2964edo: Difference between revisions

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The '''2964 equal divisions of the octave''' ('''2964edo'''), or the '''2964(-tone) equal temperament''' ('''2964tet''', '''2964et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 2964 [[equal]] parts of about 0.4048583 [[cent]]s each.

~~== Theory ==~~

In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap|26 × 57 × 2}}.

In the 13-limit, 2964edo shares the same patent val ~~than~~ [[494edo]] ~~excepting~~ for the 7th harmonic, which is corrected in an extremely ~~precise way~~ (absolute error 0.00000446 cents, relative error 0.0011%).

=== Prime harmonics ===

=== ~~Miscellaneous properties~~ ===

=== Subsets and supersets ===

Since 2964 = 6 × 494, ~~2964edo contains [[494edo]] as a subset~~.

Since 2964 factors into {{factorization|2964}}, 2964edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, and 1482 }}.

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

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 {{Infobox ET}}
-The '''2964 equal divisions of the octave''' ('''2964edo'''), or the '''2964(-tone) equal temperament''' ('''2964tet''', '''2964et''') when viewed from a [[regular temperament]] perspective, divides the [[octave]] into 2964 [[equal]] parts of about 0.4048583 [[cent]]s each.
+{{ED intro}}
-== Theory ==
+In the 13-limit, 2964edo shares the same [[patent val]] with [[494edo]] except for the [[7/1|7th harmonic]], which is corrected to an extremely accurate result (absolute error 0.00000446 cents, relative error 0.0011%). 2964 is the denominator to a [[convergent]] to log<sub>2</sub>7. Bordering 2964edo's patent val 7/1 on either side are [[26edo]]'s sharp approximation and [[57edo]]'s flat approximation of 7/1, having nearly identical 0.4048{{c}} errors; 2964edo exactly divides the octave into 26 and into 57 equal steps, splitting the difference between 160\57 and 73\26, as 2964 is expressible as {{nowrap|26 × 57 × 2}}.
-In the 13-limit, 2964edo shares the same patent val than [[494edo]] excepting for the 7th harmonic, which is corrected in an extremely precise way (absolute error 0.00000446 cents, relative error 0.0011%).
 === Prime harmonics ===
 {{Harmonics in equal|2964|columns=11|prec=3}}
-=== Miscellaneous properties ===
+=== Subsets and supersets ===
-Since 2964 = 6 × 494, 2964edo contains [[494edo]] as a subset.
+Since 2964 factors into {{factorization|2964}}, 2964edo has subset edos {{EDOs| 2, 3, 4, 6, 12, 13, 19, 26, 38, 39, 52, 57, 76, 78, 114, 156, 228, 247, 494, 741, 988, and 1482 }}.
-[[Category:Equal divisions of the octave|####]] <!-- four-digit number -->