771edo: Difference between revisions

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The '''771 equal division''' divides the octave into 771 equal parts of 1.556 cents each. It is uniquely [[consistent|consistent]] up to the 21-limit, with all of the primes to 19 having a flat tendency. In the 5-limit it tempers out the monzisma, |54 -37 2>, and |-44 -3 21>; in the 7-limit 65625/65536 and 250047/250000; in the 11-limit 3025/3024; in the 13-limit 4225/4224 and 10648/10647; in the 17-limit 833/832, 1225/1224, 2058/2057, 2431/2430 and 2601/2600; and in the 19-limit 1445/1444, 1540/1539, 1729/1728, 2926/2925, 3250/3249, 4200/4199 and 5985/5984. 771 provides the [[Optimal_patent_val|optimal patent val]] for the rank six temperament tempering out 833/832 and various other temperaments tempering it out.

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

771edo is [[consistency|distinctly consistent]] up to the [[21-odd-limit]], with all of the [[prime harmonic]]s to 19 having a flat tendency.

In the 5-limit it [[tempering out|tempers out]] the [[monzisma]], {{monzo| 54 -37 2 }}, and the [[mutt comma]], {{monzo| -44 -3 21 }}; in the 7-limit [[65625/65536]] and [[250047/250000]]; in the 11-limit [[3025/3024]]; in the 13-limit [[4225/4224]] and [[10648/10647]]; in the 17-limit [[833/832]], [[1225/1224]], [[2058/2057]], [[2431/2430]] and [[2601/2600]]; and in the 19-limit [[1445/1444]], 1540/1539, [[1729/1728]], 2926/2925, 3250/3249, 4200/4199 and 5985/5984. It provides the [[optimal patent val]] for the rank-6 temperament tempering out 833/832 and various other temperaments tempering it out.

=== Prime harmonics ===

=== Subsets and supersets ===

Since 771 factors into {{factorization|771}}, 771edo contains [[3edo]] and [[257edo]] as subsets.

[[Category:Horizmic]]

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 {{Infobox ET}}
-The '''771 equal division''' divides the octave into 771 equal parts of 1.556 cents each. It is uniquely [[consistent|consistent]] up to the 21-limit, with all of the primes to 19 having a flat tendency. In the 5-limit it tempers out the monzisma, |54 -37 2&gt;, and |-44 -3 21&gt;; in the 7-limit 65625/65536 and 250047/250000; in the 11-limit 3025/3024; in the 13-limit 4225/4224 and 10648/10647; in the 17-limit 833/832, 1225/1224, 2058/2057, 2431/2430 and 2601/2600; and in the 19-limit 1445/1444, 1540/1539, 1729/1728, 2926/2925, 3250/3249, 4200/4199 and 5985/5984. 771 provides the [[Optimal_patent_val|optimal patent val]] for the rank six temperament tempering out 833/832 and various other temperaments tempering it out.
+{{ED intro}}
-[[Category:Equal divisions of the octave|###]] <!-- 3-digit number -->
+edo is [[consistency|distinctly consistent]] up to the [[21-odd-limit]], with all of the [[prime harmonic]]s to 19 having a flat tendency.
+In the 5-limit it [[tempering out|tempers out]] the [[monzisma]], {{monzo| 54 -37 2 }}, and the [[mutt comma]], {{monzo| -44 -3 21 }}; in the 7-limit [[65625/65536]] and [[250047/250000]]; in the 11-limit [[3025/3024]]; in the 13-limit [[4225/4224]] and [[10648/10647]]; in the 17-limit [[833/832]], [[1225/1224]], [[2058/2057]], [[2431/2430]] and [[2601/2600]]; and in the 19-limit [[1445/1444]], 1540/1539, [[1729/1728]], 2926/2925, 3250/3249, 4200/4199 and 5985/5984. It provides the [[optimal patent val]] for the rank-6 temperament tempering out 833/832 and various other temperaments tempering it out.
+=== Prime harmonics ===
+{{Harmonics in equal|771}}
+=== Subsets and supersets ===
+Since 771 factors into {{factorization|771}}, 771edo contains [[3edo]] and [[257edo]] as subsets.
+[[Category:Horizmic]]