2513edo: Difference between revisions

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The '''2513 division''' divides the octave into 2513 equal parts of 0.4775 cents each. It is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until we reach the cosmically excellent [[4296edo|4296edo]]. A basis for its 5-limit commas is senior, |-17 62 -35> and fortune, |-107 47 14>; it also tempers out pirate, |-90 -15 49>. It is uniquely consistent through to the 11-limit, and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.

2513edo is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any edo until we reach the cosmically excellent [[4296edo]]. 2513 = {{factorization|2513}}, and it shares its [[harmonic]] [[3/1|3]] with [[359edo]]. A basis for its 5-limit commas consists of senior, {{monzo| -17 62 -35 }}, and fortune, {{monzo| -107 47 14 }}; it also [[tempering out|tempers out]] pirate, {{monzo| -90 -15 49 }}. It is uniquely [[consistent]] through to the [[11-odd-limit]], and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.

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

=== Prime harmonics ===

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 {{Infobox ET}}
-The '''2513 division''' divides the octave into 2513 equal parts of 0.4775 cents each. It is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean_temperament_measures#TE simple badness|relative error]] than any edo until we reach the cosmically excellent [[4296edo|4296edo]]. A basis for its 5-limit commas is senior, |-17 62 -35&gt; and fortune, |-107 47 14&gt;; it also tempers out pirate,  |-90 -15 49&gt;. It is uniquely consistent through to the 11-limit, and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.
+{{ED intro}}
-{{Primes in edo|2513|prec=4}}
+edo is a very strong 5-limit system, with a lower 5-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]] than any edo until we reach the cosmically excellent [[4296edo]]. 2513 = {{factorization|2513}}, and it shares its [[harmonic]] [[3/1|3]] with [[359edo]]. A basis for its 5-limit commas consists of senior, {{monzo| -17 62 -35 }}, and fortune, {{monzo| -107 47 14 }}; it also [[tempering out|tempers out]] pirate, {{monzo| -90 -15 49 }}. It is uniquely [[consistent]] through to the [[11-odd-limit]], and tempers out 420175/419904 in the 7-limit and 151263/151250 and 234375/234256 in the 11-limit.
-[[Category:Equal divisions of the octave|####]] <!-- 4-digit number -->
+=== Prime harmonics ===
+{{Harmonics in equal|2513|prec=4}}