Carlos Gamma

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Gamma scale

Carlos Gamma is a non-octave equal temperament invented by Wendy Carlos, with step size about 35.099 ¢. In this temperament, the interval of 20 steps approximates 3/2, that of 11 steps approximates 5/4, and that of 9 steps approximates 6/5.

Theory

Carlos provided the tuning of 35.1 ¢. 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{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)} ≃ 34.189454 }[/math]

equal steps and the fifth in 19.999549 equal steps of 35.0985422804 ¢ each. It is thus very close to the equal division of the just perfect fifth into twenty parts of 35.0978 ¢ each (20ed3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.

Carlos Gamma is closely related to the gammic temperament.

Lookalikes: 34edo, 54edt, 96ed7, 171edo

Intervals

The first steps up to two just perfect fifths should give a feeling of the granularity of this system…

Degrees
1	35.1
2	70.2
3	105.29
4	140.39
5	175.49
6	210.59
7	245.68
8	280.78
9	315.88
10	350.98
11	386.075
12	421.17
13	456.27
14	491.37
15	526.47
16	561.56
17	596.66
18	631.76
19	666.86
20	701.955
21	737.05
22	772.15
23	807.25
24	842.35
25	877.44
26	912.54
27	947.64
28	982.74
29	1017.835
30	1052.93
31	1088.03
32	1123.13
33	1158.23
34	1193.32
35	1228.42
36	1263.52
37	1298.62
38	1333.715
39	1368.81
40	1403.91

Music

Bryan Deister

• 180db_[130] - Aphex Twin (2022)

James Mulvale

• SpeedRun (2021) – 11ed5/4 tuning, microtonal chiptune

Carlo Serafini

• Adagio Gamma (2009) – play | blog
• Gammalan (2009) – play | blog
• Moonlight Gamma Serenade (2009) – play | blog
• Bix in the sky with Gamma (2009) – play | blog
• An Irishman in Guangdong (2009) – play | blog
• Chameleons in the Dark (2009) – play | blog
• East Of The Moon (2010) – blog | YouTube
• The Singing Alchemist (2010) – play | blog
• Micro Vocoder 1 (2010) – blog | YouTube
• Namul1 (2010) – play | blog
• Namul2 (2010) – play | blog
• Hal Trumpetti (2010) – play | blog
• Talking Gamma In Your Sleep (2010) – play | blog
• Gamma Raga (2010) – play | blog
• from The Solstice Song (2010)
  • "Part 1"
  • "Part 3" – 12et and Carlos gamma polysystemic
  • "Part 5" – 12et and Carlos gamma polysystemic
• Conference of Flutes (2010) – play | blog
• Bicycles and Bowls (2010) – play | blog
• Elba Gamma (2010) – blog | YouTube
• Double Trouble 1 (2010) – blog | YouTube
• Double Trouble 2 (2010) – blog | YouTube
• Invocation (2010) – blog | YouTube
• KYMI Exercise #1 (2010) – blog | YouTube
• Gammatar (2011) blog | split-notes – 9-piece album
  • "Gammatar" – play · Gamma Elegy (2009) – play | blog
  • "Glorious 61" – play · Glorious 60 (2009) – play | blog
  • "Glorious Guitars" – play · Glorious Guitars (2009) – play | blog
  • "Jingle Gamma Bells" – play · Jingle Gamma Bells (2010) – blog | YouTube
  • "Delta Gamma Blues" – play · Delta Gamma Blues (2010) – play | blog
  • "Chameleons In The Sun" – play · Chameleons In The Sun (2009) – play | blog
  • "Gamma Monk" – play · Gamma Monk (2009) – play | blog
  • "Autumnal Modulations" – play · Autumnal Modulations (2010) – play | blog
  • "Gamma Breezin'" – play · Gamma Breezin' (2010) – play | blog
• Out of Gamma Body Experience (2014) – play | blog
• Gamma Meditation (2015) – play | blog
• Sea Of Tranquility (2015) – play | blog
• Organum 1 (2015) – play | blog
• Organum 2 (2015) – play | blog
• Adagio Gamma X (2016) – blog | YouTube
• Far Away From Home (2017) – blog | YouTube
• Lament for Marco (2017) – blog | YouTube
• Forward Gamma March (2018) – play | blog
• J.F.Sebastian's Lullaby (2018) – blog | play
• Gamma Quarantine (2020) – blog | YouTube
• Babylon Gamma (2021) – play | blog
• Gamma Constant Structures (2021) – play | blog
• Early Heaven (2023) – play | blog

See also

• Carlos' equal scales
  • Carlos Alpha
  • Carlos Beta
• Carlos Harmonic
• Carlos Super Just

External links

• Wendy Carlos Pitch article | Three Asymmetric Divisions of the Octave