Carlos Alpha: Difference between revisions

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'''Carlos Alpha''' is a non-octave [[equal temperament]] with step size about 77.965 [[cent~~]]s~~ in the standard tuning<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>.

'''Carlos Alpha''' is a non-octave [[equal temperament]] with step size about 77.965{{cent}} in the standard tuning<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>. It was invented by [[Wendy Carlos]].

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]]. [[Wendy Carlos]] optimized the tuning on 3/2, 5/4 and 6/5, such that the tuning divides the octave in <math>\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}</math> ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ed3/2), corresponding to 15.3856[[edo]].

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]].

== Theory ==

~~[http:~~//~~www~~.~~wendycarlos~~.~~com/resources~~/~~pitch~~.~~html Article by Wendy Carlos~~]

Carlos optimized the tuning on 3/2, 5/4 and 6/5, such that the tuning divides the octave in <math>\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}</math> ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ed3/2), 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]].

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== Reference ==

== External links ==

* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article]

[[Category:Wendy Carlos]]

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-'''Carlos Alpha''' is a non-octave [[equal temperament]] with step size about 77.965 [[cent]]s in the standard tuning<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>.
+{{Wikipedia|Alpha scale}}
+'''Carlos Alpha''' is a non-octave [[equal temperament]] with step size about 77.965{{cent}} in the standard tuning<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>. It was invented by [[Wendy Carlos]].
-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]]. [[Wendy Carlos]] optimized the tuning on 3/2, 5/4 and 6/5, such that the tuning divides the octave in <math>\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}</math> ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ed3/2), corresponding to 15.3856[[edo]].
+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]].
 == Theory ==
-[http://www.wendycarlos.com/resources/pitch.html Article by Wendy Carlos]
+Carlos optimized the tuning on 3/2, 5/4 and 6/5, such that the tuning divides the octave in <math>\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}</math> ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ed3/2), 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]].
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 == Reference ==
 <references/>
+== External links ==
+* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article]
 [[Category:Wendy Carlos]]