78005edo: Difference between revisions
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{{Infobox ET}} | {{novelty}}{{stub}}{{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 04:05, 9 July 2023
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This page presents a novelty topic.
It may contain ideas which are less likely to find practical applications in music, or numbers or structures that are arbitrary or exceedingly small, large, or complex. Novelty topics are often developed by a single person or a small group. As such, this page may also contain idiosyncratic terms, notation, or conceptual frameworks. |
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| ← 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.