494edo: Difference between revisions
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The ''494 equal | The '''494 equal temperament''' is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. It is a [[The Riemann Zeta Function and Tuning #Zeta EDO lists|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the 17-limit. It [[tempering out|tempers out]] the [[enneadeca]], {{monzo| -14 -19 19 }}, the [[tricot comma]], {{monzo| 39 -29 3 }}, and the [[kwazy comma]], {{monzo| -53 10 16 }} in the [[5-limit]]. In the [[7-limit]], it tempers out [[4375/4374]] and [[703125/702464]]; in the [[11-limit]] [[3025/3024]] and [[9801/9800]]; in the [[13-limit]] [[1716/1715]], [[2080/2079]], [[4096/4095]], [[4225/4224]] and [[6656/6655]]; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until [[1506edo|1506]] do we reach a division with a lower 13- or 17-limit [[Tenney-Euclidean temperament measures #TE simple badness|relative error]], and it is the first past [[72edo|72]] with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247. | ||
== Intervals == | |||
{{main| Table of 494edo intervals }} | |||
[[Category:17-limit]] | |||
[[Category:494edo]] | [[Category:494edo]] | ||
[[Category:Equal divisions of the octave]] | [[Category:Equal divisions of the octave]] | ||
[[Category: | [[Category:Enneadecal]] | ||
[[Category: | [[Category:Kwazy]] | ||
[[Category: | [[Category:Tricot]] | ||
[[Category: | [[Category:Zeta]] | ||
Revision as of 10:26, 30 March 2021
The 494 equal temperament is a very strong 13- and 17-limit equal temperament. It is a zeta peak and zeta peak integer edo and uniquely consistent through the 17-limit. It tempers out the enneadeca, [-14 -19 19⟩, the tricot comma, [39 -29 3⟩, and the kwazy comma, [-53 10 16⟩ in the 5-limit. In the 7-limit, it tempers out 4375/4374 and 703125/702464; in the 11-limit 3025/3024 and 9801/9800; in the 13-limit 1716/1715, 2080/2079, 4096/4095, 4225/4224 and 6656/6655; and in the 17-limit, 1156/1155, 1275/1274, 2431/2430, and 2500/2499. Not until 1506 do we reach a division with a lower 13- or 17-limit relative error, and it is the first past 72 with a lower 17-limit relative error. 494 is divisible by 2, 13, 19, 26, 38 and 247.