78005edo: Difference between revisions
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{{Infobox ET}} | |||
{{EDO intro|78005}} While it is distinctly [[consistent]] through the 21-odd-limit, its notability stems from the fact that it is a very strong 5-limit division, with lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller edo, and lower 5-limit [[Tenney-Euclidean metrics #Logflat TE badness|TE logflat badness]] than any smaller edo excepting [[4296edo|4296]]. It tempers out {{monzo| 232 -183 25 }}, {{monzo| 324 8 -145 }}, {{monzo| 92 191 -170 }}, {{monzo| 140 -374 195 }}, the selenia {{monzo| -433 -137 280 }}, and the quark {{monzo| -573 237 85 }}. | {{EDO intro|78005}} While it is distinctly [[consistent]] through the 21-odd-limit, its notability stems from the fact that it is a very strong 5-limit division, with lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller edo, and lower 5-limit [[Tenney-Euclidean metrics #Logflat TE badness|TE logflat badness]] than any smaller edo excepting [[4296edo|4296]]. It tempers out {{monzo| 232 -183 25 }}, {{monzo| 324 8 -145 }}, {{monzo| 92 191 -170 }}, {{monzo| 140 -374 195 }}, the selenia {{monzo| -433 -137 280 }}, and the quark {{monzo| -573 237 85 }}. | ||
Revision as of 07:18, 9 July 2023
| ← 78004edo | 78005edo | 78006edo → |
Template:EDO intro While it is distinctly consistent through the 21-odd-limit, its notability stems from the fact that it is a very strong 5-limit division, with lower 5-limit relative error than any smaller edo, and lower 5-limit TE logflat badness than any smaller edo excepting 4296. It tempers out [232 -183 25⟩, [324 8 -145⟩, [92 191 -170⟩, [140 -374 195⟩, the selenia [-433 -137 280⟩, and the quark [-573 237 85⟩.
Prime harmonics
| Harmonic | 2 | 3 | 5 | 7 | 11 | 13 | 17 | 19 | 23 | 29 | 31 | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
| Error | Absolute (¢) | +0.00000 | +0.00000 | -0.00002 | +0.00430 | +0.00056 | +0.00307 | +0.00709 | +0.00637 | -0.00693 | +0.00296 | -0.00128 |
| Relative (%) | +0.0 | +0.0 | -0.1 | +27.9 | +3.7 | +20.0 | +46.1 | +41.4 | -45.0 | +19.2 | -8.3 | |
| Steps (reduced) |
78005 (0) |
123635 (45630) |
181122 (25112) |
218988 (62978) |
269853 (35838) |
288653 (54638) |
318843 (6823) |
331360 (19340) |
352860 (40840) |
378947 (66927) |
386452 (74432) | |
Subsets and supersets
78005edo contains 15601edo, from which the approximation of the 3rd harmonic is derived.