Carlos Beta
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 ¢[1][2]. 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[3]. 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
- Come (2022) – Carlos Beta version
- Elirejo de tempo – YouTube | Multitrack
- Cærulea – YouTube | Multitrack
- Tempo kaj Ĥrono – YouTube | Multitrack
- Tionmifarosalmimemkelkfoje (2012) – play | YouTube
- Cordas (2012) – play | Bandcamp | YouTube – Carlos Beta version
- 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 Harmonic
- Carlos Super Just