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.
It is a zeta peak and integral edo, though not a gap edo. This excellence is 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. A basis for its 17-limit commas is {28561/28560, 31213/31212, 37180/37179, 918750/918731, 1257795/1257728, 3070625/3070548}.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | absolute (¢) | +0.0000 | -0.0070 | -0.0205 | -0.0217 | -0.0312 | -0.0329 | -0.0215 | +0.0556 | -0.0360 | -0.0308 | +0.0234 |
| relative (%) | +0 | -4 | -12 | -13 | -18 | -19 | -13 | +33 | -21 | -18 | +14 | |
| Steps (reduced) |
7033 (0) |
11147 (4114) |
16330 (2264) |
19744 (5678) |
24330 (3231) |
26025 (4926) |
28747 (615) |
29876 (1744) |
31814 (3682) |
34166 (6034) |
34843 (6711) | |