Carlos Alpha

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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 ¢. 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. 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.

Intervals

Degrees	Cents ~ Cents octave-reduced	Approximate JI interval (11-limit)
0	0	1/1 (exact)
1	77.964990	25/24, 22/21, 21/20
2	155.929979	12/11, 35/32, 11/10
3	233.894969	8/7, 55/48
4	311.859958	6/5
5	389.824948	5/4
6	467.789937	72/55, 21/16
7	545.754927	15/11, 48/35, 11/8
8	623.719916	10/7, 63/44, 36/25
9	701.684906	3/2
10	779.6498955	25/16, 11/7, 63/40
11	857.614885	18/11, 105/64, 33/20
12	935.579875	12/7, 55/32
13	1013.544864	9/5
14	1091.509854	15/8
15	1169.474843	108/55, 63/32
16	1247.439833 ~ 47.439833	45/22, 72/35, 33/16
17	1325.404822 ~ 125.404822	15/7, 189/88, 54/25
18	1403.369812 ~ 203.369812	9/4
19	1481.3348015 ~ 281.3348015
20	1559.299791 ~ 359.299791
21	1637.264781 ~ 437.264781
22	1715.229770 ~ 515.229770
23	1793.194760 ~ 593.194769
24	1871.159749 ~ 671.159749
25	1949.124739 ~ 749.124739
26	2027.089728 ~ 827.089728
27	2105.054718 ~ 905.054718
28	2183.019707 ~ 983.019707
29	2260.984697 ~ 1060.984697
30	2330.949687 ~ 1138.949687
31	2416.914676 ~ 16.914676
32	2494.879666 ~ 94.879666
33	2572.844655 ~ 172.844655
34	2650.809645 ~ 250.809645
35	2728.774635 ~ 328.774634
36	2806.739624 ~ 406.739624

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

See also

• Carlos' equal scales
  • Carlos Beta
  • Carlos Gamma
• Carlos Harmonic
• Carlos Super Just

External links

• Wendy Carlos Pitch article | Three Asymmetric Divisions of the Octave