42ed11/5

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← 41ed11/542ed11/543ed11/5 →
Prime factorization 2 × 3 × 7
Step size 32.5001¢ 
Octave 37\42ed11/5 (1202.5¢)
Twelfth 59\42ed11/5 (1917.51¢)
Consistency limit 5
Distinct consistency limit 4

42 equal divisions of 11/5 (abbreviated 42ed11/5) is a nonoctave tuning system that divides the interval of 11/5 into 42 equal parts of about 32.5 ¢ each. Each step represents a frequency ratio of (11/5)1/42, or the 42nd root of 11/5.

Intervals

Steps Cents Approximate Ratios
0 0 1/1
1 32.5
2 65 25/24, 26/25
3 97.5
4 130 14/13
5 162.501 11/10
6 195.001 19/17, 28/25
7 227.501 8/7, 25/22
8 260.001 22/19
9 292.501 13/11, 19/16
10 325.001 23/19
11 357.501 16/13
12 390.001 5/4
13 422.501 14/11
14 455.001 13/10
15 487.502
16 520.002 23/17
17 552.502 11/8
18 585.002 7/5
19 617.502 10/7
20 650.002 16/11
21 682.502
22 715.002
23 747.502 17/11, 20/13
24 780.002 11/7
25 812.503 8/5
26 845.003 13/8
27 877.503
28 910.003 22/13
29 942.503 19/11
30 975.003 7/4
31 1007.503 25/14
32 1040.003 20/11
33 1072.503 13/7
34 1105.003 19/10
35 1137.504 25/13
36 1170.004
37 1202.504 2/1
38 1235.004
39 1267.504 25/12
40 1300.004 17/8
41 1332.504 13/6, 28/13
42 1365.004 11/5

Harmonics

Approximation of harmonics in 42ed11/5
Harmonic 2 3 4 5 6 7 8 9 10 11 12
Error Absolute (¢) +2.5 +15.6 +5.0 +8.7 -14.4 +11.2 +7.5 -1.4 +11.2 +8.7 -11.9
Relative (%) +7.7 +47.8 +15.4 +26.8 -44.4 +34.4 +23.1 -4.3 +34.5 +26.8 -36.7
Steps
(reduced)
37
(37)
59
(17)
74
(32)
86
(2)
95
(11)
104
(20)
111
(27)
117
(33)
123
(39)
128
(2)
132
(6)
Approximation of harmonics in 42ed11/5
Harmonic 13 14 15 16 17 18 19 20 21 22 23
Error Absolute (¢) +12.0 +13.7 -8.3 +10.0 +2.6 +1.1 +5.0 +13.7 -5.8 +11.2 -0.8
Relative (%) +36.9 +42.1 -25.4 +30.8 +7.9 +3.4 +15.4 +42.2 -17.7 +34.5 -2.3
Steps
(reduced)
137
(11)
141
(15)
144
(18)
148
(22)
151
(25)
154
(28)
157
(31)
160
(34)
162
(36)
165
(39)
167
(41)