Carlos harmonic scale: Difference between revisions

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[[File:Carlos_Harmonic.png|thumb|Circle diagram.]]

The '''Carlos harmonic scale''' or simply '''harmonic scale''' is a twelve note scale in [[just intonation]] that repeats at the [[octave]]. Its pitches are derived from the [[harmonic series]] of a single frequency up to the [[21/1|~~21st~~ harmonic]], meaning they go up to the [[21-odd-limit]], or the [[19-limit]]. The harmonic scale can be described as a subset of [[16afdo|mode 16 of the harmonic series]] where harmonics [[23/1|23]], [[25/1|25]], [[29/1|29]], and [[31/1|31]] are removed, producing a [[constant structure]]. It is also an example of including every harmonic as far out as possible while maintaining constant structure, which means it is an example of a [[ringer scale]].

The '''Carlos harmonic scale''' or simply '''harmonic scale''' is a twelve note scale in [[just intonation]] that repeats at the [[octave]]. Its pitches are derived from the [[harmonic series]] of a single frequency up to the [[27/1|27th harmonic]], meaning they go up to the [[27-odd-limit]], or the [[19-limit]]. The harmonic scale can be described as a subset of [[16afdo|mode 16 of the harmonic series]] where harmonics [[23/1|23]], [[25/1|25]], [[29/1|29]], and [[31/1|31]] are removed, producing a [[constant structure]]. It is also an example of including every harmonic as far out as possible while maintaining constant structure, which means it is an example of a [[ringer scale]].

== Interval table ==

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== Usage and history ==

The harmonic scale can be used as an alternative tuning for regular twelve-tone pianos to play spectral or [[otonal]] music, although it finds more regular use merely as a unique microtonal retuning of 12edo. Versions of the scale are known to have been used by composers [[Ezra Sims]], [http://www.ekmelic-music.org/en/person.php?n=RH Franz Richter Herf], [[Wendy Carlos]] in her ''Beauty ~~and~~ the Beast'' (1986)<ref>Milano, Dominic (November 1986). [http://www.wendycarlos.com/other/PDF-Files/Kbd86Tunings*.pdf "A Many-Colored Jungle of Exotic Tunings"], ''Keyboard''.</ref> and [[Ben Johnston]] in ''Suite for Microtonal Piano'' (1978).

The harmonic scale can be used as an alternative tuning for regular twelve-tone pianos to play spectral or [[otonal]] music, although it finds more regular use merely as a unique microtonal retuning of 12edo. Versions of the scale are known to have been used by composers [[Ezra Sims]], [http://www.ekmelic-music.org/en/person.php?n=RH Franz Richter Herf], [[Wendy Carlos]] in her ''Beauty in the Beast'' (1986)<ref>Milano, Dominic (November 1986). [http://www.wendycarlos.com/other/PDF-Files/Kbd86Tunings*.pdf "A Many-Colored Jungle of Exotic Tunings"], ''Keyboard''.</ref> and [[Ben Johnston]] in ''Suite for Microtonal Piano'' (1978).

== Scala file ==

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 {{Wikipedia|Harmonic scale}}
 [[File:Carlos_Harmonic.png|thumb|Circle diagram.]]
-The '''Carlos harmonic scale''' or simply '''harmonic scale''' is a twelve note scale in [[just intonation]] that repeats at the [[octave]]. Its pitches are derived from the [[harmonic series]] of a single frequency up to the [[21/1|21st harmonic]], meaning they go up to the [[21-odd-limit]], or the [[19-limit]]. The harmonic scale can be described as a subset of [[16afdo|mode 16 of the harmonic series]] where harmonics [[23/1|23]], [[25/1|25]], [[29/1|29]], and [[31/1|31]] are removed, producing a [[constant structure]]. It is also an example of including every harmonic as far out as possible while maintaining constant structure, which means it is an example of a [[ringer scale]].
+The '''Carlos harmonic scale''' or simply '''harmonic scale''' is a twelve note scale in [[just intonation]] that repeats at the [[octave]]. Its pitches are derived from the [[harmonic series]] of a single frequency up to the [[27/1|27th harmonic]], meaning they go up to the [[27-odd-limit]], or the [[19-limit]]. The harmonic scale can be described as a subset of [[16afdo|mode 16 of the harmonic series]] where harmonics [[23/1|23]], [[25/1|25]], [[29/1|29]], and [[31/1|31]] are removed, producing a [[constant structure]]. It is also an example of including every harmonic as far out as possible while maintaining constant structure, which means it is an example of a [[ringer scale]].
 == Interval table ==
@@ Line 53: / Line 53: @@
 == Usage and history ==
-The harmonic scale can be used as an alternative tuning for regular twelve-tone pianos to play spectral or [[otonal]] music, although it finds more regular use merely as a unique microtonal retuning of 12edo. Versions of the scale are known to have been used by composers [[Ezra Sims]], [http://www.ekmelic-music.org/en/person.php?n=RH Franz Richter Herf], [[Wendy Carlos]] in her ''Beauty and the Beast'' (1986)<ref>Milano, Dominic (November 1986). [http://www.wendycarlos.com/other/PDF-Files/Kbd86Tunings*.pdf "A Many-Colored Jungle of Exotic Tunings"], ''Keyboard''.</ref> and [[Ben Johnston]] in ''Suite for Microtonal Piano'' (1978).
+The harmonic scale can be used as an alternative tuning for regular twelve-tone pianos to play spectral or [[otonal]] music, although it finds more regular use merely as a unique microtonal retuning of 12edo. Versions of the scale are known to have been used by composers [[Ezra Sims]], [http://www.ekmelic-music.org/en/person.php?n=RH Franz Richter Herf], [[Wendy Carlos]] in her ''Beauty in the Beast'' (1986)<ref>Milano, Dominic (November 1986). [http://www.wendycarlos.com/other/PDF-Files/Kbd86Tunings*.pdf "A Many-Colored Jungle of Exotic Tunings"], ''Keyboard''.</ref> and [[Ben Johnston]] in ''Suite for Microtonal Piano'' (1978).
 == Scala file ==