Carlos Beta: Difference between revisions

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**Imported revision 87406481 - Original comment: **
 
→Music: Add Microtonal Improvisation in Carlos Beta by Bryan Deister
 
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
{{Wikipedia|Beta scale}}
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
'''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]].
: This revision was by author [[User:Sean_Archibald|Sean_Archibald]] and made on <tt>2009-09-06 15:43:54 UTC</tt>.<br>
 
: The original revision id was <tt>87406481</tt>.<br>
== Theory ==
: The revision comment was: <tt></tt><br>
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  
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
 
<h4>Original Wikitext content:</h4>
<math>\displaystyle
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Carlos Beta (equal division of the perfect fifth into 11 equal parts)=
\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>
==Theory==  
 
Beta is a non-octave, equally tempered scale discovered by Wendy Carlos. It divides the just perfect fifth into 11 parts. Each interval is 63.8 cents in size.
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]].
[[http://www.wendycarlos.com/resources/pitch.html|Article by Wendy Carlos]]</pre></div>
 
<h4>Original HTML content:</h4>
Carlos Beta is related to the [[sycamore family]] of temperaments – betic and [[5-limit]] sycamore in particular.
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Carlos Beta&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Carlos Beta (equal division of the perfect fifth into 11 equal parts)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Carlos Beta (equal division of the perfect fifth into 11 equal parts)&lt;/h1&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; &lt;/h1&gt;
Lookalikes: [[19edo]], [[11edf]], [[30edt]], every 5th step of [[94edo]], every 4th step of [[75edo]]
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Carlos Beta (equal division of the perfect fifth into 11 equal parts)-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Theory&lt;/h2&gt;
 
Beta is a non-octave, equally tempered scale discovered by Wendy Carlos. It divides the just perfect fifth into 11 parts. Each interval is 63.8 cents in size.&lt;br /&gt;
== Intervals ==
&lt;a class="wiki_link_ext" href="http://www.wendycarlos.com/resources/pitch.html" rel="nofollow"&gt;Article by Wendy Carlos&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
 
{| class="wikitable"
|-
! 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 ==
{{Catrel| Carlos Beta tracks }}
 
; [[Bryan Deister]]
* [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]]
* ''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]]
* ''The Dawn Of Beta'' (2011) – [http://www.seraph.it/dep/det/DawnOfBeta.mp3 play] | [http://www.seraph.it/blog_files/ca97598d4d95438f8cf18862e7f13222-87.html blog]
* ''Lonely Beta Woman'' (2011) – [http://www.seraph.it/dep/det/LonelyBetaWoman.mp3 play] | [http://www.seraph.it/blog_files/0915d7768cbd1948d46bd63e9060ef12-88.html blog]
* ''Over The Beta Rainbow'' (2011) – [http://www.seraph.it/dep/det/OverTheBetaRainbow.mp3 play] | [http://www.seraph.it/blog_files/c498a163495a549dbc2711691061db11-92.html blog]
* ''Tribalism #2'' (2011) – [http://www.seraph.it/dep/det/Tribalism2.mp3 play] | [http://www.seraph.it/blog_files/e516a6726f78b7c6232b0869222507ff-95.html blog]
* ''Beta Easter(n)'' (2011) – [http://www.seraph.it/blog_files/9d774615381a06e228b7de11a9394562-97.html blog] | [https://youtu.be/6yBY2AvsUOA3 YouTube]
* ''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]
* ''Angela B.'' (2011) – [http://www.seraph.it/dep/det/Angela.mp3 play] | [http://www.seraph.it/blog_files/2edec68ea23551591ff1c0d897e1f8fa-101.html blog]
* ''UGDoLA'' (2011) – [http://www.seraph.it/blog_files/6d6dcd64d5d817366c5608edfbed16b6-102.html blog] | [https://www.youtube.com/watch?v=mghWWIUjh9o YouTube]
* ''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 ==
* [[Mason Green's New Common Practice Notation]]
* Carlos' equal scales
** [[Carlos Alpha]]
** [[Carlos Gamma]]
* [[Carlos harm|Carlos Harmonic]]
* [[Carlos super|Carlos Super Just]]
 
== References ==
<references/>
 
== External links ==
* [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:Nonoctave]]
[[Category:Equal-step tuning]]
[[Category:Listen]]
 
{{Todo| cleanup | expand }}

Latest revision as of 07:13, 28 April 2025

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=194375"