33edf
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Prime factorization
3 × 11
Step size
21.2714¢
Octave
56\33edf (1191.2¢)
Twelfth
89\33edf (1893.15¢)
Consistency limit
2
Distinct consistency limit
2
| ← 32edf | 33edf | 34edf → |
33 equal divisions of the perfect fifth (abbreviated 33edf or 33ed3/2) is a nonoctave tuning system that divides the interval of 3/2 into 33 equal parts of about 21.3 ¢ each. Each step represents a frequency ratio of (3/2)1/33, or the 33rd root of 3/2.
33edf corresponds to 56.4139edo, similar to every fifth step of 282edo. It is related to the regular temperament which tempers out [-131 131 -33⟩ in the 5-limit, which is supported by 113-, 282-, 395-, 677-, 959-, 1072-, 1467-, and 1749edo.
Harmonics
| Harmonic | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 | 11 | 12 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -8.80 | -8.80 | +3.66 | +0.23 | +3.66 | -7.95 | -5.14 | +3.66 | -8.57 | -3.40 | -5.14 |
| Relative (%) | -41.4 | -41.4 | +17.2 | +1.1 | +17.2 | -37.4 | -24.2 | +17.2 | -40.3 | -16.0 | -24.2 | |
| Steps (reduced) |
56 (23) |
89 (23) |
113 (14) |
131 (32) |
146 (14) |
158 (26) |
169 (4) |
179 (14) |
187 (22) |
195 (30) |
202 (4) | |
| Harmonic | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +5.19 | +4.52 | -8.57 | +7.33 | +8.73 | -5.14 | +7.61 | +3.90 | +4.52 | +9.07 | -4.08 |
| Relative (%) | +24.4 | +21.2 | -40.3 | +34.5 | +41.0 | -24.2 | +35.8 | +18.3 | +21.2 | +42.6 | -19.2 | |
| Steps (reduced) |
209 (11) |
215 (17) |
220 (22) |
226 (28) |
231 (0) |
235 (4) |
240 (9) |
244 (13) |
248 (17) |
252 (21) |
255 (24) | |
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