7033edo
| ← 7032edo | 7033edo | 7034edo → |
7033 equal divisions of the octave (abbreviated 7033edo or 7033ed2), also called 7033-tone equal temperament (7033tet) or 7033 equal temperament (7033et) when viewed under a regular temperament perspective, is the tuning system that divides the octave into 7033 equal parts of about 0.171 ¢ each. Each step represents a frequency ratio of 21/7033, or the 7033rd root of 2.
7033edo is a zeta peak and integral edo, though not a gap edo. This excellence is partly explained by the fact that it is very strong in the 17-limit, with a lower relative error than any smaller division, and a lower TE logflat badness than any lower edo excepting 72. It has a flat tendency, with all the lower harmonics until 19 tuned flat. A basis for its 17-limit commas is {28561/28560, 31213/31212, 37180/37179, 918750/918731, 1257795/1257728, 3070625/3070548}. It also tempers out 123201/123200, 194481/194480, and 336141/336140, the three smallest 17-limit superparticulars.
Since the approximation to harmonic 19 is weak, it can be used as a no-19 system, in which it continues to be strong up to the 37-limit, and is consistent to the no-19 39-odd-limit.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | 37 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.0000 | -0.0070 | -0.0205 | -0.0217 | -0.0312 | -0.0329 | -0.0215 | +0.0556 | -0.0360 | -0.0308 | +0.0234 | -0.0146 |
| Relative (%) | +0.0 | -4.1 | -12.0 | -12.7 | -18.3 | -19.3 | -12.6 | +32.6 | -21.1 | -18.0 | +13.7 | -8.6 | |
| Steps (reduced) |
7033 (0) |
11147 (4114) |
16330 (2264) |
19744 (5678) |
24330 (3231) |
26025 (4926) |
28747 (615) |
29876 (1744) |
31814 (3682) |
34166 (6034) |
34843 (6711) |
36638 (1473) | |
Subsets and supersets
Since 7033 factors into 13 × 541, 7033edo contains 13edo and 541edo as subsets.