Carlos Alpha: Difference between revisions

@@ Line 1: / Line 1: @@
-'''Carlos Alpha''' is a non-octave equal temperament with step size about 77.965 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>. It is very close to [[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 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 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.
+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 ==