Carlos Alpha: Difference between revisions

Latest revision as of 19:33, 20 March 2026

English Wikipedia has an article on:

Alpha scale

Carlos Alpha is a non-octave equal temperament invented by Wendy Carlos, with step size about 77.965 ¢. In this temperament, the interval of 9 steps approximates 3/2, that of 5 steps approximates 5/4, and that of 4 steps approximates 6/5. The scale can be used with (i.e. 15L 1s) or without octaves.

Theory

Carlos provided the tuning of 78.0 ¢^[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{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)} ≃ 15.391524 }[/math]

equal steps and the fifth in 9.003464 equal steps of 77.964990 ¢ each^[3]. It is thus very close to the equal division of the just perfect fifth into nine parts of 77.995 ¢ each (9edf), corresponding to 15.3856edo.

Carlos Alpha is very closely related to valentine temperament. For a list of 11-limit dyadic chords of Carlos Alpha, see Chords of valentine.

It has a very good representation of the 7:8:10:11:12 chord from the harmonic series.

Sequence of edos with lower and lower relative error: 15, 31, 46, 77, 354 (though 354edo doesn't support valentine by patent val).

Intervals

Degrees	Cents ~(octave-reduced)	Approximate JI interval (11-limit)
0	0	1/1
1	77.965	25/24, 21/20, 22/21
2	155.930	11/10, 12/11, 35/32
3	233.895	8/7, 55/48
4	311.860	6/5
5	389.825	5/4
6	467.790	21/16, 72/55
7	545.755	11/8, 15/11, 48/35
8	623.720	10/7, 36/25, 63/44
9	701.685	3/2
10	779.650	11/7, 25/16, 63/40
11	857.615	18/11, 33/20, 105/64
12	935.580	12/7, 55/32
13	1013.545	9/5
14	1091.510	15/8
15	1169.475	63/32, 108/55
16	1247.440 ~ 47.440	72/35, 33/16, 45/22
17	1325.4045 ~ 125.405	15/7, 54/25, 189/88
18	1403.370 ~ 203.370	9/4
19	1481.335 ~ 281.335	33/14
20	1559.300 ~ 359.300	27/11 (Valentino 32/13)
21	1637.265 ~ 437.265	18/7
22	1715.230 ~ 515.230	27/20
23	1793.195 ~ 593.195	45/32
24	1871.160 ~ 671.160
25	1949.125 ~ 749.125
26	2027.090 ~ 827.090
27	2105.055 ~ 905.055
28	2183.020 ~ 983.020
29	2260.985 ~ 1060.985
30	2330.950 ~ 1138.950
31	2416.915 ~ 16.915
32	2494.880 ~ 94.880
33	2572.845 ~ 172.845
34	2650.810 ~ 250.810
35	2728.775 ~ 328.775
36	2806.740 ~ 406.740

Music

See also: Category:Carlos Alpha tracks

Bazil Müzik

Another day went by (2021) – hyperpop beat
Urban entropy (2021)
Crystallization (2021)

Bryan Deister

Microtonal Improvisation in Carlos Alpha (2023)
microtonal improvisation in Carlos Alpha (2025)

Mandrake

HUH? (2022) – in 9edf tuning

Omega9

01.03.12 W.C.a. (2012) – Bandcamp | YouTube

Jean-Pierre Poulin

Bourdigal

Carlo Serafini

Alphablues (2007)
Alphapanther (2008) – play | blog – in 9edf tuning
Alphadesert (2008) – play | blog – in 9edf tuning
Alpha Dulcimer (2011) – play | blog
AlphaTherem Waltz (2011) – play | blog
Cubana Al Cubana Pha (2011) – play | blog
DisMLosphere (2011) – blog | YouTube
Alpha El Din (2012) – play | blog
Alpha Choir (2012) – play | blog
Alpha Seems To Be The Hardest World (2012) – play | blog | YouTube
Bossa Sbilenca (2012) – play | blog
Galactic Overload (2012) – play | blog
Alpha Rain (2012) – blog | YouTube
Alpha Delinquent (2014) – play | blog
Alpha Abstract 1 (2014) – play | blog
Miles of Space (2014) – play | blog
MacAtar (2015) – blog | YouTube
Fuzzy Logic (2015) – play | blog
Alpha Asana (2016) – blog | YouTube
Alpha Penguin Tanz (2016) – blog | YouTube
White Woman Speaks Up For #blacklivesmatter (2016) – blog | YouTube
Jayni's song (2016) – play | blog

Joel Grant Taylor

Alpha study 7 - melody study

MagentaFlavouredMusic

Carlama

References

↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal, vol. 11 no. 1, 1987, pp. 29-43
↑ Wendy Carlos, Three Asymmetric Divisions of the Octave.
↑ Dave Benson, Music: A Mathematical Offering, pp. 232-233.

External links

Wendy Carlos Pitch article | Three Asymmetric Divisions of the Octave

[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.

[1]

[2]

[3]

Carlos Alpha: Difference between revisions

Latest revision as of 19:33, 20 March 2026

Contents

Theory

Intervals

Music

See also

References

External links

Navigation menu

@@ Line 1: / Line 1: @@
-<h2>IMPORTED REVISION FROM WIKISPACES</h2>
+{{interwiki
-This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
+|en = Carlos_Alpha
-: This revision was by author [[User:xenwolf|xenwolf]] and made on <tt>2010-05-30 16:03:36 UTC</tt>.<br>
+|de = Carlos_Alpha
-: The original revision id was <tt>145904645</tt>.<br>
+}}
-: The revision comment was: <tt></tt><br>
+{{Wikipedia|Alpha scale}}
-The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
+'''Carlos Alpha''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 77.965{{cent}}. In this temperament, the interval of 9 steps approximates [[3/2]], that of 5 steps approximates [[5/4]], and that of 4 steps approximates [[6/5]]. The scale can be used with (i.e. [[15L 1s]]) or without octaves.
-<h4>Original Wikitext content:</h4>
-<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 Alpha (equal division of the [[just perfect fifth]] into 9 equal parts)=
-= =
-==Theory==
-[[http://www.wendycarlos.com/resources/pitch.html|Article by Wendy Carlos]]
-==Compositions==
+== Theory ==
-[[http://www.seraph.it/XenoTunes1.html|Alphablues]] by [[Carlo Serafini]]
+Carlos provided the tuning of 78.0{{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
-[[http://www.seraph.it/dep/int/alphapanther.mp3|Alphapanther]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/37b31cf5e738413d8b6b67a16a107f40-7.html|blog entry]])
-[[http://www.seraph.it/dep/det/Alphadesert.mp3|Alphadesert]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/35cf6d4c1ad98623037c3e41897fc1ed-8.html|blog entry]])
+<math>\displaystyle
-[[@http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3|Bourdigal]] by [[@http://www.jeanpierrepoulin.com/|Jean-Pierre Poulin]]</pre></div>
+\frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)} ≃ 15.391524
-<h4>Original HTML content:</h4>
+</math>
-<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 Alpha&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 Alpha (equal division of the just perfect fifth into 9 equal parts)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Carlos Alpha (equal division of the &lt;a class="wiki_link" href="/just%20perfect%20fifth"&gt;just perfect fifth&lt;/a&gt; into 9 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;
+equal steps and the fifth in 9.003464 equal steps of 77.964990{{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 nine parts of 77.995{{cent}} each ([[9edf]]), corresponding to 15.3856[[edo]].
- &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Carlos Alpha (equal division of the just perfect fifth into 9 equal parts)-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Theory&lt;/h2&gt;
- &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;br /&gt;
+Carlos Alpha is very closely related to [[Valentine|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]].
-&lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="Carlos Alpha (equal division of the just perfect fifth into 9 equal parts)-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Compositions&lt;/h2&gt;
+It has a very good representation of the 7:8:10:11:12 chord from the [[harmonic series]].
- &lt;a class="wiki_link_ext" href="http://www.seraph.it/XenoTunes1.html" rel="nofollow"&gt;Alphablues&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt;&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/int/alphapanther.mp3" rel="nofollow"&gt;Alphapanther&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/37b31cf5e738413d8b6b67a16a107f40-7.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
+Sequence of edos with lower and lower relative error: {{EDOs| 15, 31, 46, 77, 354 }} (though 354edo doesn't support valentine by [[patent val]]).
-&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Alphadesert.mp3" rel="nofollow"&gt;Alphadesert&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/35cf6d4c1ad98623037c3e41897fc1ed-8.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
-&lt;a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3" rel="nofollow" target="_blank"&gt;Bourdigal&lt;/a&gt; by &lt;a class="wiki_link_ext" href="http://www.jeanpierrepoulin.com/" rel="nofollow" target="_blank"&gt;Jean-Pierre Poulin&lt;/a&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
+== Intervals ==
+{| class="wikitable"
+|-
+! Degrees
+! Cents<br>~(octave-reduced)
+! Approximate JI interval<br>(11-limit)
+|-
+| 0
+| 0
+| 1/1
+|-
+| 1
+| 77.965
+| 25/24, 21/20, 22/21
+|-
+| 2
+| 155.930
+| 11/10, 12/11, 35/32
+|-
+| 3
+| 233.895
+| 8/7, 55/48
+|-
+| 4
+| 311.860
+| 6/5
+|-
+| 5
+| 389.825
+| 5/4
+|-
+| 6
+| 467.790
+| 21/16, 72/55
+|-
+| 7
+| 545.755
+| 11/8, 15/11, 48/35
+|-
+| 8
+| 623.720
+| 10/7, 36/25, 63/44
+|-
+| 9
+| 701.685
+| 3/2
+|-
+| 10
+| 779.650
+| 11/7, 25/16, 63/40
+|-
+| 11
+| 857.615
+| 18/11, 33/20, 105/64
+|-
+| 12
+| 935.580
+| 12/7, 55/32
+|-
+| 13
+| 1013.545
+| 9/5
+|-
+| 14
+| 1091.510
+| 15/8
+|-
+| 15
+| 1169.475
+| 63/32, 108/55
+|-
+| 16
+| 1247.440 ~ 47.440
+| 72/35, 33/16, 45/22
+|-
+| 17
+| 1325.4045 ~ 125.405
+| 15/7, 54/25, 189/88
+|-
+| 18
+| 1403.370 ~ 203.370
+| 9/4
+|-
+| 19
+| 1481.335 ~ 281.335
+| 33/14
+|-
+| 20
+| 1559.300 ~ 359.300
+| 27/11 ([[Valentino]] 32/13)
+|-
+| 21
+| 1637.265 ~ 437.265
+| 18/7
+|-
+| 22
+| 1715.230 ~ 515.230
+| 27/20
+|-
+| 23
+| 1793.195 ~ 593.195
+| 45/32
+|-
+| 24
+| 1871.160 ~ 671.160
+|
+|-
+| 25
+| 1949.125 ~ 749.125
+|
+|-
+| 26
+| 2027.090 ~ 827.090
+|
+|-
+| 27
+| 2105.055 ~ 905.055
+|
+|-
+| 28
+| 2183.020 ~ 983.020
+|
+|-
+| 29
+| 2260.985 ~ 1060.985
+|
+|-
+| 30
+| 2330.950 ~ 1138.950
+|
+|-
+| 31
+| 2416.915 ~ 16.915
+|
+|-
+| 32
+| 2494.880 ~ 94.880
+|
+|-
+| 33
+| 2572.845 ~ 172.845
+|
+|-
+| 34
+| 2650.810 ~ 250.810
+|
+|-
+| 35
+| 2728.775 ~ 328.775
+|
+|-
+| 36
+| 2806.740 ~ 406.740
+|
+|}
+== Music ==
+{{catrel|Carlos Alpha tracks}}
+; [[Bazil Müzik]]
+* [https://www.youtube.com/watch?v=faSg7ToM5xc ''Another day went by''] (2021) – hyperpop beat
+* [https://www.youtube.com/watch?v=5LVzRu-e3G8 ''Urban entropy''] (2021)
+* [https://www.youtube.com/watch?v=fRGRMUXmskw ''Crystallization''] (2021)
+; [[Bryan Deister]]
+* [https://www.youtube.com/watch?v=zDwgCHDZpsc Microtonal Improvisation in Carlos Alpha] (2023)
+* [https://www.youtube.com/watch?v=xuDni2oQyl8 microtonal improvisation in Carlos Alpha] (2025)
+; [[Mandrake]]
+* [https://www.youtube.com/watch?v=J5gntG5LrOk ''HUH?''] (2022) – in 9edf tuning
+; [[Omega9]]
+* ''01.03.12 W.C.a.'' (2012) – [https://omega9.bandcamp.com/track/010312-w-c-a Bandcamp] | [https://www.youtube.com/watch?v=pkSIN8jU-i8 YouTube]
+; [[Jean-Pierre Poulin]]
+* [http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3 ''Bourdigal'']
+; [[Carlo Serafini]]
+* [http://www.seraph.it/dep/det/alphablues.mp3 ''Alphablues''] (2007)
+* ''Alphapanther'' (2008) – [http://www.seraph.it/dep/int/alphapanther.mp3 play] | [http://www.seraph.it/blog_files/37b31cf5e738413d8b6b67a16a107f40-7.html blog] – in 9edf tuning
+* ''Alphadesert'' (2008) – [http://www.seraph.it/dep/det/Alphadesert.mp3 play] | [http://www.seraph.it/blog_files/35cf6d4c1ad98623037c3e41897fc1ed-8.html blog] – in 9edf tuning
+* ''Alpha Dulcimer'' (2011) – [http://www.seraph.it/dep/det/AlphaDulcimer.mp3 play] | [http://www.seraph.it/blog_files/1a76f1414eac1eed79bc914a384cc1f6-113.html blog]
+* ''AlphaTherem Waltz'' (2011) – [http://www.seraph.it/dep/det/AlphaTheremWaltz.mp3 play] | [http://www.seraph.it/blog_files/79fd70dbede6a7d3ebe1588f86d6befb-114.html blog]
+* ''Cubana Al Cubana Pha'' (2011) – [http://www.seraph.it/dep/det/CubanaAlCubanaPha.mp3 play] | [http://www.seraph.it/blog_files/2434a8744c321cf19c09551424cb7453-116.html blog]
+* ''DisMLosphere'' (2011) – [http://www.seraph.it/blog_files/def789d378b3b72969210e2755e29369-118.html blog] | [https://youtu.be/3aIk7ZY3iiw YouTube]
+* ''Alpha El Din'' (2012) – [http://www.seraph.it/dep/det/AlphaElDin.mp3 play] | [http://www.seraph.it/blog_files/eb4639782f8e15d7b0c7445b55cd5917-122.html blog]
+* ''Alpha Choir'' (2012) – [http://www.seraph.it/dep/det/AlphaChoir.mp3 play] | [http://www.seraph.it/blog_files/cc743d401cc3bb5a0d50475a11f1846c-123.html blog]
+* ''Alpha Seems To Be The Hardest World'' (2012) – [http://www.seraph.it/dep/det/ASTBTHW.mp3 play] | [http://www.seraph.it/blog_files/a8ca4769f85411b076014cea9efb841e-124.html blog] | [https://youtu.be/qJrwmW4sxeQ?si=j35qCAbA9TnQc5cr YouTube]
+* ''Bossa Sbilenca'' (2012) – [http://www.seraph.it/dep/det/BossaSbilenca.mp3 play] | [http://www.seraph.it/blog_files/c26d33be7bf98e6d7c6e4d10f38a3df5-151.html blog]
+* ''Galactic Overload'' (2012) – [http://www.seraph.it/dep/det/GalacticOverload.mp3 play] | [http://www.seraph.it/blog_files/5cc59af84640b5feb03f14c4da426cbf-159.html blog]
+* ''Alpha Rain'' (2012) – [http://www.seraph.it/blog_files/c46d0a7ca80368e67afd7f2aadb46297-162.html blog] | [https://www.youtube.com/watch?v=TPNirCFQ4XY YouTube]
+* ''Alpha Delinquent'' (2014) – [http://www.seraph.it/dep/det/AlphaDelinquent.mp3 play] | [http://www.seraph.it/blog_files/ed8fc9ab1b3dfa6f5fe45103cb08365e-182.html blog]
+* ''Alpha Abstract 1'' (2014) – [http://www.seraph.it/dep/det/AlphaAbstract1.mp3 play] | [http://www.seraph.it/blog_files/351c7b45df8a68e9af24dab7d844d0c7-189.html blog]
+* ''Miles of Space'' (2014) – [http://www.seraph.it/dep/det/MilesOfSpace.mp3 play] | [http://www.seraph.it/blog_files/b1895d858c015ac923099bd356ff7a4a-194.html blog]
+* ''MacAtar'' (2015) – [http://www.seraph.it/blog_files/b8ce7f66890bacf5f184ce66efb7621d-212.html blog] | [https://www.youtube.com/watch?v=ubMVjAt12fU YouTube]
+* ''Fuzzy Logic'' (2015) – [http://www.seraph.it/dep/det/FuzzyLogic.mp3 play] | [http://www.seraph.it/blog_files/fe8d37804bc0ffb7e5eee6d410363c65-216.html blog]
+* ''Alpha Asana'' (2016) – [http://www.seraph.it/blog_files/bc3fe2f9bc3f2b75c7e4d3fb0028b817-221.html blog] | [https://youtu.be/bht4JPFbvzQ YouTube]
+* ''Alpha Penguin Tanz'' (2016) – [http://www.seraph.it/blog_files/470888af1fdbb47b97467d0331843a13-224.html blog] | [https://www.youtube.com/watch?v=7ZdN9VtP1Xw YouTube]
+* ''White Woman Speaks Up For #blacklivesmatter'' (2016) – [http://www.seraph.it/blog_files/84f2ae146db05f06153a3b47fc6a8895-227.html blog] | [https://youtu.be/-aKYVVLImOw YouTube]
+* ''Jayni's song'' (2016) – [http://www.seraph.it/dep/det/Jayni's%20song.mp3 play] | [http://www.seraph.it/blog_files/c956c1294c91e7d9407c0ea447e667cb-232.html blog]
+; [[Joel Grant Taylor]]
+* [https://web.archive.org/web/20201127012332/micro.soonlabel.com/gene_ward_smith/Others/Taylor/alpha%20study%207%20-%20melody%20study.mp3 ''Alpha study 7 - melody study'']
+; [[MagentaFlavouredMusic]]
+* [https://youtu.be/1HkykxbKBHE ''Carlama'']
+== See also ==
+* Carlos' equal scales
+** [[Carlos Beta]]
+** [[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'']
+[[Category:Wendy Carlos]]
+[[Category:Nonoctave]]
+[[Category:Equal-step tuning]]
+[[Category:Listen]]
+{{Todo| cleanup | expand }}

Carlos Alpha: Difference between revisions

Latest revision as of 19:33, 20 March 2026

Theory

Intervals

Music

See also

References

External links

Navigation menu

Search