Carlos Gamma: Difference between revisions

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'''Carlos Gamma''' is a non-octave [[equal temperament]] whose step size is 35.0985422804 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>.

'''Carlos Gamma''' is a non-octave [[equal temperament]] whose step size is 35.0985422804 [[cent]]s<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 20 steps approximates [[3/2]], that of 11 steps approximates [[5/4]], and that of 9 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{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)}</math> ≃ 34.189454 equal steps and the fifth in 19.999549 equal steps of 35.098542 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into twenty parts of 35.0978 cents each (20ed3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.

In this temperament, the interval of 20 steps approximates [[3/2]], that of 11 steps approximates [[5/4]], and that of 9 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{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)}</math> ≃ 34.189454 equal steps and the fifth in 19.999549 equal steps of 35.098542 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into twenty parts of 35.0978 cents each (20ed3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.

Gamma ~~is a non-octave scale created by Wendy Carlos. It~~ is closely related to the [[gammic]] temperament.

Carlos Gamma is closely related to the [[gammic]] temperament.

Lookalikes: [[34edo]], [[54edt]], [[96ed7]], [[171edo]]

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* [http://www.seraph.it/dep/det/BabylonGamma.mp3 Babylon Gamma] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/d33f9a1bbeed04e78c0a5f835fed784c-306.html blog entry])

* [http://www.seraph.it/dep/det/GammaConstantStructures.mp3 Gamma Constant Structures] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/3325f9fada5c4d5c3d4dd0c3ced8b2a8-308.html blog entry])

== See also ==

* [[Carlos Alpha]]

* [[Carlos Beta]]

* [[Carlos harm|Carlos Harmonic]]

== Reference ==

== External links ==

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

[[Category:Wendy Carlos]]

@@ Line 1: / Line 1: @@
-'''Carlos Gamma''' is a non-octave [[equal temperament]] whose step size is 35.0985422804 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>.
+{{Wikipedia|Gamma scale}}
+'''Carlos Gamma''' is a non-octave [[equal temperament]] whose step size is 35.0985422804 [[cent]]s<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 20 steps approximates [[3/2]], that of 11 steps approximates [[5/4]], and that of 9 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{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)}</math> ≃ 34.189454 equal steps and the fifth in 19.999549 equal steps of 35.098542 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into twenty parts of 35.0978 cents each (20ed3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.
+In this temperament, the interval of 20 steps approximates [[3/2]], that of 11 steps approximates [[5/4]], and that of 9 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{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)}</math> ≃ 34.189454 equal steps and the fifth in 19.999549 equal steps of 35.098542 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into twenty parts of 35.0978 cents each (20ed3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.
-Gamma is a non-octave scale created by Wendy Carlos. It is closely related to the [[gammic]] temperament.
+Carlos Gamma is closely related to the [[gammic]] temperament.
 Lookalikes: [[34edo]], [[54edt]], [[96ed7]], [[171edo]]
@@ Line 677: / Line 678: @@
 * [http://www.seraph.it/dep/det/BabylonGamma.mp3 Babylon Gamma] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/d33f9a1bbeed04e78c0a5f835fed784c-306.html blog entry])
 * [http://www.seraph.it/dep/det/GammaConstantStructures.mp3 Gamma Constant Structures] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/3325f9fada5c4d5c3d4dd0c3ced8b2a8-308.html blog entry])
+== See also ==
+* [[Carlos Alpha]]
+* [[Carlos Beta]]
+* [[Carlos harm|Carlos Harmonic]]
 == Reference ==
 <references/>
+== External links ==
+* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article]
 [[Category:Wendy Carlos]]