Carlos Beta

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Beta scale

Carlos Beta is a non-octave equal temperament with step size about 63.833 cents, 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]\displaystyle{ \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, 11edf, 30edt, every 5th step of 94edo, every 4th step of 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

Omega9

• cærulea
• Way Without Time OST play
• Tionmifarosalmimemkelkfoje play
• Cordas play by Omega9

Carlo Serafini

• The Dawn Of Beta (blog entry)
• Lonely Beta Woman (blog entry)
• Over The Beta Rainbow (blog entry)
• Tribalism #2 (blog entry)
• Beta Easter(n) (video) (blog entry)
• tiBETAn Dreams (blog) (entry)
• Angela B. (blog entry)
• UGDoLA (video) (blog entry)
• Austrian Fantasy (video) (blog entry)

See also

• Mason Green's New Common Practice Notation
• Carlos Alpha
• Carlos Gamma
• Carlos Harmonic
• Carlos Super Just

External links

• Wendy Carlos Pitch article (Permalink)