41ed7/3

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← 40ed7/341ed7/342ed7/3 →
Prime factorization 41 (prime)
Step size 35.7773¢ 
Octave 34\41ed7/3 (1216.43¢)
Twelfth 53\41ed7/3 (1896.2¢)
Consistency limit 2
Distinct consistency limit 2

41 equal divisions of 7/3 (abbreviated 41ed7/3) is a nonoctave tuning system that divides the interval of 7/3 into 41 equal parts of about 35.8 ¢ each. Each step represents a frequency ratio of (7/3)1/41, or the 41st root of 7/3.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 35.777
2 71.555 23/22, 26/25
3 107.332
4 143.109 25/23
5 178.887 21/19
6 214.664 17/15, 25/22, 26/23
7 250.441 15/13, 29/25
8 286.219 13/11
9 321.996 6/5
10 357.773
11 393.551
12 429.328 9/7, 23/18
13 465.105 17/13, 30/23
14 500.883
15 536.66 15/11
16 572.437 25/18
17 608.215 27/19
18 643.992
19 679.769
20 715.547
21 751.324 17/11
22 787.101 11/7
23 822.879 29/18
24 858.656 18/11, 23/14
25 894.433
26 930.211 29/17
27 965.988
28 1001.765 25/14
29 1037.543
30 1073.32 13/7
31 1109.098
32 1144.875 29/15
33 1180.652
34 1216.43
35 1252.207
36 1287.984 19/9
37 1323.762 15/7
38 1359.539 11/5
39 1395.316 29/13
40 1431.094
41 1466.871 7/3

Harmonics

Approximation of harmonics in 41ed7/3
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +16.4 -5.8 -2.9 +4.3 +10.7 -5.8 +13.5 -11.5 -15.0 -1.1 -8.7
Relative (%) +45.9 -16.1 -8.2 +12.1 +29.8 -16.1 +37.8 -32.2 -42.0 -3.2 -24.2
Steps
(reduced)
34
(34)
53
(12)
67
(26)
78
(37)
87
(5)
94
(12)
101
(19)
106
(24)
111
(29)
116
(34)
120
(38)
Approximation of harmonics in 41ed7/3
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) -4.1 +10.7 -1.4 -5.8 -3.5 +4.9 -17.1 +1.4 -11.5 +15.3 +9.9
Relative (%) -11.6 +29.8 -4.0 -16.3 -9.7 +13.7 -47.9 +3.9 -32.2 +42.7 +27.6
Steps
(reduced)
124
(1)
128
(5)
131
(8)
134
(11)
137
(14)
140
(17)
142
(19)
145
(22)
147
(24)
150
(27)
152
(29)