42ed11/5
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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
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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
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) |
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) |