Carlos Beta: Difference between revisions

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{{interwiki
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{{Wikipedia|Beta scale}}
{{Wikipedia|Beta scale}}
'''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]].
'''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]].
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</math>
</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]].
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 ([[11edf|11ed3/2]]), corresponding to 18.8046[[edo]].


Carlos Beta is related to the [[sycamore family]] of 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.
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; [[Bryan Deister]]
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=8qydnXzkbgg ''Come''] (2022) – Carlos Beta version
* [https://www.youtube.com/watch?v=8qydnXzkbgg ''Come''] (2022) – Carlos Beta version
* [https://www.youtube.com/shorts/bqbwHuBJHJQ ''Microtonal Improvisation in Carlos Beta''] (2023)


; [[Omega9|Omega9 & MÜÜR]]
; [[Omega9|Omega9 & MÜÜR]]

Latest revision as of 09:26, 2 January 2026

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 63.832933
2 127.665865
3 191.498798
4 255.331730
5 319.164663 6/5
6 382.997595 5/4
7 446.830528
8 510.663461
9 574.496393
10 638.329326
11 702.162258 3/2
12 765.995191
13 829.828123 13/8-ish
14 893.661056
15 957.493989
16 1021.326921
17 1085.159854 15/8
18 1148.992786
19 1212.825719 ~ 12.825719 2/1-ish
20 1276.658651 ~ 76.658651
21 1340.491584 ~ 140.491584
22 1404.324517 ~ 204.324517 9/4~9/8
23 1468.157449 ~ 268.157449 better 7/6
24 1531.990382 ~ 331.990382
25 1595.823314 ~ 395.823314
26 1659.656247 ~ 459.656247
27 1723.489179 ~ 523.489179
28 1787.322112 ~ 587.322112
29 1851.155045 ~ 651.155045
30 1914.987977 ~ 714.987977
31 1978.820910 ~ 778.820910
32 2042.653842 ~ 842.653842 13/4 ~ 13/8 (better)
33 2106.486775 ~ 906.486775
34 2170.319707 ~ 970.319707
35 2234.152640 ~ 1034.152640
36 2297.985573 ~ 1097.985573

Music

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

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=220585"