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{{Wikipedia|Beta scale}}
{{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]].
'''Carlos Beta''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 63.833{{cent}}, or almost exactly every fifth step of [[94edo]]. 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]].


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 provided the tuning of 63.8{{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


== Theory ==
<math>\displaystyle
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]].
\frac{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)} ≃ 18.799074
</math>
 
equal steps and the fifth in 10.996753 equal steps of 63.832933{{cent}} each<ref>Dave Benson, ''Music: A Mathematical Offering'', pp. 232-233.</ref>. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141{{cent}} 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.
Carlos Beta is related to the [[sycamore family]] of temperaments – betic and [[5-limit]] sycamore in particular.


Lookalikes: [[19edo]], [[11edf]], [[30edt]], every 5th step of [[94edo]], every 4th step of [[75edo]]
Lookalikes: [[19edo]], [[11edf]], [[30edt]], every 5th step of [[94edo]], every 4th step of [[75edo]]
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* [[Carlos super|Carlos Super Just]]
* [[Carlos super|Carlos Super Just]]


== Reference ==
== References ==
<references/>
<references/>


== External links ==
== External links ==
* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article] ([http://www.webcitation.org/5xelDVVBj Permalink])
* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article | ''Three Asymmetric Divisions of the Octave''] ([http://www.webcitation.org/5xelDVVBj Permalink])


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

Revision as of 09:14, 9 November 2023

English Wikipedia has an article on:

Carlos Beta is a non-octave equal temperament invented by Wendy Carlos, with step size about 63.833 ¢, or almost exactly every fifth step of 94edo. 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 provided the tuning of 63.8 ¢[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{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)} ≃ 18.799074 }[/math]

equal steps and the fifth in 10.996753 equal steps of 63.832933 ¢ each[3]. It is thus very close to the equal division of the just perfect fifth into eleven parts of 63.8141 ¢ each (11ed3/2), corresponding to 18.8046edo.

Carlos Beta is related to the sycamore family of temperaments – betic and 5-limit sycamore in particular.

Lookalikes: 19edo, 11edf, 30edt, every 5th step of 94edo, every 4th step of 75edo

Intervals

Degrees Cents ~ Cents octave reduced Approximate JI interval ~ octave reduced
0 0
1 64
2 128
3 191
4 255
5 319 6/5
6 383 5/4
7 447
8 510.5
9 574
10 638
11 702 3/2 (exact)
12 766
13 830 13/8-ish
14 893
15 957
16 1021
17 1085 15/8
18 1149
19 1211.5 ~ 11.5 2/1-ish
20 1276 ~ 76
21 1340 ~ 140
22 1404 ~ 204 9/4~9/8 (exact)
23 1468 ~ 268 better 7/6
24 1532 ~ 332
25 1595 ~ 395
26 1659 ~ 459
27 1723 ~ 523
28 1787 ~ 587
29 1851 ~ 651
30 1914 ~ 714
31 1978 ~ 778
32 2042 ~ 842 13/4 ~ 13/8 (better)
33 2106 ~ 906
34 2170 ~ 970
35 2233 ~ 1033
36 2297 ~ 1097

Music

See also: Category:Carlos Beta tracks
Bryan Deister
Omega9
Carlo Serafini

See also

References

  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.
  3. ↑ Dave Benson, Music: A Mathematical Offering, pp. 232-233.

External links

Retrieved from "https://en.xen.wiki/index.php?title=Carlos_Beta&oldid=127170"