1440edo: Difference between revisions

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~~From a regular temperament perspective,~~ 1440edo ~~only has a consistency~~ limit ~~of 3~~ and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.15.17.19~~.21~~.23~~.25.27~~.31~~.33~~ subgroup. It may also be considered as every third step of [[4320edo]] in this regard.

1440edo is in[[consistent]] to the [[5-odd-limit]] and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.27.15.21.33.17.19.23.31 [[subgroup]]. It may also be considered as every third step of [[4320edo]] in this regard.

=== Odd harmonics ===

=== Subsets and supersets ===

1440edo is notable for having a lot of ~~divisors~~, ~~namely~~ {{EDOs|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720}}. It is also a [[Highly composite equal division#Highly factorable numbers|highly factorable]] ~~equal division~~.

Since 1440 factors into {{factorization|1440}}, 1440edo is notable for having a lot of subset edos, the nontrivial ones being {{EDOs| 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, and 720 }}. It is also a [[Highly composite equal division #Highly factorable numbers|highly factorable equal division]].

As an interval size measure, one step of 1440edo is called ''decifarab''.

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 {{EDO intro|1440}}
-From a regular temperament perspective, 1440edo only has a consistency limit of 3 and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.15.17.19.21.23.25.27.31.33 subgroup. It may also be considered as every third step of [[4320edo]] in this regard.
+edo is in[[consistent]] to the [[5-odd-limit]] and does poorly with approximating lower harmonics. However, 1440edo is worth considering as a higher-limit system, where it has excellent representation of the 2.27.15.21.33.17.19.23.31 [[subgroup]]. It may also be considered as every third step of [[4320edo]] in this regard.
 === Odd harmonics ===
 {{Harmonics in equal|1440}}
 === Subsets and supersets ===
-edo is notable for having a lot of divisors, namely {{EDOs|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, 720}}. It is also a [[Highly composite equal division#Highly factorable numbers|highly factorable]] equal division.
+Since 1440 factors into {{factorization|1440}}, 1440edo is notable for having a lot of subset edos, the nontrivial ones being {{EDOs| 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 30, 32, 36, 40, 45, 48, 60, 72, 80, 90, 96, 120, 144, 160, 180, 240, 288, 360, 480, and 720 }}. It is also a [[Highly composite equal division #Highly factorable numbers|highly factorable equal division]].
 As an interval size measure, one step of 1440edo is called ''decifarab''.