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>.

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]]. [[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]].

== Theory ==

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[[Category:Nonoctave]]

[[Category:Equal-step tuning]]

~~[[Category:Edf]]~~

[[Category:Listen]]

~~[[Category:Microtonal]]~~

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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>.
-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]]. [[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]].
 == Theory ==
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 [[Category:Nonoctave]]
 [[Category:Equal-step tuning]]
-[[Category:Edf]]
 [[Category:Listen]]
-[[Category:Microtonal]]
-{{todo| cleanup | expand }}
+{{Todo| cleanup | expand }}