Carlos Beta: Difference between revisions
Jump to navigation
Jump to search
CompactStar (talk | contribs) No edit summary |
mNo edit summary |
||
| Line 120: | Line 120: | ||
| | 25 | | | 25 | ||
| | 1595 ~ 395 | | | 1595 ~ 395 | ||
| | |||
|- | |- | ||
| | 26 | | | 26 | ||
| | 1659 ~ 459 | | | 1659 ~ 459 | ||
| | |||
|- | |- | ||
| | 27 | | | 27 | ||
| Line 129: | Line 131: | ||
| | 28 | | | 28 | ||
| | 1787 ~ 587 | | | 1787 ~ 587 | ||
| | |||
|- | |- | ||
| | 29 | | | 29 | ||
| | 1851 ~ 651 | | | 1851 ~ 651 | ||
| | |||
|- | |- | ||
| | 30 | | | 30 | ||
| | 1914 ~ 714 | | | 1914 ~ 714 | ||
| | |||
|- | |- | ||
| | 31 | | | 31 | ||
| | 1978 ~ 778 | | | 1978 ~ 778 | ||
| | |||
|- | |- | ||
| | 32 | | | 32 | ||
| Line 145: | Line 151: | ||
| | 33 | | | 33 | ||
| | 2106 ~ 906 | | | 2106 ~ 906 | ||
| | |||
|- | |- | ||
| | 34 | | | 34 | ||
| | 2170 ~ 970 | | | 2170 ~ 970 | ||
| | |||
|- | |- | ||
| | 35 | | | 35 | ||
| | 2233 ~ 1033 | | | 2233 ~ 1033 | ||
| | |||
|- | |- | ||
| | 36 | | | 36 | ||
| | 2297 ~ 1097 | | | 2297 ~ 1097 | ||
| | |||
|} | |} | ||
| Line 162: | Line 172: | ||
* [http://www.seraph.it/dep/det/OverTheBetaRainbow.mp3 Over The Beta Rainbow] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/c498a163495a549dbc2711691061db11-92.html blog entry]) | * [http://www.seraph.it/dep/det/OverTheBetaRainbow.mp3 Over The Beta Rainbow] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/c498a163495a549dbc2711691061db11-92.html blog entry]) | ||
* [http://www.seraph.it/dep/det/Tribalism2.mp3 Tribalism #2] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/e516a6726f78b7c6232b0869222507ff-95.html blog entry]) | * [http://www.seraph.it/dep/det/Tribalism2.mp3 Tribalism #2] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/e516a6726f78b7c6232b0869222507ff-95.html blog entry]) | ||
* [ | * [https://youtu.be/6yBY2AvsUOA3 Beta Easter(n) (video)] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/9d774615381a06e228b7de11a9394562-97.html blog entry]) | ||
* [http://www.seraph.it/dep/det/tiBETAnDreams.mp3 tiBETAn Dreams] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/9029519d60cf978db21549a608ef4ea3-99.html blog]) ([http://www.seraph.it/blog_files/7f1eb6f7799c4f90d796396cbade30ce-98.html entry]) | * [http://www.seraph.it/dep/det/tiBETAnDreams.mp3 tiBETAn Dreams] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/9029519d60cf978db21549a608ef4ea3-99.html blog]) ([http://www.seraph.it/blog_files/7f1eb6f7799c4f90d796396cbade30ce-98.html entry]) | ||
* [http://www.seraph.it/dep/det/Angela.mp3 Angela B.] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/2edec68ea23551591ff1c0d897e1f8fa-101.html blog entry]) | * [http://www.seraph.it/dep/det/Angela.mp3 Angela B.] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/2edec68ea23551591ff1c0d897e1f8fa-101.html blog entry]) | ||
* [ | * [https://www.youtube.com/watch?v=mghWWIUjh9o UGDoLA (video)] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/6d6dcd64d5d817366c5608edfbed16b6-102.html blog entry]) | ||
* [ | * [https://youtu.be/v4F38G4XKLc Austrian Fantasy (video)] by [[Carlo_Serafini|Carlo Serafini]] ([http://www.seraph.it/blog_files/49d276aa03bebbf3a0c831f0bc3bdea5-107.html blog entry]) | ||
* [ | * [https://www.youtube.com/watch?v=qnIKaWhjZj0 cærulea] by Omega9 | ||
* [ | * [https://soundcloud.com/omega9/way-without-time-ost Way Without Time OST] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Way%20Without%20Time%20OST.mp3 play] by Omega9 | ||
* [ | * [https://www.youtube.com/watch?v=eWgb-ZbgvJI Tionmifarosalmimemkelkfoje] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Tionmifarosalmimemkelkfoje.mp3 play] by Omega9 | ||
* [ | * [https://www.youtube.com/watch?v=-fwA6egaqc4 Cordas] [http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Cordas%20(Carlos%20Beta).mp3 play] by Omega9 | ||
== See also == | == See also == | ||
Revision as of 21:26, 5 April 2023
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 was invented by Wendy 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.
Theory
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.
Carlos Beta is related to the sycamore 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
- 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
- Mason Green's New Common Practice Notation
- Carlos Alpha
- Carlos Gamma
- Carlos Harmonic
- Carlos Super Just
Reference
- ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43