78005edo: Difference between revisions

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~~'''78005EDO''' is the [[~~EDO|~~equal division of the octave]] into~~ 78005 ~~parts of 0.01538363 [[cent]]s each.~~ While it is distinctly consistent through the 21 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 |232 -183 25~~>~~, |324 8 -145~~>~~, |92 191 -170~~>~~, |140 -374 195~~>~~, the selenia |-433 -137 280~~>~~, and the quark |-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 }}.

[[~~Category:Equal divisions~~ of the ~~octave|#####]] ~~

=== Prime harmonics ===

=== Subsets and supersets ===

78005edo contains [[15601edo]], from which the approximation of the 3rd harmonic is derived.

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 {{Infobox ET}}
-'''78005EDO''' is the [[EDO|equal division of the octave]] into 78005 parts of 0.01538363 [[cent]]s each. While it is distinctly consistent through the 21 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 |232 -183 25&gt;, |324 8 -145&gt;, |92 191 -170&gt;, |140 -374 195&gt;, the selenia |-433 -137 280&gt;, and the quark |-573 237 85&gt;.
+{{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 }}.
-[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
+=== Prime harmonics ===
+{{Harmonics in equal|78005}}
+=== Subsets and supersets ===
+edo contains [[15601edo]], from which the approximation of the 3rd harmonic is derived.