4320edo: Difference between revisions

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=== Divisors ===

4320's divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160. In addition to being largely composite, it is [[oeis:A002093|highly abundant]] (although not superabundant). It's abundancy index is 2.5 = exactly 5/2.

4320's divisors are {{EDOs|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160}}. In addition to being largely composite, it is [[oeis:A002093|highly abundant]] (although not superabundant). It's abundancy index is 2.5 = exactly 5/2.

Out of the harmonics in the 23-limit approximated by 4320edo, only 3 and 5 have step sizes coprime with the number 4320. The 7th harmonic comes from [[135edo]], 11th harmonic comes from [[864edo]], 13th harmonic derives from [[2160edo]], 17th harmonic derives from [[80edo]], 19th harmonic derives from [[480edo]], and the 23rd harmonic comes from [[720edo]].

Other notable divisors 4320edo has are [[12edo]], the dominant tuning system in the world today, [[15edo]], known for use by [[Easley Blackwood Jr]]., [[72edo]], which has found usage in Byzantine chanting and various other applications, [[96edo]] notable for its use by Julian Carrillo, [[270edo]], notable for its excellent closed representation of the 13-limit, [[360edo]], notable for being a number of degrees in a circle and carrying the interval size measure ~~Drobisch~~ angle.

Other notable divisors 4320edo has are [[12edo]], the dominant tuning system in the world today, [[15edo]], known for use by [[Easley Blackwood Jr]]., [[72edo]], which has found usage in Byzantine chanting and various other applications, [[96edo]] notable for its use by Julian Carrillo, [[270edo]], notable for its excellent closed representation of the 13-limit relative to its size, [[360edo]], notable for being a number of degrees in a circle and carrying the interval size measure Dröbisch angle.

=== Regular temperament theory ===

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 === Divisors ===
-'s divisors are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160. In addition to being largely composite, it is [[oeis:A002093|highly abundant]] (although not superabundant). It's abundancy index is 2.5 = exactly 5/2.
+'s divisors are {{EDOs|1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 16, 18, 20, 24, 27, 30, 32, 36, 40, 45, 48, 54, 60, 72, 80, 90, 96, 108, 120, 135, 144, 160, 180, 216, 240, 270, 288, 360, 432, 480, 540, 720, 864, 1080, 1440, 2160}}. In addition to being largely composite, it is [[oeis:A002093|highly abundant]] (although not superabundant). It's abundancy index is 2.5 = exactly 5/2.
 Out of the harmonics in the 23-limit approximated by 4320edo, only 3 and 5 have step sizes coprime with the number 4320. The 7th harmonic comes from [[135edo]], 11th harmonic comes from [[864edo]], 13th harmonic derives from [[2160edo]], 17th harmonic derives from [[80edo]], 19th harmonic derives from [[480edo]], and the 23rd harmonic comes from [[720edo]].
-Other notable divisors 4320edo has are [[12edo]], the dominant tuning system in the world today, [[15edo]], known for use by [[Easley Blackwood Jr]]., [[72edo]], which has found usage in Byzantine chanting and various other applications, [[96edo]] notable for its use by Julian Carrillo, [[270edo]], notable for its excellent closed representation of the 13-limit, [[360edo]], notable for being a number of degrees in a circle and carrying the interval size measure Drobisch angle.
+Other notable divisors 4320edo has are [[12edo]], the dominant tuning system in the world today, [[15edo]], known for use by [[Easley Blackwood Jr]]., [[72edo]], which has found usage in Byzantine chanting and various other applications, [[96edo]] notable for its use by Julian Carrillo, [[270edo]], notable for its excellent closed representation of the 13-limit relative to its size, [[360edo]], notable for being a number of degrees in a circle and carrying the interval size measure Dröbisch angle.
 === Regular temperament theory ===