
7 205.509 9/8, 26/23
8 234.867 8/7, 23/20
9 264.225 7/6
10 293.584 13/11, 19/16, 25/21
11 322.942 6/5, 23/19
12 352.3
13 381.659 5/4
14 411.017 19/15, 24/19
15 440.375 9/7, 22/17
16 469.734 17/13, 21/16, 25/19
17 499.092 4/3
18 528.45 19/14, 23/17, 27/20
19 557.809
20 587.167 7/5
21 616.526 10/7, 27/19
22 645.884
23 675.242 25/17, 28/19
24 704.601 3/2
25 733.959 23/15, 26/17
26 763.317 14/9
27 792.676 19/12
28 822.034 8/5
29 851.392 23/14
30 880.751 5/3
31 910.109 17/10, 22/13, 27/16
32 939.468 12/7
33 968.826 7/4

Harmonics

Approximation of harmonics in 33ed7/4
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +3.7 +6.3 +7.4 +2.7 +10.0 +7.4 +11.1 +12.7 +6.4 -11.8 +13.7
Relative (%) +12.6 +21.6 +25.2 +9.3 +34.2 +25.2 +37.7 +43.2 +21.9 -40.2 +46.7
Steps
(reduced)
41
(8)
65
(32)
82
(16)
95
(29)
106
(7)
115
(16)
123
(24)
130
(31)
136
(4)
141
(9)
147
(15)
Approximation of harmonics in 33ed7/4
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -7.4 +11.1 +9.1 -14.6 -2.1 -13.0 +10.8 +10.1 +13.7 -8.1 +3.0
Relative (%) -25.3 +37.7 +30.9 -49.7 -7.2 -44.2 +36.9 +34.5 +46.7 -27.6 +10.3
Steps
(reduced)
151
(19)
156
(24)
160
(28)
163
(31)
167
(2)
170
(5)
174
(9)
177
(12)
180
(15)
182
(17)
185
(20)