Carlos Gamma: Difference between revisions

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{{Wikipedia|Gamma scale}}
{{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]].
'''Carlos Gamma''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 35.099{{cent}}. 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]].


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 ==
Carlos provided the tuning of 35.1{{cent}}<ref>Wendy Carlos, "Tuning: At the Crossroads", ''Computer Music Journal'', vol. 11 no. 1, 1987, pp. 29-43</ref><ref>Wendy Carlos, ''Three Asymmetric Divisions of the Octave''. </ref>. Based on her work, Dave Benson optimized the temperament for 3/2, 5/4, and 6/5, such that the tuning divides the octave in
 
<math>\displaystyle
\frac{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)} ≃ 34.189454
</math>


== Theory ==
equal steps and the fifth in 19.999549 equal steps of 35.0985422804{{cent}} each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into twenty parts of 35.0978{{cent}} each ([[20ed3/2]]), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.
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.


Carlos Gamma is closely related to the [[gammic]] temperament.
Carlos Gamma is closely related to the [[gammic]] temperament.
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|1403.91
|1403.91
|}
|}
== Music ==
== Music ==
; [[Bryan Deister]]
; [[Bryan Deister]]
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== External links ==
== External links ==
* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article]
* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article | ''Three Asymmetric Divisions of the Octave'']


[[Category:Wendy Carlos]]
[[Category:Wendy Carlos]]

Revision as of 09:20, 9 November 2023

English Wikipedia has an article on:

Carlos Gamma is a non-octave equal temperament invented by Wendy Carlos, with step size about 35.099 ¢. 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

Carlos provided the tuning of 35.1 ¢[1][2]. Based on her work, Dave Benson optimized the temperament for 3/2, 5/4, and 6/5, such that the tuning divides the octave in

[math]\displaystyle{ \displaystyle \frac{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)} ≃ 34.189454 }[/math]

equal steps and the fifth in 19.999549 equal steps of 35.0985422804 ¢ each. It is thus very close to the equal division of the just perfect fifth into twenty parts of 35.0978 ¢ each (20ed3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.

Carlos Gamma is closely related to the gammic temperament.

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

Intervals

The first steps up to two just perfect fifths should give a feeling of the granularity of this system…

Degrees
1 35.1
2 70.2
3 105.29
4 140.39
5 175.49
6 210.59
7 245.68
8 280.78
9 315.88
10 350.98
11 386.075
12 421.17
13 456.27
14 491.37
15 526.47
16 561.56
17 596.66
18 631.76
19 666.86
20 701.955
21 737.05
22 772.15
23 807.25
24 842.35
25 877.44
26 912.54
27 947.64
28 982.74
29 1017.835
30 1052.93
31 1088.03
32 1123.13
33 1158.23
34 1193.32
35 1228.42
36 1263.52
37 1298.62
38 1333.715
39 1368.81
40 1403.91

Music

Bryan Deister
James Mulvale
Carlo Serafini

See also

Reference

  1. ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal, vol. 11 no. 1, 1987, pp. 29-43
  2. ↑ Wendy Carlos, Three Asymmetric Divisions of the Octave.

External links

Retrieved from "https://en.xen.wiki/index.php?title=Carlos_Gamma&oldid=127171"