Carlos Alpha: Difference between revisions
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{{Wikipedia|Alpha scale}} | {{Wikipedia|Alpha scale}} | ||
'''Carlos Alpha''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 77.965{{cent}}. In this temperament, the interval of 9 steps approximates [[3/2]], that of 5 steps approximates [[5/4]], and that of 4 steps approximates [[6/5]]. | '''Carlos Alpha''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 77.965{{cent}}. In this temperament, the interval of 9 steps approximates [[3/2]], that of 5 steps approximates [[5/4]], and that of 4 steps approximates [[6/5]]. The scale can be used with (i.e. [[15L 1s]]) or without octaves. | ||
== Theory == | == Theory == | ||
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</math> | </math> | ||
equal steps and the fifth in 9.003464 equal steps of 77.964990{{cent}} each<ref>Dave Benson, ''Music: A Mathematical Offering'', pp. 232-233.</ref>. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995{{cent}} each ([[9edf | equal steps and the fifth in 9.003464 equal steps of 77.964990{{cent}} each<ref>Dave Benson, ''Music: A Mathematical Offering'', pp. 232-233.</ref>. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995{{cent}} each ([[9edf]]), corresponding to 15.3856[[edo]]. | ||
Carlos Alpha is very closely related to [[ | Carlos Alpha is very closely related to [[Valentine|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]]. | ||
It has a very good representation of the 7:8:10:11:12 chord from the [[harmonic series]]. | It has a very good representation of the 7:8:10:11:12 chord from the [[harmonic series]]. | ||
Sequence of edos with lower and lower relative error: {{EDOs| 15, 31, 46, 77, 354 }}. | Sequence of edos with lower and lower relative error: {{EDOs| 15, 31, 46, 77, 354 }}. | ||
== Intervals == | == Intervals == | ||
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; [[Bryan Deister]] | ; [[Bryan Deister]] | ||
* [https://www.youtube.com/watch?v=zDwgCHDZpsc Microtonal Improvisation in Carlos Alpha] (2023) | * [https://www.youtube.com/watch?v=zDwgCHDZpsc Microtonal Improvisation in Carlos Alpha] (2023) | ||
* [https://www.youtube.com/watch?v=xuDni2oQyl8 microtonal improvisation in Carlos Alpha] (2025) | |||
; [[Mandrake]] | ; [[Mandrake]] | ||
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; [[Jean-Pierre Poulin]] | ; [[Jean-Pierre Poulin]] | ||
* [http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3 Bourdigal] | * [http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3 ''Bourdigal''] | ||
; [[Carlo Serafini]] | ; [[Carlo Serafini]] | ||
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; [[Joel Grant Taylor]] | ; [[Joel Grant Taylor]] | ||
* [https://web.archive.org/web/20201127012332/micro.soonlabel.com/gene_ward_smith/Others/Taylor/alpha%20study%207%20-%20melody%20study.mp3 ''Alpha study 7 - melody study''] | * [https://web.archive.org/web/20201127012332/micro.soonlabel.com/gene_ward_smith/Others/Taylor/alpha%20study%207%20-%20melody%20study.mp3 ''Alpha study 7 - melody study''] | ||
; [[MagentaFlavouredMusic]] | |||
* [https://youtu.be/1HkykxbKBHE ''Carlama''] | |||
== See also == | == See also == | ||
* [[Carlos Beta]] | * Carlos' equal scales | ||
* [[Carlos Gamma]] | ** [[Carlos Beta]] | ||
** [[Carlos Gamma]] | |||
* [[Carlos harm|Carlos Harmonic]] | * [[Carlos harm|Carlos Harmonic]] | ||
* [[Carlos super|Carlos Super Just]] | * [[Carlos super|Carlos Super Just]] | ||