# Carlos Alpha

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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

$\displaystyle \frac{9^2 + 5^2 + 4^2}{9\log_2(3/2) + 5\log_2(5/4) + 4\log_2(6/5)} ≃ 15.391524$

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 (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

Bazil Müzik
Bryan Deister
Mandrake
• HUH? (2022) – in 9edf tuning
Omega9
Jean-Pierre Poulin
Carlo Serafini
Joel Grant Taylor
MagentaFlavouredMusic