7033edo: Difference between revisions
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{{EDO intro|7033}} | {{EDO intro|7033}} | ||
7033edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|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 [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller division, and a lower [[Tenney-Euclidean temperament measures #TE simple badness|TE logflat badness]] than any lower edo excepting [[72edo|72]]. A basis for its 17-limit commas is {28561/28560, 31213/31212, 37180/37179, 918750/918731, 1257795/1257728, 3070625/3070548}. | |||
=== Prime harmonics === | === Prime harmonics === | ||
{{Harmonics in equal|7033}} | {{Harmonics in equal|7033}} | ||
=== Subsets and supersets === | |||
Since 7033 factors into {{factorization|7033}}, 7033edo contains [[13edo]] and [[541edo]] as subsets. | |||
Revision as of 16:52, 20 August 2024
| ← 7032edo | 7033edo | 7034edo → |
7033edo 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 (%) | +0.0 | -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) | |
Subsets and supersets
Since 7033 factors into 13 × 541, 7033edo contains 13edo and 541edo as subsets.