Carlos Alpha

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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
Bazil Müzik
Bryan Deister
Mandrake
Omega9
Jean-Pierre Poulin
Carlo Serafini
Joel Grant Taylor

See also

References

  1. Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43

External links