78005edo: Difference between revisions

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~~The 78005 division divides the octave into 78005 equal parts of 0.01538 cents 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 ~~loglfat~~ 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~~>~~.

While 78005edo is [[consistency|distinctly consistent]] through the [[21-odd-limit]], its notability stems from the fact that it is a very strong [[5-limit]] system, with lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller edo, and lower 5-limit [[TE logflat badness]] than any smaller edo excepting [[4296edo|4296]]. The equal temperament [[tempering out|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 }}.

=== Prime harmonics ===

=== Subsets and supersets ===

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

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-The 78005 division divides the octave into 78005 equal parts of 0.01538 cents 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 loglfat 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;.
+{{Infobox ET}}
+{{ED intro}}
+While 78005edo is [[consistency|distinctly consistent]] through the [[21-odd-limit]], its notability stems from the fact that it is a very strong [[5-limit]] system, with lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any smaller edo, and lower 5-limit [[TE logflat badness]] than any smaller edo excepting [[4296edo|4296]]. The equal temperament [[tempering out|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 }}.
+=== Prime harmonics ===
+{{Harmonics in equal|78005}}
+=== Subsets and supersets ===
+edo contains [[15601edo]], from which the approximation of the 3rd harmonic is derived.