16edo: Difference between revisions

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== Theory ==

16edo is not especially good at representing most ~~low-odd-limit~~ musical intervals, but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Four steps of it gives the 300 ~~cent~~ minor third interval~~, the same of that~~ 12edo~~, giving it four diminished seventh chords exactly like those~~ of [[~~12edo~~]], and a diminished ~~triad~~ on ~~each~~ scale step.

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.

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]].

=== Odd harmonics ===

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16edo notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. The Armodue model uses a 4-line staff for 16edo.

Mos scales like mavila[7] (or "inverse/anti-diatonic" which reverses step sizes of diatonic from LLsLLLs to ssLsssL in the heptatonic variation) can work as an alternative to the traditional diatonic scale, while maintaining conventional A-G #/b notation as described above. Alternatively, one can utilize the Mavila[9] MOS, for a sort of "hyper-diatonic" scale of 7 large steps and 2 small steps. [[Armodue_theory|Armodue notation]] of 16-EDO "Mavila-[9] Staff" does just this, and places the arrangement (222122221) on nine white "natural" keys of the 16edo keyboard. If the 9-note "Enneatonic" MOS is adopted as a notational basis for 16edo, then we need an entirely different set of interval classes than any of the heptatonic classes described above; perhaps it even makes sense to refer to ~~octaves as~~ 2/1, "[[decave]]".

Mos scales like mavila[7] (or "inverse/anti-diatonic" which reverses step sizes of diatonic from LLsLLLs to ssLsssL in the heptatonic variation) can work as an alternative to the traditional diatonic scale, while maintaining conventional A-G #/b notation as described above. Alternatively, one can utilize the Mavila[9] MOS, for a sort of "hyper-diatonic" scale of 7 large steps and 2 small steps. [[Armodue_theory|Armodue notation]] of 16-EDO "Mavila-[9] Staff" does just this, and places the arrangement (222122221) on nine white "natural" keys of the 16edo keyboard. If the 9-note "Enneatonic" MOS is adopted as a notational basis for 16edo, then we need an entirely different set of interval classes than any of the heptatonic classes described above; perhaps it even makes sense to refer to the octave ([[2/1]]) as the "[[decave]]".

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== Chord names ==

16edo chords can be named using ups and downs. Using harmonic interval names, the names are easy to find, but they bear little relationship to the sound. 4:5:6 is a ~~minor~~ chord ~~and~~ 10:12:15 is a ~~major chord~~! ~~Using~~ melodic names, the chord names will match the sound, but finding the name is ~~much~~ more complicated (see below).

16edo chords can be named using ups and downs. Using harmonic (circle-of-fifths) interval names, the names are easy to find, but they bear little relationship to the sound: a minor chord (spelled A-C-E) sounds like [[4:5:6]], the classical major triad, and a major chord (spelled C-E-G) sounds like [[10:12:15]], a classical minor triad! Instead, using melodic names, the chord names will match the sound—but finding the name from the spelling is more complicated (see below).

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 == Theory ==
-edo is not especially good at representing most low-odd-limit musical intervals, but it has a [[7/4]] which is only six cents sharp, and a [[5/4]] which is only eleven cents flat. Four steps of it gives the 300 cent minor third interval, the same of that 12edo, giving it four diminished seventh chords exactly like those of [[12edo]], and a diminished triad on each scale step.
+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.
+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]].
 === Odd harmonics ===
@@ Line 208: / Line 210: @@
 edo notation can be easy utilizing Goldsmith's Circle of keys, nominals, and respective notation. The nominals for a 6 line staff can be switched for Wilson's Beta and Epsilon additions to A-G. The Armodue model uses a 4-line staff for 16edo.
-Mos scales like mavila[7] (or "inverse/anti-diatonic" which reverses step sizes of diatonic from LLsLLLs to ssLsssL in the heptatonic variation) can work as an alternative to the traditional diatonic scale, while maintaining conventional A-G #/b notation as described above. Alternatively, one can utilize the Mavila[9] MOS, for a sort of "hyper-diatonic" scale of 7 large steps and 2 small steps. [[Armodue_theory|Armodue notation]] of 16-EDO "Mavila-[9] Staff" does just this, and places the arrangement (222122221) on nine white "natural" keys of the 16edo keyboard. If the 9-note "Enneatonic" MOS is adopted as a notational basis for 16edo, then we need an entirely different set of interval classes than any of the heptatonic classes described above; perhaps it even makes sense to refer to octaves as 2/1, "[[decave]]".
+Mos scales like mavila[7] (or "inverse/anti-diatonic" which reverses step sizes of diatonic from LLsLLLs to ssLsssL in the heptatonic variation) can work as an alternative to the traditional diatonic scale, while maintaining conventional A-G #/b notation as described above. Alternatively, one can utilize the Mavila[9] MOS, for a sort of "hyper-diatonic" scale of 7 large steps and 2 small steps. [[Armodue_theory|Armodue notation]] of 16-EDO "Mavila-[9] Staff" does just this, and places the arrangement (222122221) on nine white "natural" keys of the 16edo keyboard. If the 9-note "Enneatonic" MOS is adopted as a notational basis for 16edo, then we need an entirely different set of interval classes than any of the heptatonic classes described above; perhaps it even makes sense to refer to the octave ([[2/1]]) as the "[[decave]]".
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 == Chord names ==
-edo chords can be named using ups and downs. Using harmonic interval names, the names are easy to find, but they bear little relationship to the sound. 4:5:6 is a minor chord and 10:12:15 is a major chord! Using melodic names, the chord names will match the sound, but finding the name is much more complicated (see below).
+edo chords can be named using ups and downs. Using harmonic (circle-of-fifths) interval names, the names are easy to find, but they bear little relationship to the sound: a minor chord (spelled A-C-E) sounds like [[4:5:6]], the classical major triad, and a major chord (spelled C-E-G) sounds like [[10:12:15]], a classical minor triad! Instead, using melodic names, the chord names will match the sound&mdash;but finding the name from the spelling is more complicated (see below).
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