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{{interwiki
|en = Carlos_Alpha
|de = Carlos_Alpha
}}
{{Wikipedia|Alpha scale}}
{{Wikipedia|Alpha scale}}
'''Carlos Alpha''' is a non-octave [[equal temperament]] with step size about 77.965{{cent}} in the standard tuning<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>. It was invented by [[Wendy Carlos]].
'''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.


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]].
== Theory ==
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


== 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{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)}</math> ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ed3/2), corresponding to 15.3856[[edo]].
\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{{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]].


Carlos Alpha is very closely related to [[Starling temperaments #Valentine temperament|valentine temperament]]. For a list of 11-limit [[dyadic chord]]s of Carlos Alpha, see [[Chords of valentine]].
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]].


It has a very good representation of the 7:8:10:11:12 chord from the harmonic series.
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: {{EDOs| 15, 31, 46, 77, 354}}
Sequence of edos with lower and lower relative error: {{EDOs| 15, 31, 46, 77, 354 }} (though 354edo doesn't support valentine by [[patent val]]).


== Intervals ==
== Intervals ==
Line 18: Line 26:
|-
|-
! Degrees
! Degrees
! Cents ~ Cents octave-reduced
! Cents<br>~(octave-reduced)
! Approximate JI interval (11-limit)
! Approximate JI interval<br>(11-limit)
|-
|-
| 0
| 0
| 0
| 0
| | 1/1 (exact)
| 1/1
|-
|-
| | 1
| 1
| | 78
| 77.965
| |25/24, 22/21, 21/20
| 25/24, 21/20, 22/21
|-
|-
| | 2
| 2
| | 156
| 155.930
| | 12/11, 35/32, 11/10
| 11/10, 12/11, 35/32
|-
|-
| | 3
| 3
| | 234
| 233.895
| | 8/7, 55/48
| 8/7, 55/48
|-
|-
| | 4
| 4
| | 312
| 311.860
| | 6/5
| 6/5
|-
|-
| | 5
| 5
| | 390
| 389.825
| | 5/4
| 5/4
|-
|-
| | 6
| 6
| | 468
| 467.790
| | 72/55, 21/16
| 21/16, 72/55
|-
|-
| | 7
| 7
| | 546
| 545.755
| | 15/11, 48/35, 11/8
| 11/8, 15/11, 48/35
|-
|-
| | 8
| 8
| | 624
| 623.720
| | 10/7, 63/44, 36/25
| 10/7, 36/25, 63/44
|-
|-
| | 9
| 9
| | 702
| 701.685
| | 3/2 (exact)
| 3/2
|-
|-
| | 10
| 10
| | 780
| 779.650
| | 25/16, 11/7, 63/40
| 11/7, 25/16, 63/40
|-
|-
| | 11
| 11
| | 858
| 857.615
| | 18/11, 105/64, 33/20
| 18/11, 33/20, 105/64
|-
|-
| | 12
| 12
| | 936
| 935.580
| | 12/7, 55/32
| 12/7, 55/32
|-
|-
| | 13
| 13
| | 1014
| 1013.545
| | 9/5
| 9/5
|-
|-
| | 14
| 14
| | 1092
| 1091.510
| | 15/8
| 15/8
|-
|-
| | 15
| 15
| | 1170
| 1169.475
|108/55, 63/32
| 63/32, 108/55
|-
|-
| | 16
| 16
| | 1248 ~ 48
| 1247.440 ~ 47.440
| | 45/22, 72/35, 33/16
| 72/35, 33/16, 45/22
|-
|-
| | 17
| 17
| | 1326 ~ 126
| 1325.4045 ~ 125.405
| |15/7, 189/88, 54/25
| 15/7, 54/25, 189/88
|-
|-
| | 18
| 18
| | 1404 ~ 204
| 1403.370 ~ 203.370
| | 9/4 (exact)
| 9/4
|-
|-
| | 19
| 19
| | 1482 ~ 282
| 1481.335 ~ 281.335
| 33/14
|-
|-
| | 20
| 20
| | 1560 ~ 360
| 1559.300 ~ 359.300
| 27/11 ([[Valentino]] 32/13)
|-
|-
| | 21
| 21
| | 1638 ~ 438
| 1637.265 ~ 437.265
| 18/7
|-
|-
| | 22
| 22
| | 1716 ~ 516
| 1715.230 ~ 515.230
| 27/20
|-
|-
| | 23
| 23
| | 1794 ~ 594
| 1793.195 ~ 593.195
| 45/32
|-
|-
| | 24
| 24
| | 1872 ~ 672
| 1871.160 ~ 671.160
|  
|-
|-
| | 25
| 25
| | 1950 ~ 750
| 1949.125 ~ 749.125
|
|-
|-
| | 26
| 26
| | 2028 ~ 828
| 2027.090 ~ 827.090
|
|-
|-
| | 27
| 27
| | 2106 ~ 906
| 2105.055 ~ 905.055
|
|-
|-
| | 28
| 28
| | 2184 ~ 984
| 2183.020 ~ 983.020
|
|-
|-
| | 29
| 29
| | 2262 ~ 1062
| 2260.985 ~ 1060.985
|
|-
|-
| | 30
| 30
| | 2340 ~ 1140
| 2330.950 ~ 1138.950
|
|-
|-
| | 31
| 31
| | 2418 ~ 18
| 2416.915 ~ 16.915
|
|-
|-
| | 32
| 32
| | 2496 ~ 96
| 2494.880 ~ 94.880
|
|-
|-
| | 33
| 33
| | 2574 ~ 174
| 2572.845 ~ 172.845
|
|-
|-
| | 34
| 34
| | 2652 ~ 252
| 2650.810 ~ 250.810
|
|-
|-
| | 35
| 35
| | 2730 ~ 330
| 2728.775 ~ 328.775
|
|-
|-
| | 36
| 36
| | 2808 ~ 408
| 2806.740 ~ 406.740
|
|}
|}


== Music ==
== Music ==
{{See also|:Category:Carlos Alpha tracks}}
{{catrel|Carlos Alpha tracks}}
* ''[http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3 Bourdigal]'' by [[Jean-Pierre Poulin]]
 
* ''[http://micro.soonlabel.com/gene_ward_smith/Others/Taylor/alpha%20study%207%20-%20melody%20study.mp3 Alpha study 7 - melody study]'' by [[Joel Grant Taylor]] {{dead link}}
; [[Bazil Müzik]]
* ''[http://www.seraph.it/dep/det/alphablues.mp3 Alphablues]'' by [[Carlo Serafini]]
* [https://www.youtube.com/watch?v=faSg7ToM5xc ''Another day went by''] (2021) – hyperpop beat
* ''[http://www.seraph.it/dep/int/alphapanther.mp3 Alphapanther]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/37b31cf5e738413d8b6b67a16a107f40-7.html blog entry])
* [https://www.youtube.com/watch?v=5LVzRu-e3G8 ''Urban entropy''] (2021)
* ''[http://www.seraph.it/dep/det/Alphadesert.mp3 Alphadesert]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/35cf6d4c1ad98623037c3e41897fc1ed-8.html blog entry])
* [https://www.youtube.com/watch?v=fRGRMUXmskw ''Crystallization''] (2021)
* ''[http://www.seraph.it/dep/det/AlphaDulcimer.mp3 AlphaDulcimer]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/1a76f1414eac1eed79bc914a384cc1f6-113.html blog entry])
 
* ''[http://www.seraph.it/dep/det/AlphaTheremWaltz.mp3 AlphaTherem Waltz]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/79fd70dbede6a7d3ebe1588f86d6befb-114.html blog entry])
; [[Bryan Deister]]
* ''[http://www.seraph.it/dep/det/CubanaAlCubanaPha.mp3 Cubana Al Cubana Pha]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/2434a8744c321cf19c09551424cb7453-116.html blog entry])
* [https://www.youtube.com/watch?v=zDwgCHDZpsc Microtonal Improvisation in Carlos Alpha] (2023)
* ''[http://youtu.be/3aIk7ZY3iiw DisMLosphere - video]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/def789d378b3b72969210e2755e29369-118.html blog entry])
* [https://www.youtube.com/watch?v=xuDni2oQyl8 microtonal improvisation in Carlos Alpha] (2025)
* ''[http://www.seraph.it/dep/det/AlphaElDin.mp3 Alpha El Din]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/eb4639782f8e15d7b0c7445b55cd5917-122.html blog entry])
 
* ''[http://www.seraph.it/dep/det/AlphaChoir.mp3 Alpha Choir]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/cc743d401cc3bb5a0d50475a11f1846c-123.html blog entry])
; [[Mandrake]]
* ''[http://www.seraph.it/dep/det/ASTBTHW.mp3 Alpha Seems To Be The Hardest World]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/a8ca4769f85411b076014cea9efb841e-124.html blog entry])
* [https://www.youtube.com/watch?v=J5gntG5LrOk ''HUH?''] (2022) – in 9edf tuning
* ''[http://www.seraph.it/dep/det/BossaSbilenca.mp3 Bossa Sbilenca]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/c26d33be7bf98e6d7c6e4d10f38a3df5-151.html blog entry])
 
* ''[http://www.seraph.it/dep/det/GalacticOverload.mp3 Galactic Overload]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/5cc59af84640b5feb03f14c4da426cbf-159.html blog entry])
; [[Omega9]]
* ''[http://www.youtube.com/watch?v=TPNirCFQ4XY Alpha Rain (video)]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/c46d0a7ca80368e67afd7f2aadb46297-162.html blog entry])
* ''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]
* ''[http://www.seraph.it/dep/det/AlphaDelinquent.mp3 Alpha Delinquent]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/ed8fc9ab1b3dfa6f5fe45103cb08365e-182.html blog entry])
 
* ''[http://www.seraph.it/dep/det/AlphaAbstract1.mp3 Alpha Abstract 1]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/351c7b45df8a68e9af24dab7d844d0c7-189.html blog entry])
; [[Jean-Pierre Poulin]]
* ''[http://www.seraph.it/dep/det/MilesOfSpace.mp3 Miles of Space]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/b1895d858c015ac923099bd356ff7a4a-194.html blog entry])
* [http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3 ''Bourdigal'']
* ''[https://www.youtube.com/watch?v=ubMVjAt12fU MacAtar (video)]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/b8ce7f66890bacf5f184ce66efb7621d-212.html blog entry])
 
* ''[http://www.seraph.it/dep/det/FuzzyLogic.mp3 Fuzzy Logic]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/fe8d37804bc0ffb7e5eee6d410363c65-216.html blog entry])
; [[Carlo Serafini]]
* ''[https://youtu.be/bht4JPFbvzQ Alpha Asana (video)]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/bc3fe2f9bc3f2b75c7e4d3fb0028b817-221.html blog entry])
* [http://www.seraph.it/dep/det/alphablues.mp3 ''Alphablues''] (2007)
* ''[https://www.youtube.com/watch?v=7ZdN9VtP1Xw Alpha Penguin Tanz (video)]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/470888af1fdbb47b97467d0331843a13-224.html blog entry])
* ''Alphapanther'' (2008) – [http://www.seraph.it/dep/int/alphapanther.mp3 play] | [http://www.seraph.it/blog_files/37b31cf5e738413d8b6b67a16a107f40-7.html blog] – in 9edf tuning
* ''[https://youtu.be/-aKYVVLImOw White Woman Speaks Up For #blacklivesmatter (video)]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/84f2ae146db05f06153a3b47fc6a8895-227.html blog entry])
* ''Alphadesert'' (2008) – [http://www.seraph.it/dep/det/Alphadesert.mp3 play] | [http://www.seraph.it/blog_files/35cf6d4c1ad98623037c3e41897fc1ed-8.html blog] – in 9edf tuning
* ''[http://www.seraph.it/dep/det/Jayni's%20song.mp3 Jayni's song]'' by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/c956c1294c91e7d9407c0ea447e667cb-232.html blog entry])
* ''Alpha Dulcimer'' (2011) – [http://www.seraph.it/dep/det/AlphaDulcimer.mp3 play] | [http://www.seraph.it/blog_files/1a76f1414eac1eed79bc914a384cc1f6-113.html blog]
* [https://www.youtube.com/watch?v=pkSIN8jU-i8 01.03.12 W.C.a.] by [[Omega9]]
* ''AlphaTherem Waltz'' (2011) – [http://www.seraph.it/dep/det/AlphaTheremWaltz.mp3 play] | [http://www.seraph.it/blog_files/79fd70dbede6a7d3ebe1588f86d6befb-114.html blog]
* [https://www.youtube.com/watch?v=faSg7ToM5xc Another day went by] by [[Bazil Müzik]]
* ''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 ==
== See also ==
* [[Carlos Beta]]
* Carlos' equal scales
* [[Carlos Gamma]]
** [[Carlos Beta]]
** [[Carlos Gamma]]
* [[Carlos harm|Carlos Harmonic]]
* [[Carlos harm|Carlos Harmonic]]
* [[Carlos super|Carlos Super Just]]
* [[Carlos super|Carlos Super Just]]
Line 191: Line 240:


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


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

Latest revision as of 19:33, 20 March 2026

English Wikipedia has an article on:

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
Bryan Deister
Mandrake
  • HUH? (2022) – in 9edf tuning
Omega9
Jean-Pierre Poulin
Carlo Serafini
Joel Grant Taylor
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

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