Carlos Beta: Difference between revisions
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'''Carlos Beta''' is a non-octave equal temperament with step size about 63.833 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>, or almost exactly every fifth step of [[94edo]]. It is very close to [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141 cents each (11ED3/2), corresponding to 18.8046 [[edo]]. | '''Carlos Beta''' is a non-octave equal temperament with step size about 63.833 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>, or almost exactly every fifth step of [[94edo]]. It is very close to [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141 cents each (11ED3/2), corresponding to 18.8046 [[edo]]. | ||
Carlos Beta divides the octave in <nowiki><math>\frac{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)}</math></nowiki> ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. | Carlos Beta divides the octave in <nowiki><math>\frac{11^2 + 6^2 + 5^2}{11\log_2(3/2) + 6\log_2(5/4) + 5\log_2(6/5)}</math></nowiki> ≃ 18.799074 equal steps and the fifth in 10.996753 equal steps of 63.832933 cents each. | ||
Revision as of 10:35, 26 December 2021
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 is very close to equal division of the just perfect fifth into eleven parts of 63.8141 cents each (11ED3/2), corresponding to 18.8046 edo.
Carlos Beta 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.
Theory
Carlos Beta is a non-octave, equally tempered scale discovered by Wendy Carlos. It is related to the sycamore temperaments; betic and 5-limit sycamore in particular.
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
- The Dawn Of Beta by Carlo Serafini (blog entry)
- Lonely Beta Woman by Carlo Serafini (blog entry)
- Over The Beta Rainbow by Carlo Serafini (blog entry)
- Tribalism #2 by Carlo Serafini (blog entry)
- Beta Easter(n) (video) by Carlo Serafini (blog entry)
- tiBETAn Dreams by Carlo Serafini (blog) (entry)
- Angela B. by Carlo Serafini (blog entry)
- UGDoLA (video) by Carlo Serafini (blog entry)
- Austrian Fantasy (video) by Carlo Serafini (blog entry)
- cærulea by Omega9
- Way Without Time OST play by Omega9
- Tionmifarosalmimemkelkfoje play by Omega9
- Cordas play by Omega9
See also
Reference
- ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43