494edo: Difference between revisions

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The '''494 equal divisions of the octave''' ('''494edo'''), or the '''494(-tone) equal temperament''' ('''494tet''', '''494et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 494 [[equal]] parts of about 2.43 [[cent]]s each~~. It is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. The step size is close to [[729/728]], the squbema, and a step is a '''squb'''~~.

The '''494 equal divisions of the octave''' ('''494edo'''), or the '''494(-tone) equal temperament''' ('''494tet''', '''494et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 494 [[equal]] parts of about 2.43 [[cent]]s each.

== Theory ==

494edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the [[17-odd-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.

494 is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. 494edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the [[17-odd-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.

Since the step size is close to [[729/728]], the squbema, the accepted name for 494edo's step is ''squb''

=== Prime harmonics ===

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 {{Infobox ET}}
-The '''494 equal divisions of the octave''' ('''494edo'''), or the '''494(-tone) equal temperament''' ('''494tet''', '''494et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 494 [[equal]] parts of about 2.43 [[cent]]s each. It is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. The step size is close to [[729/728]], the squbema, and a step is a '''squb'''.
+The '''494 equal divisions of the octave''' ('''494edo'''), or the '''494(-tone) equal temperament''' ('''494tet''', '''494et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 494 [[equal]] parts of about 2.43 [[cent]]s each.
 == Theory ==
-edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the [[17-odd-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.
+is a very strong [[13-limit|13]]- and [[17-limit]] equal temperament. 494edo is a [[The Riemann zeta function and tuning #Zeta EDO lists|zeta peak and zeta peak integer edo]] and uniquely [[consistent]] through the [[17-odd-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.
+Since the step size is close to [[729/728]], the squbema, the accepted name for 494edo's step is ''squb''
 === Prime harmonics ===
 {{Harmonics in equal|494|columns=11|prec=3}}