1edo: Difference between revisions

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'''1 equal divisions of the octave''' (abbreviated '''1edo'''), or '''1-tone equal temperament''' ('''1tet'''), '''1 equal temperament''' ('''1et)''' when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that contains a single pitch and pitches [[octave]]s above and below that pitch. Each step of 1edo represents a frequency ratio of [[2/1]], or exactly the octave.

== Theory ==

One note repeated in octaves is an example of a [[trivial temperament]]; most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every [[edo]]. ~~However, in~~ terms of JI representation, ~~it is simply the~~ [[~~2-limit~~]] ~~with all other primes~~ tempered to some amount of octaves.

One note repeated in octaves is an example of a [[trivial temperament]]; most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every [[edo]]. In terms of [[JI]] representation, all [[prime harmonic]]s but 2 are tempered to some amount of octaves.

The first piece of ''Musica ricercata'' by {{w|György Ligeti}} simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.

1edo is equivalent to [[AFDO|1afdo]] and [[IFDO|1ifdo]].

1edo is equivalent to the [[2-limit]], [[1-odd-limit]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO|1afdo]] and [[IFDO|1ifdo]]).

=== Odd harmonics ===

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 {{Infobox ET}}
 '''1 equal divisions of the octave''' (abbreviated '''1edo'''), or '''1-tone equal temperament''' ('''1tet'''), '''1 equal temperament''' ('''1et)''' when viewed under a [[regular temperament]] perspective, is the [[tuning system]] that contains a single pitch and pitches [[octave]]s above and below that pitch. Each step of 1edo represents a frequency ratio of [[2/1]], or exactly the octave.
 == Theory ==
-One note repeated in octaves is an example of a [[trivial temperament]]; most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every [[edo]]. However, in terms of JI representation, it is simply the [[2-limit]] with all other primes tempered to some amount of octaves.
+One note repeated in octaves is an example of a [[trivial temperament]]; most existing styles of music would find little use for a single set of octaves. That said, it does retain some musical value, particularly as 1edo is contained as a subset of every [[edo]]. In terms of [[JI]] representation, all [[prime harmonic]]s but 2 are tempered to some amount of octaves.
 The first piece of ''Musica ricercata'' by {{w|György Ligeti}} simulates 1edo by playing only one pitch class (A) throughout different octaves on the piano, though the piano is not itself tuned to 1edo. The last chord of the piece uses another pitch class (D), breaking the pattern.
-edo is equivalent to [[AFDO|1afdo]] and [[IFDO|1ifdo]].
+edo is equivalent to the [[2-limit]], [[1-odd-limit]], and 1-''p''-fdo with arbitrary value of ''p'' (including [[AFDO|1afdo]] and [[IFDO|1ifdo]]).
 === Odd harmonics ===