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'''Carlos Alpha''' is the [[EDF|equal division of the just perfect fifth]] into nine parts of 77.9950 [[cent|cents]] each (9ED3/2), corresponding to 15.3856 [[edo]].
{{Wikipedia|Alpha scale}}
'''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.  


==Theory==
== Theory ==
[http://www.wendycarlos.com/resources/pitch.html Article by Wendy Carlos]
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


Carlos Alpha is very closely related to [[Starling_temperaments#Valentine temperament|valentine temperament]]. For a list of 11-limit [[Dyadic_chord|dyadic chords]] of Carlos Alpha, see [[Chords_of_valentine|Chords of valentine]].
<math>\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>


==Intervals==
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 [[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]].
 
Sequence of edos with lower and lower relative error: {{EDOs| 15, 31, 46, 77, 354 }}.
 
== Intervals ==


{| class="wikitable"
{| class="wikitable"
|-
|-
| | Degrees
! Degrees
| | Cents ~ Cents octave-reduced
! Cents ~ Cents octave-reduced
! Approximate JI interval (11-limit)
|-
|-
| | 0
| 0
| | 0
| 0
| | 1/1 (exact)
|-
|-
| | 1
| | 1
| | 78
| | 77.964990
| |25/24, 22/21, 21/20
|-
|-
| | 2
| | 2
| | 156
| | 155.929979
| | 12/11, 35/32, 11/10
|-
|-
| | 3
| | 3
| | 234
| | 233.894969
| | 8/7, 55/48
|-
|-
| | 4
| | 4
| | 312
| | 311.859958
| | 6/5
|-
|-
| | 5
| | 5
| | 390
| | 389.824948
| | 5/4
|-
|-
| | 6
| | 6
| | 468
| | 467.789937
| | 72/55, 21/16
|-
|-
| | 7
| | 7
| | 546
| | 545.754927
| | 15/11, 48/35, 11/8
|-
|-
| | 8
| | 8
| | 624
| | 623.719916
| | 10/7, 63/44, 36/25
|-
|-
| | 9
| | 9
| | 702
| | 701.684906
| | 3/2
|-
|-
| | 10
| | 10
| | 780
| | 779.6498955
| | 25/16, 11/7, 63/40
|-
|-
| | 11
| | 11
| | 858
| | 857.614885
| | 18/11, 105/64, 33/20
|-
|-
| | 12
| | 12
| | 936
| | 935.579875
| | 12/7, 55/32
|-
|-
| | 13
| | 13
| | 1014
| | 1013.544864
| | 9/5
|-
|-
| | 14
| | 14
| | 1092
| | 1091.509854
| | 15/8
|-
|-
| | 15
| | 15
| | 1170
| | 1169.474843
|108/55, 63/32
|-
|-
| | 16
| | 16
| | 1248 ~ 48
| | 1247.439833 ~ 47.439833
| | 45/22, 72/35, 33/16
|-
|-
| | 17
| | 17
| | 1326 ~ 126
| | 1325.404822 ~ 125.404822
| |15/7, 189/88, 54/25
|-
|-
| | 18
| | 18
| | 1404 ~ 204
| | 1403.369812 ~ 203.369812
| | 9/4
|-
|-
| | 19
| | 19
| | 1482 ~ 282
| | 1481.3348015 ~ 281.3348015
|
|-
|-
| | 20
| | 20
| | 1560 ~ 360
| | 1559.299791 ~ 359.299791
|
|-
|-
| | 21
| | 21
| | 1638 ~ 438
| | 1637.264781 ~ 437.264781
|
|-
|-
| | 22
| | 22
| | 1716 ~ 516
| | 1715.229770 ~ 515.229770
|
|-
|-
| | 23
| | 23
| | 1794 ~ 594
| | 1793.194760 ~ 593.194769
|
|-
|-
| | 24
| | 24
| | 1872 ~ 672
| | 1871.159749 ~ 671.159749
|
|-
|-
| | 25
| | 25
| | 1950 ~ 750
| | 1949.124739 ~ 749.124739
|
|-
|-
| | 26
| | 26
| | 2028 ~ 828
| | 2027.089728 ~ 827.089728
|
|-
|-
| | 27
| | 27
| | 2106 ~ 906
| | 2105.054718 ~ 905.054718
|
|-
|-
| | 28
| | 28
| | 2184 ~ 984
| | 2183.019707 ~ 983.019707
|
|-
|-
| | 29
| | 29
| | 2262 ~ 1062
| | 2260.984697 ~ 1060.984697
|
|-
|-
| | 30
| | 30
| | 2340 ~ 1140
| | 2330.949687 ~ 1138.949687
|
|-
|-
| | 31
| | 31
| | 2418 ~ 18
| | 2416.914676 ~ 16.914676
|
|-
|-
| | 32
| | 32
| | 2496 ~ 96
| | 2494.879666 ~ 94.879666
|
|-
|-
| | 33
| | 33
| | 2574 ~ 174
| | 2572.844655 ~ 172.844655
|
|-
|-
| | 34
| | 34
| | 2652 ~ 252
| | 2650.809645 ~ 250.809645
|
|-
|-
| | 35
| | 35
| | 2730 ~ 330
| | 2728.774635 ~ 328.774634
|
|-
|-
| | 36
| | 36
| | 2808 ~ 408
| | 2806.739624 ~ 406.739624
|
|}
|}


==Compositions==
== Music ==
''[http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3 Bourdigal]'' by [[Jean-Pierre_Poulin|Jean-Pierre Poulin]]
{{catrel|Carlos Alpha tracks}}


''[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|Joel Grant Taylor]]
; [[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)


''[http://www.seraph.it/dep/det/alphablues.mp3 Alphablues]'' by [[Carlo_Serafini|Carlo Serafini]]
; [[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)


''[http://www.seraph.it/dep/int/alphapanther.mp3 Alphapanther]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/37b31cf5e738413d8b6b67a16a107f40-7.html blog entry])
; [[Mandrake]]
* [https://www.youtube.com/watch?v=J5gntG5LrOk ''HUH?''] (2022) – in 9edf tuning


''[http://www.seraph.it/dep/det/Alphadesert.mp3 Alphadesert]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/35cf6d4c1ad98623037c3e41897fc1ed-8.html blog entry])
; [[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]


''[http://www.seraph.it/dep/det/AlphaDulcimer.mp3 AlphaDulcimer]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/1a76f1414eac1eed79bc914a384cc1f6-113.html blog entry])
; [[Jean-Pierre Poulin]]
* [http://www.jeanpierrepoulin.com/mp3/Bourdigal.mp3 ''Bourdigal'']


''[http://www.seraph.it/dep/det/AlphaTheremWaltz.mp3 AlphaTherem Waltz]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/79fd70dbede6a7d3ebe1588f86d6befb-114.html blog entry])
; [[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]


''[http://www.seraph.it/dep/det/CubanaAlCubanaPha.mp3 Cubana Al Cubana Pha]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/2434a8744c321cf19c09551424cb7453-116.html blog entry])
; [[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'']


''[http://youtu.be/3aIk7ZY3iiw DisMLosphere - video]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/def789d378b3b72969210e2755e29369-118.html blog entry])
; [[MagentaFlavouredMusic]]
* [https://youtu.be/1HkykxbKBHE ''Carlama'']


''[http://www.seraph.it/dep/det/AlphaElDin.mp3 Alpha El Din]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/eb4639782f8e15d7b0c7445b55cd5917-122.html blog entry])
== See also ==
* Carlos' equal scales
** [[Carlos Beta]]
** [[Carlos Gamma]]
* [[Carlos harm|Carlos Harmonic]]
* [[Carlos super|Carlos Super Just]]


''[http://www.seraph.it/dep/det/AlphaChoir.mp3 Alpha Choir]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/cc743d401cc3bb5a0d50475a11f1846c-123.html blog entry])
== References ==
<references/>


''[http://www.seraph.it/dep/det/ASTBTHW.mp3 Alpha Seems To Be The Hardest World]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/a8ca4769f85411b076014cea9efb841e-124.html blog entry])
== External links ==
* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article | ''Three Asymmetric Divisions of the Octave'']


''[http://www.seraph.it/dep/det/BossaSbilenca.mp3 Bossa Sbilenca]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/c26d33be7bf98e6d7c6e4d10f38a3df5-151.html blog entry])
[[Category:Wendy Carlos]]
 
''[http://www.seraph.it/dep/det/GalacticOverload.mp3 Galactic Overload]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/5cc59af84640b5feb03f14c4da426cbf-159.html blog entry])
 
''[http://www.youtube.com/watch?v=TPNirCFQ4XY Alpha Rain (video)]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/c46d0a7ca80368e67afd7f2aadb46297-162.html blog entry])
 
''[http://www.seraph.it/dep/det/AlphaDelinquent.mp3 Alpha Delinquent]'' by [[Carlo_Serafini|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|Carlo Serafini]] ([http://www.seraph.it/blog_files/351c7b45df8a68e9af24dab7d844d0c7-189.html blog entry])
 
''[http://www.seraph.it/dep/det/MilesOfSpace.mp3 Miles of Space]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/b1895d858c015ac923099bd356ff7a4a-194.html blog entry])
 
''[https://www.youtube.com/watch?v=ubMVjAt12fU MacAtar (video)]'' by [[Carlo_Serafini|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|Carlo Serafini]] ([http://www.seraph.it/blog_files/fe8d37804bc0ffb7e5eee6d410363c65-216.html blog entry])
 
''[https://youtu.be/bht4JPFbvzQ Alpha Asana (video)]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/bc3fe2f9bc3f2b75c7e4d3fb0028b817-221.html blog entry])
 
''[https://www.youtube.com/watch?v=7ZdN9VtP1Xw Alpha Penguin Tanz (video)]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/470888af1fdbb47b97467d0331843a13-224.html blog entry])
 
''[https://youtu.be/-aKYVVLImOw White Woman Speaks Up For #blacklivesmatter (video)]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/84f2ae146db05f06153a3b47fc6a8895-227.html blog entry])
 
''[http://www.seraph.it/dep/det/Jayni's%20song.mp3 Jayni's song]'' by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/c956c1294c91e7d9407c0ea447e667cb-232.html blog entry])
 
[https://www.youtube.com/watch?v=pkSIN8jU-i8 01.03.12 W.C.a.] by Omega9
[[Category:Carlos]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Edf]]
[[Category:Equal-step tuning]]
[[Category:Listen]]
[[Category:Listen]]
[[Category:Microtonal]]
 
{{Todo| cleanup | expand }}
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