Carlos Beta

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Carlos Beta is a non-octave equal temperament with step size about 63.833 cents[1], or almost exactly every fifth step of 94edo. It was invented by Wendy Carlos.

In this temperament, the interval of 11 steps approximates 3/2, that of 6 steps approximates 5/4, and that of 5 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{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)}[/math] ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. It is thus very close to the equal division of the just perfect fifth into eleven parts of 63.8141 cents each (11ed3/2), corresponding to 18.8046edo.

Carlos Beta is related to the sycamore temperaments; betic and 5-limit sycamore in particular.

Lookalikes: 19edo, 30edt, 94edo, 75edo

Intervals

Degrees Cents ~ Cents octave reduced Approximate JI interval ~ octave reduced
0 0
1 64
2 128
3 191
4 255
5 319 6/5
6 383 5/4
7 447
8 510.5
9 574
10 638
11 702 3/2 (exact)
12 766
13 830 13/8-ish
14 893
15 957
16 1021
17 1085 15/8
18 1149
19 1211.5 ~ 11.5 2/1-ish
20 1276 ~ 76
21 1340 ~ 140
22 1404 ~ 204 9/4~9/8 (exact)
23 1468 ~ 268 better 7/6
24 1532 ~ 332
25 1595 ~ 395
26 1659 ~ 459
27 1723 ~ 523
28 1787 ~ 587
29 1851 ~ 651
30 1914 ~ 714
31 1978 ~ 778
32 2042 ~ 842 13/4 ~ 13/8 (better)
33 2106 ~ 906
34 2170 ~ 970
35 2233 ~ 1033
36 2297 ~ 1097

Music

See also: Category:Carlos Beta tracks

See also

Reference

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

External links