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>.

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

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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-'''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;.
+{{Infobox ET}}
+{{ED intro}}
-[[Category:Equal divisions of the octave|#####]] <!-- 5-digit number -->
+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.