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 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| 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 (%) | +0.0 | -4.1 | -12.0 | -12.7 | -18.3 | -19.3 | -12.6 | +32.6 | -21.1 | -18.0 | +13.7 | |
| Steps (reduced) |
7033 (0) |
11147 (4114) |
16330 (2264) |
19744 (5678) |
24330 (3231) |
26025 (4926) |
28747 (615) |
29876 (1744) |
31814 (3682) |
34166 (6034) |
34843 (6711) | |
| Harmonic | 37 | 41 | 43 | 47 | 53 | 59 | 61 | 67 | 71 | 73 | 79 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | -0.0146 | +0.0575 | +0.0136 | -0.0722 | -0.0793 | +0.0634 | +0.0212 | +0.0332 | -0.0293 | -0.0062 | -0.0836 |
| Relative (%) | -8.6 | +33.7 | +8.0 | -42.3 | -46.5 | +37.1 | +12.4 | +19.5 | -17.1 | -3.6 | -49.0 | |
| Steps (reduced) |
36638 (1473) |
37680 (2515) |
38163 (2998) |
39065 (3900) |
40284 (5119) |
41373 (6208) |
41711 (6546) |
42663 (465) |
43251 (1053) |
43533 (1335) |
44334 (2136) | |
Subsets and supersets
Since 7033 factors into primes as 13 × 541, 7033edo contains 13edo and 541edo as subsets.