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 | '''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]]. | ||
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]]. [[Wendy Carlos]] optimized the tuning on 3/2, 5/4, and 6/5, such that the tuning 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. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141 cents each (11ed3/2), corresponding to 18.8046[[edo]]. | ||
== Theory == | == Theory == | ||
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== See also == | == See also == | ||
* [[ | * [[Mason Green's New Common Practice Notation]] | ||
== Reference == | == Reference == | ||
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[[Category:Nonoctave]] | [[Category:Nonoctave]] | ||
[[Category:Equal-step tuning]] | [[Category:Equal-step tuning]] | ||
[[Category:Listen]] | [[Category:Listen]] | ||
{{ | {{Todo| cleanup | expand }} | ||
Revision as of 14:09, 18 March 2022
Carlos Beta is a non-octave equal temperament with step size about 63.833 cents[1], 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. Wendy 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.
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.
Lookalikes: 19edo, 30edt, 94edo
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