Carlos Gamma: Difference between revisions

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== Intervals ==
== Intervals ==
The first steps up to two just perfect fifths should give a feeling of the granularity of this system…
The first steps up to two perfect fifths should give a feeling of the granularity of this system…
{| class="wikitable"
{| class="wikitable"
!Degrees
!Degrees
Line 22: Line 22:
|-
|-
|1
|1
|35.1
|35.098542
|-
|-
| |2
| |2
| |70.2
| |70.197085
|-
|-
| |3
| |3
| | 105.29
| | 105.295627
|-
|-
| |4
| |4
| |140.39
| |140.394169
|-
|-
| |5
| |5
| |175.49
| |175.492711
|-
|-
| |6
| |6
| |210.59
| |210.591254
|-
|-
| |7
| |7
| |245.68
| |245.689796
|-
|-
| |8
| |8
| | 280.78
| | 280.788338
|-
|-
| |9
| |9
| |315.88
| |315.886881
|-
|-
| |10
| |10
| |350.98
| |350.985423
|-
|-
| |11
| |11
| |386.075
| |386.083965
|-
|-
| |12
| |12
| |421.17
| |421.182507
|-
|-
| |13
| |13
| |456.27
| |456.281050
|-
|-
| |14
| |14
| |491.37
| |491.379592
|-
|-
| |15
| |15
| |526.47
| |526.478134
|-
|-
| |16
| |16
| |561.56
| |561.576676
|-
|-
| |17
| |17
| |596.66
| |596.675219
|-
|-
| |18
| |18
| |631.76
| |631.773761
|-
|-
| |19
| |19
| |666.86
| |666.872303
|-
|-
| |20
| |20
| |701.955
| |701.970846
|-
|-
|21
|21
| 737.05
| 737.069388
|-
|-
|22
|22
|772.15
|772.167930
|-
|-
|23
|23
|807.25
|807.266472
|-
|-
| 24
| 24
|842.35
|842.365015
|-
|-
|25
|25
|877.44
|877.463557
|-
|-
| 26
| 26
|912.54
|912.562099
|-
|-
|27
|27
| 947.64
| 947.660642
|-
|-
|28
|28
| 982.74
| 982.759184
|-
|-
|29
|29
|1017.835
|1017.857726
|-
|-
| 30
| 30
|1052.93
|1052.956268
|-
|-
| 31
| 31
|1088.03
|1088.054811
|-
|-
|32
|32
|1123.13
|1123.153353
|-
|-
|33
|33
|1158.23
|1158.251895
|-
|-
| 34
| 34
|1193.32
|1193.350438
|-
|-
|35
|35
| 1228.42
| 1228.448980
|-
|-
|36
|36
|1263.52
|1263.547522
|-
|-
| 37
| 37
|1298.62
|1298.646064
|-
|-
|38
|38
|1333.715
|1333.744607
|-
|-
|39
|39
|1368.81
|1368.843149
|-
|-
|40
|40
|1403.91
|1403.941691
|}
|}


Revision as of 09:52, 8 December 2024

English Wikipedia has an article on:

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 ¢[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{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 (20edf), 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 perfect fifths should give a feeling of the granularity of this system…

Degrees
1 35.098542
2 70.197085
3 105.295627
4 140.394169
5 175.492711
6 210.591254
7 245.689796
8 280.788338
9 315.886881
10 350.985423
11 386.083965
12 421.182507
13 456.281050
14 491.379592
15 526.478134
16 561.576676
17 596.675219
18 631.773761
19 666.872303
20 701.970846
21 737.069388
22 772.167930
23 807.266472
24 842.365015
25 877.463557
26 912.562099
27 947.660642
28 982.759184
29 1017.857726
30 1052.956268
31 1088.054811
32 1123.153353
33 1158.251895
34 1193.350438
35 1228.448980
36 1263.547522
37 1298.646064
38 1333.744607
39 1368.843149
40 1403.941691

Music

Bryan Deister
James Mulvale
  • SpeedRun (2021) – 11ed5/4 tuning, microtonal chiptune
Carlo Serafini
MagentaFlavouredMusic

See also

Reference

  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.

External links

Retrieved from "https://en.xen.wiki/index.php?title=Carlos_Gamma&oldid=169468"