Carlos Alpha
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.
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 \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.
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
- Another day went by (2021) – hyperpop beat
- Urban entropy (2021)
- Crystallization (2021)
- HUH? (2022) – in 9edf tuning
- 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
See also
- Carlos' equal scales
- Carlos Harmonic
- Carlos Super Just