Carlos Beta: Difference between revisions

Latest revision as of 07:13, 28 April 2025

English Wikipedia has an article on:

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 ¢^[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{ \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

Bryan Deister

Come (2022) – Carlos Beta version
Microtonal Improvisation in Carlos Beta (2023)

Omega9 & MÜÜR

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

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 #1 blog #2
Angela B. (2011) – play | blog
UGDoLA (2011) – blog | YouTube
Austrian Fantasy (2011) – blog | YouTube

MagentaFlavouredMusic

Carlama

References

↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal, vol. 11 no. 1, 1987, pp. 29-43
↑ Wendy Carlos, Three Asymmetric Divisions of the Octave.
↑ Dave Benson, Music: A Mathematical Offering, pp. 232-233.

External links

Wendy Carlos Pitch article | Three Asymmetric Divisions of the Octave (Permalink)

[1] Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal, vol. 11 no. 1, 1987, pp. 29-43

[2] Wendy Carlos, Three Asymmetric Divisions of the Octave.

[3] Dave Benson, Music: A Mathematical Offering, pp. 232-233.

[1]

[2]

[3]

@@ Line 9: / Line 9: @@
 </math>
-equal steps and the fifth in 10.996753 equal steps of 63.832933{{cent}} each<ref>Dave Benson, ''Music: A Mathematical Offering'', pp. 232-233.</ref>. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141{{cent}} each (11ed3/2), corresponding to 18.8046[[edo]].
+equal steps and the fifth in 10.996753 equal steps of 63.832933{{cent}} each<ref>Dave Benson, ''Music: A Mathematical Offering'', pp. 232-233.</ref>. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into eleven parts of 63.8141{{cent}} each ([[11edf|11ed3/2]]), corresponding to 18.8046[[edo]].
 Carlos Beta is related to the [[sycamore family]] of temperaments – betic and [[5-limit]] sycamore in particular.
@@ Line 28: / Line 28: @@
 |-
 | | 1
-| | 64
+| | 63.832933
 | |
 |-
 | | 2
-| | 128
+| | 127.665865
 | |
 |-
 | | 3
-| | 191
+| | 191.498798
 | |
 |-
 | | 4
-| | 255
+| | 255.331730
 | |
 |-
 | | 5
-| | 319
+| | 319.164663
-| | 6/5
+| | [[6/5]]
 |-
 | | 6
-| | 383
+| | 382.997595
-| | 5/4
+| | [[5/4]]
 |-
 | | 7
-| | 447
+| | 446.830528
 | |
 |-
 | | 8
-| | 510.5
+| | 510.663461
 | |
 |-
 | | 9
-| | 574
+| | 574.496393
 | |
 |-
 | | 10
-| | 638
+| | 638.329326
 |-
 | | 11
-| | 702
+| | 702.162258
-| | 3/2 (exact)
+| | [[3/2]]
 |-
 | | 12
-| | 766
+| | 765.995191
 | |
 |-
 | | 13
-| | 830
+| | 829.828123
-| | 13/8-ish
+| | [[13/8]]-ish
 |-
 | | 14
-| | 893
+| | 893.661056
 | |
 |-
 | | 15
-| | 957
+| | 957.493989
 | |
 |-
 | | 16
-| | 1021
+| | 1021.326921
 | |
 |-
 | | 17
-| | 1085
+| | 1085.159854
-| | 15/8
+| | [[15/8]]
 |-
 | | 18
-| | 1149
+| | 1148.992786
 | |
 |-
 | | 19
-| | 1211.5 ~ 11.5
+| | 1212.825719 ~ 12.825719
-| | 2/1-ish
+| | [[2/1]]-ish
 |-
 | | 20
-| | 1276 ~ 76
+| | 1276.658651 ~ 76.658651
 | |
 |-
 | | 21
-| | 1340 ~ 140
+| | 1340.491584 ~ 140.491584
 | |
 |-
 | | 22
-| | 1404 ~ 204
+| | 1404.324517 ~ 204.324517
-| | 9/4~9/8 (exact)
+| | [[9/4]]~[[9/8]]
 |-
 | | 23
-| | 1468 ~ 268
+| | 1468.157449 ~ 268.157449
-| | better 7/6
+| | better [[7/6]]
 |-
 | | 24
-| | 1532 ~ 332
+| | 1531.990382 ~ 331.990382
 | |
 |-
 | | 25
-| | 1595 ~ 395
+| | 1595.823314 ~ 395.823314
 |
 |-
 | | 26
-| | 1659 ~ 459
+| | 1659.656247 ~ 459.656247
 |
 |-
 | | 27
-| | 1723 ~ 523
+| | 1723.489179 ~ 523.489179
 |-
 | | 28
-| | 1787 ~ 587
+| | 1787.322112 ~ 587.322112
 |
 |-
 | | 29
-| | 1851 ~ 651
+| | 1851.155045 ~ 651.155045
 |
 |-
 | | 30
-| | 1914 ~ 714
+| | 1914.987977 ~ 714.987977
 |
 |-
 | | 31
-| | 1978 ~ 778
+| | 1978.820910 ~ 778.820910
 |
 |-
 | | 32
-| | 2042 ~ 842
+| | 2042.653842 ~ 842.653842
-| | 13/4 ~ 13/8 (better)
+| | [[13/4]] ~ [[13/8]] (better)
 |-
 | | 33
-| | 2106 ~ 906
+| | 2106.486775 ~ 906.486775
 |
 |-
 | | 34
-| | 2170 ~ 970
+| | 2170.319707 ~ 970.319707
 |
 |-
 | | 35
-| | 2233 ~ 1033
+| | 2234.152640 ~ 1034.152640
 |
 |-
 | | 36
-| | 2297 ~ 1097
+| | 2297.985573 ~ 1097.985573
 |
 |}
@@ Line 175: / Line 175: @@
 ; [[Bryan Deister]]
 * [https://www.youtube.com/watch?v=8qydnXzkbgg ''Come''] (2022) – Carlos Beta version
+* [https://www.youtube.com/shorts/bqbwHuBJHJQ ''Microtonal Improvisation in Carlos Beta''] (2023)
-; [[Omega9]]
+; [[Omega9|Omega9 & MÜÜR]]
-* [https://www.youtube.com/watch?v=qnIKaWhjZj0 ''cærulea'']{{dead link}}
+* ''Elirejo de tempo'' – [https://www.youtube.com/watch?v=qWXeoVCxL5k YouTube] | [https://blend.io/project/5e0459e6573b324b537f3682 Multitrack]
-* ''Way Without Time OST'' – [https://web.archive.org/web/20201127014140/http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Way%20Without%20Time%20OST.mp3 play] | [https://soundcloud.com/omega9/way-without-time-ost SoundCloud]{{dead link}}
+* ''Cærulea'' – [https://www.youtube.com/watch?v=NBfW6LC-Vec YouTube] | [https://blend.io/project/5e0459e61a4f113326352b85 Multitrack]
-* ''Tionmifarosalmimemkelkfoje'' (2012) – [https://web.archive.org/web/20201127015039/http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Tionmifarosalmimemkelkfoje.mp3 play] | [https://www.youtube.com/watch?v=eWgb-ZbgvJI YouTube]
+* ''Tempo kaj Ĥrono'' – [https://www.youtube.com/watch?v=OfQwGcJjMAo YouTube] | [https://blend.io/project/5e045a48f24d7af73aa4edf4 Multitrack]
+*''Tionmifarosalmimemkelkfoje'' (2012) – [https://web.archive.org/web/20201127015039/http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Tionmifarosalmimemkelkfoje.mp3 play] | [https://www.youtube.com/watch?v=eWgb-ZbgvJI YouTube]
 * ''Cordas'' (2012) – [https://web.archive.org/web/20201127015302/http://micro.soonlabel.com/gene_ward_smith/Others/Omega9/Omega9%20-%20Cordas%20(Carlos%20Beta).mp3 play] | [https://omega9.bandcamp.com/track/cordas-carlos-beta Bandcamp] | [https://www.youtube.com/watch?v=-fwA6egaqc4 YouTube] – Carlos Beta version

Carlos Beta: Difference between revisions

Latest revision as of 07:13, 28 April 2025

Contents

Theory

Intervals

Music

See also

References

External links

Navigation menu

Carlos Beta: Difference between revisions

Latest revision as of 07:13, 28 April 2025

Theory

Intervals

Music

See also

References

External links

Navigation menu

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