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'''Carlos Gamma''' is a non-octave [[equal temperament]] whose step size is 35.0985422804 [[cent]]s<ref>Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43</ref>.
{{interwiki
|en = Carlos_Gamma
|de = Carlos_Gamma
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{{Wikipedia|Gamma scale}}
'''Carlos Gamma''' is a non-octave [[equal temperament]] invented by [[Wendy Carlos]], with step size about 35.099{{cent}}. 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]].


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]]. [[Wendy Carlos]] optimized the tuning on 3/2, 5/4, and 6/5, such that the tuning divides the octave in <math>\frac{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)}</math> ≃ 34.189454 equal steps and the fifth in 19.999549 equal steps of 35.098542 cents each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into twenty parts of 35.0978 cents each (20ed3/2), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.
== Theory ==
Carlos provided the tuning of 35.1{{cent}}<ref>Wendy Carlos, "Tuning: At the Crossroads", ''Computer Music Journal'', vol. 11 no. 1, 1987, pp. 29-43</ref><ref>Wendy Carlos, ''Three Asymmetric Divisions of the Octave''. </ref>. 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


== Theory ==
<math>\displaystyle
[http://www.wendycarlos.com/resources/pitch.html Article by Wendy Carlos]
\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{{cent}} each. It is thus very close to the [[EDF|equal division of the just perfect fifth]] into twenty parts of 35.0978{{cent}} each ([[20edf]]), which has been oft-misquoted as actually being Wendy Carlos's gamma scale.


Gamma is a non-octave scale created by Wendy Carlos. It is closely related to the [[gammic]] temperament.
Carlos Gamma is closely related to the [[gammic]] temperament.


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


== 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"
! rowspan="2" |Degrees
!Degrees
! rowspan="2" |''ed233\420-5¢''
!
! rowspan="2" |ed31\54
! rowspan="2" |ed121/81 (~ed11\19)
! rowspan="2" |ed696¢ (~69ed4!)
! rowspan="2" |ed32\55
! rowspan="2" |ed700¢=''r¢''
! rowspan="2" |ed3/2
! colspan="2" |Pyrite
! rowspan="2" |ed708¢
! rowspan="2" |ed122/81 (~ed13\22)
! rowspan="2" |ed34\57
! rowspan="2" |''ed37\60+5¢''
|-
!(~ed17\29)
!(~ed10\17)
|-
|-
| | 1
|1
|''33.04-33.29''
|35.098542
|34.44
|34.74
|34.8
|34.91
|''35''
| | 35.1
|35.18
|35.29
|35.4
|35.45
|35.79
|''37-37.25''
|-
|-
| | 2
| |2
|''66.07-66.''57
| |70.197085
|68.89
|69.48
|69.6
|69.82
|''70''
| | 70.2
|70.36
|70.59
|70.8
|70.91
|71.58
|''74-74.5''
|-
|-
| | 3
| |3
|''99.11-99.86''
| | 105.295627
|103.33
|104.22
|104.4
|104.73
|''105''
| | 105.29
|105.545
|105.88
|106.2
|106.36
|107.37
|''111-111.75''
|-
|-
| | 4
| |4
|''132.14-133.14''
| |140.394169
|137.78
|138.96
|139.2
|139.64
|''140''
| | 140.39
|140.72
|141.17
|141.6
|141.81
|143.16
|''148-149''
|-
|-
| | 5
| |5
|''165.18-166.43''
| |175.492711
|172.22
|173.7
|174
|174.545
|''175''
| | 175.49
|175.91
|176.46
|177
|177.27
|178.95
|''185-186.25''
|-
|-
| | 6
| |6
|''198.21-199.71''
| |210.591254
|206.67
|208.445
|208.8
|209.455
|''210''
| | 210.59
|211.09
|211.76
|212.4
|212.72
|214.74
|''222-223.5''
|-
|-
| | 7
| |7
|''231.25-233''
| |245.689796
|241.11
|243.19
|243.6
|244.36
|''245''
| | 245.68
|246.27
|247.05
|247.8
|248.17
|250.53
|''259-260.75''
|-
|-
| | 8
| |8
|''264.29-266.29''
| | 280.788338
|275.56
|277.93
|278.4
|279.27
|''280''
| | 280.78
|281.45
|282.34
|283.2
|283.63
|286.32
|''296-298''
|-
|-
| | 9
| |9
|''297.32-299.57''
| |315.886881
|310
|312.67
|313.2
|314.18
|''315''
| | 315.88
|316.64
|317.635
|318.6
|319.08
|322.105
|''333-335.25''
|-
|-
| | 10
| |10
|''330.35-332.86''
| |350.985423
|344.44
|347.41
|348
|349.09
|''350''
| | 350.98
|351.82
|352.93
|354
|354.53
|357.895
|''370-372.5''
|-
|-
| | 11
| |11
|''363.39-366.14''
| |386.083965
|378.89
|382.15
|382.8
|384
|''385''
| | 386.075
|387
|388.22
|389.4
|389.99
|393.68
|''407-409.75''
|-
|-
| | 12
| |12
|''396.43-399.43''
| |421.182507
|413.33
|416.89
|417.6
|418.91
|''420''
| | 421.17
|422.18
|423.51
|424.8
|425.44
|429.47
|''444-447''
|-
|-
| | 13
| |13
|''429.46-432.71''
| |456.281050
|447.78
|451.63
|452.4
|453.82
|''455''
| | 456.27
|457.36
|458.81
|460.2
|460.89
|465.26
|''481-484.25''
|-
|-
| | 14
| |14
|''462.5-466''
| |491.379592
|482.22
|486.37
|487.2
|488.73
|''490''
| |491.37
|492.545
|494.1
|495.6
|496.345
|501.05
|''518-521.5''
|-
|-
| | 15
| |15
|''495.54-499.29''
| |526.478134
|516.67
|521.11
|522
|523.64
|''525''
| | 526.47
|527.73
|529.39
|531
|531.8
|536.84
|''555-558.75''
|-
|-
| | 16
| |16
|''528.57-532.57''
| |561.576676
|551.11
|555.85
|556.8
|558.545
|''560''
| | 561.56
|562.91
|564.68
|566.4
|567.25
|572.63
|''592-596''
|-
|-
| | 17
| |17
|''561.61-565.86''
| |596.675219
|585.56
|590.59
|591.6
|593.455
|''595''
| | 596.66
|598.09
|599.98
|601.8
|602.705
|608.42
|''629-633.25''
|-
|-
| | 18
| |18
|''594.64-599.14''
| |631.773761
|620
|625.33
|626.4
|628.36
|''630''
| | 631.76
|633.27
|635.27
|637.2
|638.16
|644.21
|''666-670.5''
|-
|-
| | 19
| |19
|''627.68-632.43''
| |666.872303
|654.44
|660.075
|661.2
|663.27
|''665''
| | 666.86
|668.45
|670.56
|672.6
|673.61
|680
|''703-707.75''
|-
|-
| | 20
| |20
|''660.71-665.71''
| |701.970846
|688.89
|694.82
|696
|698.18
|''700''
| | 701.955
|703.64
|705.86
|708
|709.065
|715.79
|''740-745''
|-
|-
|21
|21
|''693.75-699''
| 737.069388
|723.33
|729.56
|732.8
|733.09
|''735''
|737.05
|738.82
|741.15
|743.4
|744.52
|751.58
|''777-782.25''
|-
|-
|22
|22
|''726.79-732.29''
|772.167930
|757.78
|764.3
|765.6
|768
|''770''
|772.15
|774
|776.44
|778.8
|779.97
|787.37
|''814-819.5''
|-
|-
|23
|23
|''759.82-765.57''
|807.266472
|792.22
|799.04
|800.4
|802.91
|''805''
|807.25
|809.18
|811.73
|813.2
|815.425
|823.16
|''851-856.75''
|-
|-
|24
| 24
|''792.86-798.86''
|842.365015
|826.67
|833.78
|835.2
|837.82
|''840''
|842.35
|844.36
|847.03
|848.6
|850.88
|858.95
|''888-894''
|-
|-
|25
|25
|''825.89-832.14''
|877.463557
|861.11
|868.52
|870
|872.73
|''875''
|877.44
|879.545
|882.32
|885
|886.33
|894.74
|''925-931.25''
|-
|-
|26
| 26
|''858.93-865.43''
|912.562099
|895.6
|903.26
|904.8
|907.64
|''910''
|912.54
|914.73
|917.61
|920.4
|921.78
|930.53
|''962-968.5''
|-
|-
|27
|27
|''891.96-898.71''
| 947.660642
|930
|938
|939.6
|942.545
|''945''
|947.64
|949.91
|952.905
|955.8
|957.24
|966.32
|''999-1005.75''
|-
|-
|28
|28
|''925-932''
| 982.759184
|964.4
|972.74
|974.4
|977.455
|''980''
|982.74
|985.09
|988.2
|991.2
|992.69
|1002.105
|''1036-1043''
|-
|-
|29
|29
|''958.04-965.29''
|1017.857726
|998.89
|1007.48
|1009.2
|1012.36
|''1015''
|1017.835
|1020.27
|1023.49
|1026.6
|1028.14
|1039.895
|''1073-1081.25''
|-
|-
|30
| 30
|''991.07-998.''57
|1052.956268
|1033.33
|1042.22
|1044
|1047.27
|''1050''
|1052.93
|1055.45
|1058.78
|1062
|1063.6
|1073.68
|''1110-1117.5''
|-
|-
|31
| 31
|''1024.11-1031.86''
|1088.054811
|1067.78
|1076.965
|1078.8
|1082.18
|''1085''
|1088.03
|1090.64
|1094.08
|1097.4
|1099.05
|1109.47
|''1147-1154.75''
|-
|-
|32
|32
|''1057.14-1065.14''
|1123.153353
|1102.22
|1111.705
|1113.6
|1117.09
|''1120''
|1123.13
|1125.82
|1129.37
|1132.8
|1134.5
|1145.26
|''1184-1192''
|-
|-
|33
|33
|''1090.18-1098.43''
|1158.251895
|1136.67
|1146.45
|1148.4
|1152
|''1155''
|1158.23
|1161
|1164.66
|1168.2
|1169.96
|1181.05
|''1221-1229.25''
|-
|-
|34
| 34
|''1123.21-1131.71''
|1193.350438
|1171.1
|1181.19
|1183.2
|1186.91
|''1190''
|1193.32
|1196.18
|1199.95
|1203.6
|1205.41
|1216.84
|''1258-1266.5''
|-
|-
|35
|35
|''1156.25-1165''
| 1228.448980
|1205.56
|1215.93
|1218
|1221.82
|''1225''
|1228.42
|1231.36
|1235.25
|1239
|1240.86
|1252.63
|''1295-1303.75''
|-
|-
|36
|36
|''1189.29-1198.29''
|1263.547522
|1240
|1250.67
|1252.8
|1256.73
|''1260''
|1263.52
|1266.545
|1270.54
|1274.4
|1276.32
|1288.42
|''1332-1341''
|-
|-
|37
| 37
|''1222.32-1231.57''
|1298.646064
|1274.44
|1285.41
|1287.6
|1291.64
|''1295''
|1298.62
|1301.73
|1305.83
|1309.8
|1311.77
|1324.42
|''1369-1377.25''
|-
|-
|38
|38
|''1255.36-1263.''86
|1333.744607
|1308.89
|1320.15
|1322.4
|1326.545
|''1330''
|1333.715
|1336.91
|1341.125
|1345.2
|1347.22
|1360
|''1406-1415.5''
|-
|-
|39
|39
|''1288.39-1298.14''
|1368.843149
|1343.33
|1354.89
|1357.2
|1361.455
|''1365''
|1368.81
|1372.09
|1376.42
|1380.6
|1382.68
|1395.79
|''1443-1452.75''
|-
|-
|40
|40
|''1321.43-1331.43''
|1403.941691
|1377.78
|1389.6
|1392
|1396.36
|''1400''
|1403.91
|1407.27
|1411.71
|1416
|1418.13
|1431.6
|''1480-1490''
|}
|}


== Compositions ==
== Music ==
* [http://www.seraph.it/dep/det/AdagioGamma.mp3 Adagio Gamma] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/140006ae42b0d87bb0903cdd857fa62c-24.html blog entry])
; [[Bryan Deister]]
* [http://www.seraph.it/dep/det/Gammalan.mp3 Gammalan] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/ef1a7e2088ff6ad32fc50cbd4b2a601d-25.html blog entry])
* [https://www.youtube.com/watch?v=MCNtpptAgLE ''180db_{{lbrack}}130{{rbrack}} - Aphex Twin''] (2022)
* [http://www.seraph.it/dep/det/moonlightgammaserenade.mp3 Moonlight Gamma Serenade] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/91c9f8975a11199a130e18bbc1c436ae-31.html blog entry])
* [https://www.youtube.com/shorts/f-d_RMhgLOE ''Microtonal Improvisation in Carlos Gamma''] (2023)
* [http://www.seraph.it/dep/det/BixInTheSkyWithGamma.mp3 Bix In The Sky With Gamma] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/3be0c8f6ba38f8985d0d33aa529f51cd-40.html blog entry])
 
* [http://www.seraph.it/dep/det/AnIrishmanInGuangdong.mp3 An Irishman In Guangdong] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/eea975e524f69f869408c8fccc3ff274-41.html blog entry])
; [[James Mulvale]]
* [http://www.seraph.it/dep/det/ChameleonsInTheDark.mp3 Chameleons In The Dark] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/f743270786dc14253dae1d90fd827c5a-43.html blog entry])
* [https://youtu.be/2MseEBUhZBQ ''SpeedRun''] (2021) – 11ed5/4 tuning, microtonal chiptune
* [http://www.seraph.it/dep/det/GammaElegy.mp3 Gamma Elegy] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/dada89373d85adfc7c01a844eb0d4693-46.html blog entry])
 
* [http://www.seraph.it/dep/det/GloriousGuitars.mp3 Glorious Guitars] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/e8a36018d6b782c8ff7bc2416fa7ea5b-47.html blog entry])
; [[Carlo Serafini]]
* [http://www.seraph.it/dep/det/ChameleonsInTheSun.mp3 Chameleons In The Sun] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/5b5e9af886df068be22fdfe37523eba3-48.html blog entry])
* ''Adagio Gamma'' (2009) – [http://www.seraph.it/dep/det/AdagioGamma.mp3 play] | [http://www.seraph.it/blog_files/140006ae42b0d87bb0903cdd857fa62c-24.html blog]
* [http://www.seraph.it/dep/det/GammaMonk.mp3 Gamma Monk] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/c883c0c218b0e1a9767e1ae71d700e8f-49.html blog entry])
* ''Gammalan'' (2009) – [http://www.seraph.it/dep/det/Gammalan.mp3 play] | [http://www.seraph.it/blog_files/ef1a7e2088ff6ad32fc50cbd4b2a601d-25.html blog]
* [http://www.youtube.com/watch?v=o8dIJmpt8IY East Of The Moon (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/5dfe4aeb16f360dd16dd93bada02c021-53.html blog entry])
* ''Moonlight Gamma Serenade'' (2009) – [http://www.seraph.it/dep/det/moonlightgammaserenade.mp3 play] | [http://www.seraph.it/blog_files/91c9f8975a11199a130e18bbc1c436ae-31.html blog]
* [http://www.seraph.it/dep/det/TheSingingAlchemist.mp3 The Singing Alchemist] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/dc22d50ef807215177743a8c0adb6e8b-55.html blog entry])
* ''Bix in the sky with Gamma'' (2009) – [http://www.seraph.it/dep/det/BixInTheSkyWithGamma.mp3 play] | [http://www.seraph.it/blog_files/3be0c8f6ba38f8985d0d33aa529f51cd-40.html blog]
* [http://www.youtube.com/watch?v=r3xMmAI_DgM&feature=player_embedded Micro Vocoder 1 (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/b7fcede2a50aa768948bf462836670d6-56.html blog entry])
* ''An Irishman in Guangdong'' (2009) – [http://www.seraph.it/dep/det/AnIrishmanInGuangdong.mp3 play] | [http://www.seraph.it/blog_files/eea975e524f69f869408c8fccc3ff274-41.html blog]
* [http://www.seraph.it/dep/det/Namul1.mp3 Namul1] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/a71f095266803b874c26f7b13c3bd20b-58.html blog entry])
* ''Chameleons in the Dark'' (2009) – [http://www.seraph.it/dep/det/ChameleonsInTheDark.mp3 play] | [http://www.seraph.it/blog_files/f743270786dc14253dae1d90fd827c5a-43.html blog]
* [http://www.seraph.it/dep/det/Namul2.mp3 Namul 2] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/21e1fd914125f5840789ab05eda26643-59.html blog entry])
* ''East Of The Moon'' (2010) – [http://www.seraph.it/blog_files/5dfe4aeb16f360dd16dd93bada02c021-53.html blog] | [https://www.youtube.com/watch?v=o8dIJmpt8IY YouTube]
* [http://www.seraph.it/dep/det/DeltaGammaBlues.mp3 Delta Gamma Blues] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/90950fe2c088f39d304b8c4f2f1d0c3e-60.html blog entry])
* ''The Singing Alchemist'' (2010) – [http://www.seraph.it/dep/det/TheSingingAlchemist.mp3 play] | [http://www.seraph.it/blog_files/dc22d50ef807215177743a8c0adb6e8b-55.html blog]
* [http://www.seraph.it/dep/det/HalTrumpetti.mp3 Hal Trumpetti] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/7dc6017950283556600a376bec4dd354-62.html blog entry])
* ''Micro Vocoder 1'' (2010) – [http://www.seraph.it/blog_files/b7fcede2a50aa768948bf462836670d6-56.html blog] | [https://www.youtube.com/watch?v=r3xMmAI_DgM&feature=player_embedded YouTube]
* [http://www.seraph.it/dep/det/TalkingGammaInYourSleep.mp3 Talking Gamma In Your Sleep] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/39c23a1e5e5bdeb4e0fd2c574a21ca58-63.html blog entry])
* ''Namul1'' (2010) – [http://www.seraph.it/dep/det/Namul1.mp3 play] | [http://www.seraph.it/blog_files/a71f095266803b874c26f7b13c3bd20b-58.html blog]
* [http://www.seraph.it/dep/det/GammaRaga.mp3 Gamma Raga] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/cc6f0d7f9c85257c843f6a5990a8beff-64.html blog entry])
* ''Namul2'' (2010) – [http://www.seraph.it/dep/det/Namul2.mp3 play] | [http://www.seraph.it/blog_files/21e1fd914125f5840789ab05eda26643-59.html blog]
* [http://www.seraph.it/dep/sol/SolsticeSongP5.mp3 The Solstice Song - Part 5] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/b7d1e65adf0e9d93eeed220bea2d4479-66.html blog entry])
* ''Hal Trumpetti'' (2010) – [http://www.seraph.it/dep/det/HalTrumpetti.mp3 play] | [http://www.seraph.it/blog_files/7dc6017950283556600a376bec4dd354-62.html blog]
* [http://www.seraph.it/dep/det/GammaBreezin.mp3 Gamma Breezin'] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/e4692c0e583f1f86d8efdc705e5d0b0c-67.html blog entry])
* ''Talking Gamma In Your Sleep'' (2010) – [http://www.seraph.it/dep/det/TalkingGammaInYourSleep.mp3 play] | [http://www.seraph.it/blog_files/39c23a1e5e5bdeb4e0fd2c574a21ca58-63.html blog]
* [http://www.seraph.it/dep/det/ConferenceOfFlutes.mp3 Conference of Flutes] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/e9b86c48d498ced631139e0af8f20a5a-69.html blog entry])
* ''Gamma Raga'' (2010) – [http://www.seraph.it/dep/det/GammaRaga.mp3 play] | [http://www.seraph.it/blog_files/cc6f0d7f9c85257c843f6a5990a8beff-64.html blog]
* [http://www.seraph.it/dep/det/BicyclesAndBowls.mp3 Bicycles and Bowls] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/931ae9c9f594da7bcead8d69300349f1-73.html blog entry])
* from [http://www.seraph.it/blog_files/b7d1e65adf0e9d93eeed220bea2d4479-66.html ''The Solstice Song''] (2010)
* [http://www.youtube.com/watch?v=uEQTzRVZWkE&feature=player_embedded Elba Gamma (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/ce09fb08fffa7470ebb4200702129edf-75.html blog entry])
** [http://www.seraph.it/dep/sol/SolsticeSongP1.mp3 "Part 1"]
* [http://www.youtube.com/watch?v=iI8qoM_7KNA Double Trouble 1 (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html blog entry])
** [http://www.seraph.it/dep/sol/SolsticeSongP1.mp3 "Part 3"] – 12et and Carlos gamma polysystemic
* [http://www.youtube.com/watch?v=dNNJ1hoQkhw&feature=related Double Trouble 2 (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html blog entry])
** [http://www.seraph.it/dep/sol/SolsticeSongP5.mp3 "Part 5"] – 12et and Carlos gamma polysystemic
* [http://www.seraph.it/dep/det/AutumnalModulations.mp3 Autumnal Modulations] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/15eb9cc6a8a58abab04319e332ac65d5-81.html blog entry])
* ''Conference of Flutes'' (2010) – [http://www.seraph.it/dep/det/ConferenceOfFlutes.mp3 play] | [http://www.seraph.it/blog_files/e9b86c48d498ced631139e0af8f20a5a-69.html blog]
* [http://www.youtube.com/watch?v=s7pcu8U7BAU Invocation (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/cba5fea101e97ae6e80d4fcafeff5564-83.html blog entry])
* ''Bicycles and Bowls'' (2010) – [http://www.seraph.it/dep/det/BicyclesAndBowls.mp3 play] | [http://www.seraph.it/blog_files/931ae9c9f594da7bcead8d69300349f1-73.html blog]
* [http://www.youtube.com/watch?v=cY6S-Gc7joM KYMI #1 (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/9487bd24fa4b8670cb306e57069cf328-84.html blog entry])
* ''Elba Gamma'' (2010) – [http://www.seraph.it/blog_files/ce09fb08fffa7470ebb4200702129edf-75.html blog] | [https://www.youtube.com/watch?v=uEQTzRVZWkE&feature=player_embedded YouTube]
* [http://www.youtube.com/watch?v=QHrESeeUEGk Jingle Gamma Bells (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/93d1553538122dc28f0bb1f5a46fedeb-86.html blog entry])
* ''Double Trouble 1'' (2010) – [http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html blog] | [https://www.youtube.com/watch?v=iI8qoM_7KNA YouTube]
* [http://split-notes.com/spnt006.php Gammatar (the album)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/9a58ec270939f33b70f9db0d76cabfae-90.html blog entry])
* ''Double Trouble 2'' (2010) – [http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html blog] | [https://www.youtube.com/watch?v=dNNJ1hoQkhw&feature=related YouTube]
* [http://electro-music.com/forum/phpbb-files/outofgammabodyexperience_149.mp3 Out of Gamma Body Experience] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/0ae0c7d29d4539d36e2ccc4a74f8207c-186.html blog entry])
* ''Invocation'' (2010) – [http://www.seraph.it/blog_files/cba5fea101e97ae6e80d4fcafeff5564-83.html blog] | [https://www.youtube.com/watch?v=s7pcu8U7BAU YouTube]
* [http://www.seraph.it/dep/det/GammaMeditation.mp3 Gamma Meditation] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/f4e2f44d30b32bb1b90f3c00d6c0c480-197.html blog entry])
* ''KYMI Exercise #1'' (2010) – [http://www.seraph.it/blog_files/9487bd24fa4b8670cb306e57069cf328-84.html blog] | [https://www.youtube.com/watch?v=cY6S-Gc7joM YouTube]
* [http://www.seraph.it/dep/det/SeaOfTranquility.mp3 Sea Of Tranquility] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/e3c9fec40b5356be42308033c2c2fb61-200.html blog entry])
* ''Gammatar'' (2011) [http://www.seraph.it/blog_files/9a58ec270939f33b70f9db0d76cabfae-90.html blog] | [http://split-notes.com/spnt006.php split-notes] – 9-piece album
* [http://www.seraph.it/dep/det/Organum1.mp3 Organum 1] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/dafd0e7332751c89286253d38df0da2a-201.html blog entry])
** "Gammatar" – [http://www.seraph.it/dep/gtr/01Gammatar.mp3 play] · ''Gamma Elegy'' (2009) – [http://www.seraph.it/dep/det/GammaElegy.mp3 play] | [http://www.seraph.it/blog_files/dada89373d85adfc7c01a844eb0d4693-46.html blog]
* [http://www.seraph.it/dep/det/Organum2.mp3 Organum 2] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/dafd0e7332751c89286253d38df0da2a-201.html blog entry])
** "Glorious 61" – [http://www.seraph.it/dep/gtr/02Glorious61.mp3 play] · ''Glorious 60'' (2009) – [http://www.seraph.it/dep/det/Glorious60.mp3 play] | [http://www.seraph.it/blog_files/e70b1f26417497ff77c1effb949bd604-50.html blog]
* [https://www.youtube.com/watch?v=8Brkwkf60qY Adagio Gamma X (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/e7cd6fb47169acbedac4aaf4d7d02086-226.html blog entry])
** "Glorious Guitars" – [http://www.seraph.it/dep/gtr/03GloriousGuitars.mp3 play] · ''Glorious Guitars'' (2009) – [http://www.seraph.it/dep/det/GloriousGuitars.mp3 play] | [http://www.seraph.it/blog_files/e8a36018d6b782c8ff7bc2416fa7ea5b-47.html blog]
* [https://youtu.be/xxpk5_X7elA Far Away From Home (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/25c9c788b3cd642d7c4954fdfe889310-243.html blog entry])
** "Jingle Gamma Bells" – [http://www.seraph.it/dep/gtr/04JingleGammaBells.mp3 play] · ''Jingle Gamma Bells'' (2010) – [http://www.seraph.it/blog_files/93d1553538122dc28f0bb1f5a46fedeb-86.html blog] | [https://www.youtube.com/watch?v=QHrESeeUEGk YouTube]
* [https://youtu.be/d-J9IQdwWuw Lament for Marco (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/ce7b875eb4f02eb597666fd61111226b-251.html blog entry])
** "Delta Gamma Blues" – [http://www.seraph.it/dep/gtr/05DeltaGammaBlues.mp3 play] · ''Delta Gamma Blues'' (2010) – [http://www.seraph.it/dep/det/DeltaGammaBlues.mp3 play] | [http://www.seraph.it/blog_files/90950fe2c088f39d304b8c4f2f1d0c3e-60.html blog]
* [http://www.seraph.it/dep/det/ForwardGammaMarch.mp3 Forward Gamma March] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/0f88fc9f63abb474c4905ab8b367dce1-252.html blog entry])
** "Chameleons In The Sun" – [http://www.seraph.it/dep/gtr/06ChameleonsInTheSun.mp3 play] · ''Chameleons In The Sun'' (2009) – [http://www.seraph.it/dep/det/ChameleonsInTheSun.mp3 play] | [http://www.seraph.it/blog_files/5b5e9af886df068be22fdfe37523eba3-48.html blog]
* [http://www.seraph.it/dep/det/J.F.Sebastian's%20Lullaby.mp3 J.F.Sebastian's Lullaby] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/aa384d59ce236c5213161037463fb51e-256.html blog entry])
** "Gamma Monk" – [http://www.seraph.it/dep/gtr/07GammaMonk.mp3 play] · ''Gamma Monk'' (2009) – [http://www.seraph.it/dep/det/GammaMonk.mp3 play] | [http://www.seraph.it/blog_files/c883c0c218b0e1a9767e1ae71d700e8f-49.html blog]
* [https://youtu.be/JVclaUbeKEs Gamma Quarantine (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/915d7be76fa98daf44f6e754adb9dbab-286.html blog entry])
** "Autumnal Modulations" – [http://www.seraph.it/dep/gtr/08AutumnalModulations.mp3 play] · ''Autumnal Modulations'' (2010) – [http://www.seraph.it/dep/det/AutumnalModulations.mp3 play] | [http://www.seraph.it/blog_files/15eb9cc6a8a58abab04319e332ac65d5-81.html blog]
* [http://www.seraph.it/dep/det/BabylonGamma.mp3 Babylon Gamma] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/d33f9a1bbeed04e78c0a5f835fed784c-306.html blog entry])
** "Gamma Breezin'" – [http://www.seraph.it/dep/gtr/09GammaBreezin.mp3 play] · ''Gamma Breezin''' (2010) – [http://www.seraph.it/dep/det/GammaBreezin.mp3 play] | [http://www.seraph.it/blog_files/e4692c0e583f1f86d8efdc705e5d0b0c-67.html blog]
* [http://www.seraph.it/dep/det/GammaConstantStructures.mp3 Gamma Constant Structures] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/3325f9fada5c4d5c3d4dd0c3ced8b2a8-308.html blog entry])
* ''Out of Gamma Body Experience'' (2014) – [http://electro-music.com/forum/phpbb-files/outofgammabodyexperience_149.mp3 play] | [http://www.seraph.it/blog_files/0ae0c7d29d4539d36e2ccc4a74f8207c-186.html blog]
* ''Gamma Meditation'' (2015) – [http://www.seraph.it/dep/det/GammaMeditation.mp3 play] | [http://www.seraph.it/blog_files/f4e2f44d30b32bb1b90f3c00d6c0c480-197.html blog]
* ''Sea Of Tranquility'' (2015) – [http://www.seraph.it/dep/det/SeaOfTranquility.mp3 play] | [http://www.seraph.it/blog_files/e3c9fec40b5356be42308033c2c2fb61-200.html blog]
* ''Organum 1'' (2015) – [http://www.seraph.it/dep/det/Organum1.mp3 play] | [http://www.seraph.it/blog_files/dafd0e7332751c89286253d38df0da2a-201.html blog]
* ''Organum 2'' (2015) – [http://www.seraph.it/dep/det/Organum2.mp3 play] | [http://www.seraph.it/blog_files/dafd0e7332751c89286253d38df0da2a-201.html blog]
* ''Adagio Gamma X'' (2016) – [http://www.seraph.it/blog_files/e7cd6fb47169acbedac4aaf4d7d02086-226.html blog] | [https://www.youtube.com/watch?v=8Brkwkf60qY YouTube]
* ''Far Away From Home'' (2017) – [http://www.seraph.it/blog_files/25c9c788b3cd642d7c4954fdfe889310-243.html blog] | [https://youtu.be/xxpk5_X7elA YouTube]
* ''Lament for Marco'' (2017) – [http://www.seraph.it/blog_files/ce7b875eb4f02eb597666fd61111226b-251.html blog] | [https://youtu.be/d-J9IQdwWuw YouTube]
* ''Forward Gamma March'' (2018) – [http://www.seraph.it/dep/det/ForwardGammaMarch.mp3 play] | [http://www.seraph.it/blog_files/0f88fc9f63abb474c4905ab8b367dce1-252.html blog]
* ''J.F.Sebastian's Lullaby'' (2018) – [http://www.seraph.it/blog_files/aa384d59ce236c5213161037463fb51e-256.html blog] | [http://www.seraph.it/dep/det/J.F.Sebastian's%20Lullaby.mp3 play]
* ''Gamma Quarantine'' (2020) – [http://www.seraph.it/blog_files/915d7be76fa98daf44f6e754adb9dbab-286.html blog] | [https://youtu.be/JVclaUbeKEs YouTube]
* ''Babylon Gamma'' (2021) – [http://www.seraph.it/dep/det/BabylonGamma.mp3 play] | [http://www.seraph.it/blog_files/d33f9a1bbeed04e78c0a5f835fed784c-306.html blog]
* ''Gamma Constant Structures'' (2021) – [http://www.seraph.it/dep/det/GammaConstantStructures.mp3 play] | [http://www.seraph.it/blog_files/3325f9fada5c4d5c3d4dd0c3ced8b2a8-308.html blog]
* ''Early Heaven'' (2023) – [http://www.seraph.it/dep/det/EarlyHeaven.mp3 play] | [http://www.seraph.it/blog_files/82c7c1e31eb84e1449658e657550c256-338.html blog]
 
; [[MagentaFlavouredMusic]]
* [https://youtu.be/1HkykxbKBHE ''Carlama'']
 
== See also ==
* Carlos' equal scales
** [[Carlos Alpha]]
** [[Carlos Beta]]
* [[Carlos harm|Carlos Harmonic]]
* [[Carlos super|Carlos Super Just]]


== Reference ==
== Reference ==
<references/>
<references/>


[[Category:Carlos]]
== External links ==
* [http://www.wendycarlos.com/resources/pitch.html Wendy Carlos Pitch article | ''Three Asymmetric Divisions of the Octave'']
 
[[Category:Wendy Carlos]]
[[Category:Nonoctave]]
[[Category:Nonoctave]]
[[Category:Equal-step tuning]]
[[Category:Equal-step tuning]]

Latest revision as of 09:25, 2 January 2026

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=220584"