Carlos Beta

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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 \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	63.832933
2	127.665865
3	191.498798
4	255.331730
5	319.164663	6/5
6	382.997595	5/4
7	446.830528
8	510.663461
9	574.496393
10	638.329326
11	702.162258	3/2
12	765.995191
13	829.828123	13/8-ish
14	893.661056
15	957.493989
16	1021.326921
17	1085.159854	15/8
18	1148.992786
19	1212.825719 ~ 12.825719	2/1-ish
20	1276.658651 ~ 76.658651
21	1340.491584 ~ 140.491584
22	1404.324517 ~ 204.324517	9/4~9/8
23	1468.157449 ~ 268.157449	better 7/6
24	1531.990382 ~ 331.990382
25	1595.823314 ~ 395.823314
26	1659.656247 ~ 459.656247
27	1723.489179 ~ 523.489179
28	1787.322112 ~ 587.322112
29	1851.155045 ~ 651.155045
30	1914.987977 ~ 714.987977
31	1978.820910 ~ 778.820910
32	2042.653842 ~ 842.653842	13/4 ~ 13/8 (better)
33	2106.486775 ~ 906.486775
34	2170.319707 ~ 970.319707
35	2234.152640 ~ 1034.152640
36	2297.985573 ~ 1097.985573

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

MagentaFlavouredMusic

• Carlama

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)