Carlos Alpha

Carlos Alpha is a non-octave equal temperament with step size about 77.965 ¢ in the standard tuning[1]. It was invented by Wendy Carlos.
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 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 equal division of the just perfect fifth into nine parts of 77.995 cents each (9ed3/2), 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
- Alphablues
- Alphapanther (blog entry)
- Alphadesert (blog entry)
- AlphaDulcimer (blog entry)
- AlphaTherem Waltz (blog entry)
- Cubana Al Cubana Pha (blog entry)
- DisMLosphere - video (blog entry)
- Alpha El Din (blog entry)
- Alpha Choir (blog entry)
- Alpha Seems To Be The Hardest World (blog entry)
- Bossa Sbilenca (blog entry)
- Galactic Overload (blog entry)
- Alpha Rain (video) (blog entry)
- Alpha Delinquent (blog entry)
- Alpha Abstract 1 (blog entry)
- Miles of Space (blog entry)
- MacAtar (video) (blog entry)
- Fuzzy Logic (blog entry)
- Alpha Asana (video) (blog entry)
- Alpha Penguin Tanz (video) (blog entry)
- White Woman Speaks Up For #blacklivesmatter (video) (blog entry)
- Jayni's song (blog entry)
See also
References
- ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43