Carlos Alpha: Difference between revisions

(3 intermediate revisions by 3 users not shown)

Line 1:

'''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 ==

Line 9:

</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~~|9ed3/2~~]]), corresponding to 15.3856[[edo]].

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 [[~~Starling temperaments #~~Valentine ~~temperament~~|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]].

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]].

Sequence of edos with lower and lower relative error: {{EDOs| 15, 31, 46, 77, 354 }}.

== Intervals ==

Line 184:

; [[Bryan Deister]]

* [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]]

@@ Line 1: / Line 1: @@
 {{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 ==
@@ Line 9: / Line 9: @@
 </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|9ed3/2]]), corresponding to 15.3856[[edo]].
+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 [[Starling temperaments #Valentine temperament|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]].
+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]].
 Sequence of edos with lower and lower relative error: {{EDOs| 15, 31, 46, 77, 354 }}.
 == Intervals ==
@@ Line 184: / Line 184: @@
 ; [[Bryan Deister]]
 * [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]]