Carlos Alpha: Difference between revisions

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'''Carlos Alpha''' is a non-octave equal temperament with step size about 77.965 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>. It is very close to [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2), corresponding to 15.3856 [[edo]].
'''Carlos Alpha''' is a non-octave equal temperament with step size about 77.965 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>. It is very close to [[EDF|equal division of the just perfect fifth]] into nine parts of 77.995 cents each (9ED3/2), corresponding to 15.3856 [[edo]].
Carlos Alpha 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.


== Theory ==
== Theory ==

Revision as of 13:20, 26 December 2021

Carlos Alpha is a non-octave equal temperament with step size about 77.965 cents[1]. It is very close to equal division of the just perfect fifth into nine parts of 77.995 cents each (9ED3/2), corresponding to 15.3856 edo.

Carlos Alpha 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)} }[/math] ≃ 15.391524 equal steps and the fifth in 9.003464 equal steps of 77.964990 cents each.

Theory

Article by Wendy Carlos

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.

Intervals

Degrees Cents ~ Cents octave-reduced Approximate JI interval (11-limit)
0 0 1/1 (exact)
1 78 25/24, 22/21, 21/20
2 156 12/11, 35/32, 11/10
3 234 8/7, 55/48
4 312 6/5
5 390 5/4
6 468 72/55, 21/16
7 546 15/11, 48/35, 11/8
8 624 10/7, 63/44, 36/25
9 702 3/2 (exact)
10 780 25/16, 11/7, 63/40
11 858 18/11, 105/64, 33/20
12 936 12/7, 55/32
13 1014 9/5
14 1092 15/8
15 1170 108/55, 63/32
16 1248 ~ 48 45/22, 72/35, 33/16
17 1326 ~ 126 15/7, 189/88, 54/25
18 1404 ~ 204 9/4 (exact)
19 1482 ~ 282
20 1560 ~ 360
21 1638 ~ 438
22 1716 ~ 516
23 1794 ~ 594
24 1872 ~ 672
25 1950 ~ 750
26 2028 ~ 828
27 2106 ~ 906
28 2184 ~ 984
29 2262 ~ 1062
30 2340 ~ 1140
31 2418 ~ 18
32 2496 ~ 96
33 2574 ~ 174
34 2652 ~ 252
35 2730 ~ 330
36 2808 ~ 408

Music

See also: Category:Carlos Alpha tracks

Reference

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