1080edo: Difference between revisions

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1080 is a largely composite EDO, meaning it's notable for its divisors. Its [[number of the divisors|32 divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540. 1080's abundancy index is 2.33..., or exactly 7/3.

Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however ~~1080 itself cannot be consistently read through~~ their approximation alone. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.

Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however the patent val of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.

=== Regular temperament theory ===

In the 13-limit, 1080edo is contorted order-4, with the same tuning as [[270edo]]. In the 1080e val, which puts the 11th harmonic on 3737, it tempers out 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].

=== Harmonics ===

== Table of intervals ==

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 is a largely composite EDO, meaning it's notable for its divisors. Its [[number of the divisors|32 divisors]] are 1, 2, 3, 4, 5, 6, 8, 9, 10, 12, 15, 18, 20, 24, 27, 30, 36, 40, 45, 54, 60, 72, 90, 108, 120, 135, 180, 216, 270, 360, 540. 1080's abundancy index is 2.33..., or exactly 7/3.
-Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however 1080 itself cannot be consistently read through their approximation alone. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.
+Notable subsets of 1080edo are [[270edo]] and [[72edo]], as they both belong to [[The Riemann Zeta Function and Tuning#Zeta EDO lists|the ''zeta peak edos'', ''zeta integral edos'' and ''zeta gap edos'' sequences]], however the patent val of 1080edo does not consist of their approximation alone, as the 17th harmonic comes from [[540edo]]. In addition, [[12edo]] is the dominant tuning system in the world, and [[360edo]] is a highly composite EDO.
 === Regular temperament theory ===
 In the 13-limit, 1080edo is contorted order-4, with the same tuning as [[270edo]]. In the 1080e val, which puts the 11th harmonic on 3737, it tempers out 114345/114244, and in the 1080ef val it tempers out [[2080/2079]].
+=== Harmonics ===
+{{Harmonics in equal|1080}}
 == Table of intervals ==