Carlos Beta: Difference between revisions

Line 1:

'''Carlos Beta''' is a non-octave [[equal temperament]] with step size about 63.833 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>, or almost exactly every fifth step of [[94edo]].

'''Carlos Beta''' is a non-octave [[equal temperament]] with step size about 63.833 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>, or almost exactly every fifth step of [[94edo]]. It was invented by [[Wendy Carlos]].

In this temperament, the interval of 11 steps approximates [[3/2]], that of 6 steps approximates [[5/4]], and that of 5 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{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)}</math> ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141 cents each (11ed3/2), corresponding to 18.8046[[edo]].

In this temperament, the interval of 11 steps approximates [[3/2]], that of 6 steps approximates [[5/4]], and that of 5 steps approximates [[6/5]].

== Theory ==

Carlos ~~Beta~~ is ~~a non-octave~~, ~~equally tempered scale discovered by~~ [[~~Wendy Carlos~~]]. It is related to the [[Sycamore family|sycamore temperaments]]; betic and [[5-limit]] sycamore in particular.

Carlos optimized the tuning on 3/2, 5/4, and 6/5, such that the tuning divides the octave in <math>\frac{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)}</math> ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141 cents each (11ed3/2), corresponding to 18.8046[[edo]].

Carlos Beta is related to the [[Sycamore family|sycamore temperaments]]; betic and [[5-limit]] sycamore in particular.

Lookalikes: [[19edo]], [[30edt]], [[94edo]]

Line 176:

Line 179:

== External links ==

* [http://www.wendycarlos.com/resources/pitch.html ~~Article by~~ Wendy Carlos] ([http://www.webcitation.org/5xelDVVBj Permalink])

* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article] ([http://www.webcitation.org/5xelDVVBj Permalink])

[[Category:Wendy Carlos]]

@@ Line 1: / Line 1: @@
-'''Carlos Beta''' is a non-octave [[equal temperament]] with step size about 63.833 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>, or almost exactly every fifth step of [[94edo]].
+{{Wikipedia|Beta scale}}
+'''Carlos Beta''' is a non-octave [[equal temperament]] with step size about 63.833 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>, or almost exactly every fifth step of [[94edo]]. It was invented by [[Wendy Carlos]].
-In this temperament, the interval of 11 steps approximates [[3/2]], that of 6 steps approximates [[5/4]], and that of 5 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{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)}</math> ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141 cents each (11ed3/2), corresponding to 18.8046[[edo]].
+In this temperament, the interval of 11 steps approximates [[3/2]], that of 6 steps approximates [[5/4]], and that of 5 steps approximates [[6/5]].
 == Theory ==
-Carlos Beta is a non-octave, equally tempered scale discovered by [[Wendy Carlos]]. It is related to the [[Sycamore family|sycamore temperaments]]; betic and [[5-limit]] sycamore in particular.
+Carlos optimized the tuning on 3/2, 5/4, and 6/5, such that the tuning divides the octave in <math>\frac{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)}</math> ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141 cents each (11ed3/2), corresponding to 18.8046[[edo]].
+Carlos Beta is related to the [[Sycamore family|sycamore temperaments]]; betic and [[5-limit]] sycamore in particular.
 Lookalikes: [[19edo]], [[30edt]], [[94edo]]
@@ Line 176: / Line 179: @@
 == External links ==
-* [http://www.wendycarlos.com/resources/pitch.html Article by Wendy Carlos] ([http://www.webcitation.org/5xelDVVBj Permalink])
+* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article] ([http://www.webcitation.org/5xelDVVBj Permalink])
 [[Category:Wendy Carlos]]