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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 ([[11edf|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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|-
|-
| | 1
| | 1
| | 64
| | 63.832933
| |
| |
|-
|-
| | 2
| | 2
| | 128
| | 127.665865
| |
| |
|-
|-
| | 3
| | 3
| | 191
| | 191.498798
| |
| |
|-
|-
| | 4
| | 4
| | 255
| | 255.331730
| |  
| |  
|-
|-
| | 5
| | 5
| | 319
| | 319.164663
| | 6/5
| | [[6/5]]
|-
|-
| | 6
| | 6
| | 383
| | 382.997595
| | 5/4
| | [[5/4]]
|-
|-
| | 7
| | 7
| | 447
| | 446.830528
| |  
| |  
|-
|-
| | 8
| | 8
| | 510.5
| | 510.663461
| |  
| |  
|-
|-
| | 9
| | 9
| | 574
| | 574.496393
| |
| |
|-
|-
| | 10
| | 10
| | 638
| | 638.329326
|-
|-
| | 11
| | 11
| | 702
| | 702.162258
| | 3/2 (exact)
| | [[3/2]]
|-
|-
| | 12
| | 12
| | 766
| | 765.995191
| |
| |
|-
|-
| | 13
| | 13
| | 830
| | 829.828123
| | 13/8-ish
| | [[13/8]]-ish
|-
|-
| | 14
| | 14
| | 893
| | 893.661056
| |
| |
|-
|-
| | 15
| | 15
| | 957
| | 957.493989
| |
| |
|-
|-
| | 16
| | 16
| | 1021
| | 1021.326921
| |
| |
|-
|-
| | 17
| | 17
| | 1085
| | 1085.159854
| | 15/8
| | [[15/8]]
|-
|-
| | 18
| | 18
| | 1149
| | 1148.992786
| |
| |
|-
|-
| | 19
| | 19
| | 1211.5 ~ 11.5
| | 1212.825719 ~ 12.825719
| | 2/1-ish
| | [[2/1]]-ish
|-
|-
| | 20
| | 20
| | 1276 ~ 76
| | 1276.658651 ~ 76.658651
| |
| |
|-
|-
| | 21
| | 21
| | 1340 ~ 140
| | 1340.491584 ~ 140.491584
| |
| |
|-
|-
| | 22
| | 22
| | 1404 ~ 204
| | 1404.324517 ~ 204.324517
| | 9/4~9/8 (exact)
| | [[9/4]]~[[9/8]]
|-
|-
| | 23
| | 23
| | 1468 ~ 268
| | 1468.157449 ~ 268.157449
| | better 7/6
| | better [[7/6]]
|-
|-
| | 24
| | 24
| | 1532 ~ 332
| | 1531.990382 ~ 331.990382
| |
| |
|-
|-
| | 25
| | 25
| | 1595 ~ 395
| | 1595.823314 ~ 395.823314
|
|
|-
|-
| | 26
| | 26
| | 1659 ~ 459
| | 1659.656247 ~ 459.656247
|
|
|-
|-
| | 27
| | 27
| | 1723 ~ 523
| | 1723.489179 ~ 523.489179
|-
|-
| | 28
| | 28
| | 1787 ~ 587
| | 1787.322112 ~ 587.322112
|
|
|-
|-
| | 29
| | 29
| | 1851 ~ 651
| | 1851.155045 ~ 651.155045
|
|
|-
|-
| | 30
| | 30
| | 1914 ~ 714
| | 1914.987977 ~ 714.987977
|
|
|-
|-
| | 31
| | 31
| | 1978 ~ 778
| | 1978.820910 ~ 778.820910
|
|
|-
|-
| | 32
| | 32
| | 2042 ~ 842
| | 2042.653842 ~ 842.653842
| | 13/4 ~ 13/8 (better)
| | [[13/4]] ~ [[13/8]] (better)
|-
|-
| | 33
| | 33
| | 2106 ~ 906
| | 2106.486775 ~ 906.486775
|
|
|-
|-
| | 34
| | 34
| | 2170 ~ 970
| | 2170.319707 ~ 970.319707
|
|
|-
|-
| | 35
| | 35
| | 2233 ~ 1033
| | 2234.152640 ~ 1034.152640
|
|
|-
|-
| | 36
| | 36
| | 2297 ~ 1097
| | 2297.985573 ~ 1097.985573
|
|
|}
|}


== Music ==
== Music ==
{{Catrel|Carlos Beta tracks}}
{{Catrel| Carlos Beta tracks }}


; [[Omega9]]
; [[Bryan Deister]]
* [https://www.youtube.com/watch?v=qnIKaWhjZj0 cærulea]
* [https://www.youtube.com/watch?v=8qydnXzkbgg ''Come''] (2022) – Carlos Beta version
* [https://soundcloud.com/omega9/way-without-time-ost Way Without Time OST] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Way%20Without%20Time%20OST.mp3 play]
* [https://www.youtube.com/shorts/bqbwHuBJHJQ ''Microtonal Improvisation in Carlos Beta''] (2023)
* [https://www.youtube.com/watch?v=eWgb-ZbgvJI Tionmifarosalmimemkelkfoje] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Tionmifarosalmimemkelkfoje.mp3 play]
 
* [https://www.youtube.com/watch?v=-fwA6egaqc4 Cordas] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Cordas%20(Carlos%20Beta).mp3 play] by Omega9
; [[Omega9|Omega9 & MÜÜR]]
* ''Elirejo de tempo'' – [https://www.youtube.com/watch?v=qWXeoVCxL5k YouTube] | [https://blend.io/project/5e0459e6573b324b537f3682 Multitrack]
* ''Cærulea'' – [https://www.youtube.com/watch?v=NBfW6LC-Vec YouTube] | [https://blend.io/project/5e0459e61a4f113326352b85 Multitrack]
* ''Tempo kaj Ĥrono'' – [https://www.youtube.com/watch?v=OfQwGcJjMAo YouTube] | [https://blend.io/project/5e045a48f24d7af73aa4edf4 Multitrack]
*''Tionmifarosalmimemkelkfoje'' (2012) – [https://web.archive.org/web/20201127015039/http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Tionmifarosalmimemkelkfoje.mp3 play] | [https://www.youtube.com/watch?v=eWgb-ZbgvJI YouTube]
* ''Cordas'' (2012) – [https://web.archive.org/web/20201127015302/http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Cordas%20(Carlos%20Beta).mp3 play] | [https://omega9.bandcamp.com/track/cordas-carlos-beta Bandcamp] | [https://www.youtube.com/watch?v=-fwA6egaqc4 YouTube] – Carlos Beta version


; [[Carlo Serafini]]
; [[Carlo Serafini]]
* [http://www.seraph.it/dep/det/DawnOfBeta.mp3 The Dawn Of Beta] ([http://www.seraph.it/blog_files/ca97598d4d95438f8cf18862e7f13222-87.html blog entry])
* ''The Dawn Of Beta'' (2011) – [http://www.seraph.it/dep/det/DawnOfBeta.mp3 play] | [http://www.seraph.it/blog_files/ca97598d4d95438f8cf18862e7f13222-87.html blog]
* [http://www.seraph.it/dep/det/LonelyBetaWoman.mp3 Lonely Beta Woman] ([http://www.seraph.it/blog_files/0915d7768cbd1948d46bd63e9060ef12-88.html blog entry])
* ''Lonely Beta Woman'' (2011) – [http://www.seraph.it/dep/det/LonelyBetaWoman.mp3 play] | [http://www.seraph.it/blog_files/0915d7768cbd1948d46bd63e9060ef12-88.html blog]
* [http://www.seraph.it/dep/det/OverTheBetaRainbow.mp3 Over The Beta Rainbow] ([http://www.seraph.it/blog_files/c498a163495a549dbc2711691061db11-92.html blog entry])
* ''Over The Beta Rainbow'' (2011) – [http://www.seraph.it/dep/det/OverTheBetaRainbow.mp3 play] | [http://www.seraph.it/blog_files/c498a163495a549dbc2711691061db11-92.html blog]
* [http://www.seraph.it/dep/det/Tribalism2.mp3 Tribalism #2] ([http://www.seraph.it/blog_files/e516a6726f78b7c6232b0869222507ff-95.html blog entry])
* ''Tribalism #2'' (2011) – [http://www.seraph.it/dep/det/Tribalism2.mp3 play] | [http://www.seraph.it/blog_files/e516a6726f78b7c6232b0869222507ff-95.html blog]
* [https://youtu.be/6yBY2AvsUOA3 Beta Easter(n) (video)] ([http://www.seraph.it/blog_files/9d774615381a06e228b7de11a9394562-97.html blog entry])
* ''Beta Easter(n)'' (2011) – [http://www.seraph.it/blog_files/9d774615381a06e228b7de11a9394562-97.html blog] | [https://youtu.be/6yBY2AvsUOA3 YouTube]
* [http://www.seraph.it/dep/det/tiBETAnDreams.mp3 tiBETAn Dreams] ([http://www.seraph.it/blog_files/9029519d60cf978db21549a608ef4ea3-99.html blog]) ([http://www.seraph.it/blog_files/7f1eb6f7799c4f90d796396cbade30ce-98.html entry])
* ''tiBETAn Dreams'' (2011) – [http://www.seraph.it/dep/det/tiBETAnDreams.mp3 play] | [http://www.seraph.it/blog_files/7f1eb6f7799c4f90d796396cbade30ce-98.html blog #1][http://www.seraph.it/blog_files/9029519d60cf978db21549a608ef4ea3-99.html blog #2]
* [http://www.seraph.it/dep/det/Angela.mp3 Angela B.] ([http://www.seraph.it/blog_files/2edec68ea23551591ff1c0d897e1f8fa-101.html blog entry])
* ''Angela B.'' (2011) – [http://www.seraph.it/dep/det/Angela.mp3 play] | [http://www.seraph.it/blog_files/2edec68ea23551591ff1c0d897e1f8fa-101.html blog]
* [https://www.youtube.com/watch?v=mghWWIUjh9o UGDoLA (video)] ([http://www.seraph.it/blog_files/6d6dcd64d5d817366c5608edfbed16b6-102.html blog entry])
* ''UGDoLA'' (2011) – [http://www.seraph.it/blog_files/6d6dcd64d5d817366c5608edfbed16b6-102.html blog] | [https://www.youtube.com/watch?v=mghWWIUjh9o YouTube]
* [https://youtu.be/v4F38G4XKLc Austrian Fantasy (video)] ([http://www.seraph.it/blog_files/49d276aa03bebbf3a0c831f0bc3bdea5-107.html blog entry])
* ''Austrian Fantasy'' (2011) – [http://www.seraph.it/blog_files/49d276aa03bebbf3a0c831f0bc3bdea5-107.html blog] | [https://youtu.be/v4F38G4XKLc YouTube]
 
; [[MagentaFlavouredMusic]]
* [https://youtu.be/1HkykxbKBHE ''Carlama'']


== See also ==
== See also ==
* [[Mason Green's New Common Practice Notation]]
* [[Mason Green's New Common Practice Notation]]
* [[Carlos Alpha]]
* Carlos' equal scales
* [[Carlos Gamma]]
** [[Carlos Alpha]]
** [[Carlos Gamma]]
* [[Carlos harm|Carlos Harmonic]]
* [[Carlos harm|Carlos Harmonic]]
* [[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]]
Retrieved from "https://en.xen.wiki/w/Carlos_Beta"