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{{interwiki
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{{Wikipedia|Alpha scale}}
{{Wikipedia|Alpha scale}}
'''Carlos Alpha''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 77.965{{cent}}. 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.  
'''Carlos Alpha''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 77.965{{cent}}. 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 ==
== Theory ==

Revision as of 08:23, 2 January 2026

English Wikipedia has an article on:

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 ¢[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{ \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 77.965 25/24, 22/21, 21/20
2 155.930 12/11, 35/32, 11/10
3 233.895 8/7, 55/48
4 311.860 6/5
5 389.825 5/4
6 467.790 72/55, 21/16
7 545.755 15/11, 48/35, 11/8
8 623.720 10/7, 63/44, 36/25
9 701.685 3/2
10 779.650 25/16, 11/7, 63/40
11 857.615 18/11, 105/64, 33/20
12 935.580 12/7, 55/32
13 1013.545 9/5
14 1091.510 15/8
15 1169.475 108/55, 63/32
16 1247.440 ~ 47.440 45/22, 72/35, 33/16
17 1325.4045 ~ 125.405 15/7, 189/88, 54/25
18 1403.370 ~ 203.370 9/4
19 1481.335 ~ 281.335
20 1559.300 ~ 359.300
21 1637.265 ~ 437.265
22 1715.230 ~ 515.230
23 1793.195 ~ 593.195
24 1871.160 ~ 671.160
25 1949.125 ~ 749.125
26 2027.090 ~ 827.090
27 2105.055 ~ 905.055
28 2183.020 ~ 983.020
29 2260.985 ~ 1060.985
30 2330.950 ~ 1138.950
31 2416.915 ~ 16.915
32 2494.880 ~ 94.880
33 2572.845 ~ 172.845
34 2650.810 ~ 250.810
35 2728.775 ~ 328.775
36 2806.740 ~ 406.740

Music

See also: Category:Carlos Alpha tracks
Bazil Müzik
Bryan Deister
Mandrake
  • HUH? (2022) – in 9edf tuning
Omega9
Jean-Pierre Poulin
Carlo Serafini
Joel Grant Taylor
MagentaFlavouredMusic

See also

References

  1. ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal, vol. 11 no. 1, 1987, pp. 29-43
  2. ↑ Wendy Carlos, Three Asymmetric Divisions of the Octave.
  3. ↑ Dave Benson, Music: A Mathematical Offering, pp. 232-233.

External links

Retrieved from "https://en.xen.wiki/index.php?title=Carlos_Alpha&oldid=220583"