Carlos Beta

English Wikipedia has an article on:

Beta scale

Carlos Beta is a non-octave equal temperament invented by Wendy Carlos, with step size about 63.833 ¢, or almost exactly every fifth step of 94edo. 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 provided the tuning of 63.8 ¢. 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{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)} ≃ 18.799074 }[/math]

equal steps and the fifth in 10.996753 equal steps of 63.832933 ¢ each. It is thus very close to the equal division of the just perfect fifth into eleven parts of 63.8141 ¢ each (11ed3/2), corresponding to 18.8046edo.

Carlos Beta is related to the sycamore family of 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

Bryan Deister

• Come (2022) – Carlos Beta version

Omega9

• cærulea^{[dead link]}
• Way Without Time OST – play | SoundCloud^{[dead link]}
• Tionmifarosalmimemkelkfoje (2012) – play | YouTube
• Cordas (2012) – play | Bandcamp | YouTube – Carlos Beta version

Carlo Serafini

• The Dawn Of Beta (2011) – play | blog
• Lonely Beta Woman (2011) – play | blog
• Over The Beta Rainbow (2011) – play | blog
• Tribalism #2 (2011) – play | blog
• Beta Easter(n) (2011) – blog | YouTube
• tiBETAn Dreams (2011) – play | blog #1blog #2
• Angela B. (2011) – play | blog
• UGDoLA (2011) – blog | YouTube
• Austrian Fantasy (2011) – blog | YouTube

See also

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

External links

• Wendy Carlos Pitch article | Three Asymmetric Divisions of the Octave (Permalink)