16edo: Difference between revisions

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== Theory ==

16edo is not especially good at representing most musical intervals involving prime [[2/1|2]], but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Most low odd harmonics are tuned very flat, but some such as [[21/16|21]]:[[11/8|22]]:[[23/16|23]]:[[3/2|24]]:[[25/16|25]]:[[13/8|26]] are well in tune with each other. Having a [[Stretched_and_compressed_tuning|flat tendency]], ~~16-[[Equal-step_tuning|ET]]~~ is best tuned with the octave approximately 5{{c}} sharp, slightly improving the accuracy of wide-voiced JI chords and [[rooted]] harmonics.

16edo is not especially good at representing most musical intervals involving prime [[2/1|2]], but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Most low odd harmonics are tuned very flat, but some such as [[21/16|21]]:[[11/8|22]]:[[23/16|23]]:[[3/2|24]]:[[25/16|25]]:[[13/8|26]] are well in tune with each other. Having a [[Stretched_and_compressed_tuning|flat tendency]], 16et is best tuned with the octave approximately 5{{c}} sharp, slightly improving the accuracy of wide-voiced JI chords and [[rooted]] harmonics.

Four steps of 16edo gives the 300{{c}} minor third interval shared by [[12edo]] (and other multiples of [[4edo]]), and thus the familiar [[diminished seventh chord]] may be built on any scale step with 4 unique tetrads up to [[~~pitch_class|~~octave-equivalence]].

Four steps of 16edo gives the 300{{c}} minor third interval shared by [[12edo]] (and other multiples of [[4edo]]), and thus the familiar [[diminished seventh chord]] may be built on any scale step with 4 unique tetrads up to [[octave equivalence]].

=== Odd harmonics ===

=== Subsets and supersets ===

Since 16 factors into primes as 2<sup>4</sup>, 16edo has subset edos {{EDOs| 2, 4, and 8 }}.

== Intervals ==

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 == Theory ==
-edo is not especially good at representing most musical intervals involving prime [[2/1|2]], but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Most low odd harmonics are tuned very flat, but some such as [[21/16|21]]:[[11/8|22]]:[[23/16|23]]:[[3/2|24]]:[[25/16|25]]:[[13/8|26]] are well in tune with each other. Having a [[Stretched_and_compressed_tuning|flat tendency]], 16-[[Equal-step_tuning|ET]] is best tuned with the octave approximately 5{{c}} sharp, slightly improving the accuracy of wide-voiced JI chords and [[rooted]] harmonics.
+edo is not especially good at representing most musical intervals involving prime [[2/1|2]], but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Most low odd harmonics are tuned very flat, but some such as [[21/16|21]]:[[11/8|22]]:[[23/16|23]]:[[3/2|24]]:[[25/16|25]]:[[13/8|26]] are well in tune with each other. Having a [[Stretched_and_compressed_tuning|flat tendency]], 16et is best tuned with the octave approximately 5{{c}} sharp, slightly improving the accuracy of wide-voiced JI chords and [[rooted]] harmonics.
-Four steps of 16edo gives the 300{{c}} minor third interval shared by [[12edo]] (and other multiples of [[4edo]]), and thus the familiar [[diminished seventh chord]] may be built on any scale step with 4 unique tetrads up to [[pitch_class|octave-equivalence]].
+Four steps of 16edo gives the 300{{c}} minor third interval shared by [[12edo]] (and other multiples of [[4edo]]), and thus the familiar [[diminished seventh chord]] may be built on any scale step with 4 unique tetrads up to [[octave equivalence]].
 === Odd harmonics ===
 {{Harmonics in equal|16}}
+=== Subsets and supersets ===
+Since 16 factors into primes as 2<sup>4</sup>, 16edo has subset edos {{EDOs| 2, 4, and 8 }}.
 == Intervals ==