Carlos Gamma: Difference between revisions
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* [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]) | * [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]) | ||
* [http://www.seraph.it/dep/det/GammaMonk.mp3 Gamma Monk] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/c883c0c218b0e1a9767e1ae71d700e8f-49.html blog entry]) | * [http://www.seraph.it/dep/det/GammaMonk.mp3 Gamma Monk] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/c883c0c218b0e1a9767e1ae71d700e8f-49.html blog entry]) | ||
* [ | * [https://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]) | ||
* [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]) | * [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]) | ||
* [ | * [https://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]) | ||
* [http://www.seraph.it/dep/det/Namul1.mp3 Namul1] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/a71f095266803b874c26f7b13c3bd20b-58.html blog entry]) | * [http://www.seraph.it/dep/det/Namul1.mp3 Namul1] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/a71f095266803b874c26f7b13c3bd20b-58.html blog entry]) | ||
* [http://www.seraph.it/dep/det/Namul2.mp3 Namul 2] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/21e1fd914125f5840789ab05eda26643-59.html blog entry]) | * [http://www.seraph.it/dep/det/Namul2.mp3 Namul 2] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/21e1fd914125f5840789ab05eda26643-59.html blog entry]) | ||
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* [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]) | * [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]) | ||
* [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]) | * [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]) | ||
* [ | * [https://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]) | ||
* [ | * [https://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]) | ||
* [ | * [https://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/det/AutumnalModulations.mp3 Autumnal Modulations] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/15eb9cc6a8a58abab04319e332ac65d5-81.html blog entry]) | * [http://www.seraph.it/dep/det/AutumnalModulations.mp3 Autumnal Modulations] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/15eb9cc6a8a58abab04319e332ac65d5-81.html blog entry]) | ||
* [ | * [https://www.youtube.com/watch?v=s7pcu8U7BAU Invocation (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/cba5fea101e97ae6e80d4fcafeff5564-83.html blog entry]) | ||
* [ | * [https://www.youtube.com/watch?v=cY6S-Gc7joM KYMI #1 (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/9487bd24fa4b8670cb306e57069cf328-84.html blog entry]) | ||
* [ | * [https://www.youtube.com/watch?v=QHrESeeUEGk Jingle Gamma Bells (video)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/93d1553538122dc28f0bb1f5a46fedeb-86.html blog entry]) | ||
* [http://split-notes.com/spnt006.php Gammatar (the album)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/9a58ec270939f33b70f9db0d76cabfae-90.html blog entry]) | * [http://split-notes.com/spnt006.php Gammatar (the album)] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/9a58ec270939f33b70f9db0d76cabfae-90.html blog entry]) | ||
* [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]) | * [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]) | ||
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* [http://www.seraph.it/dep/det/BabylonGamma.mp3 Babylon Gamma] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/d33f9a1bbeed04e78c0a5f835fed784c-306.html blog entry]) | * [http://www.seraph.it/dep/det/BabylonGamma.mp3 Babylon Gamma] by [[Carlo Serafini]] ([http://www.seraph.it/blog_files/d33f9a1bbeed04e78c0a5f835fed784c-306.html blog entry]) | ||
* [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]) | * [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]) | ||
* [https://youtu.be/2MseEBUhZBQ <nowiki>FASTFAST SpeedRun [Microtonal Chiptune] - Carlos Gamma</nowiki>] | |||
== See also == | == See also == | ||
Revision as of 16:33, 5 December 2022
Carlos Gamma is a non-octave equal temperament whose step size is 35.0985422804 cents[1]. It was invented by Wendy Carlos.
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 optimized the tuning on 3/2, 5/4, and 6/5, such that the tuning divides the octave in [math]\displaystyle{ \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 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.
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 | ed233\420-5¢ | ed31\54 | ed121/81 (~ed11\19) | ed696¢ (~69ed4!) | ed32\55 | ed700¢=r¢ | ed3/2 | Pyrite | ed708¢ | ed122/81 (~ed13\22) | ed34\57 | ed37\60+5¢ | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|---|
| (~ed17\29) | (~ed10\17) | ||||||||||||
| 1 | 33.04-33.29 | 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 | 66.07-66.57 | 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 | 99.11-99.86 | 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 | 132.14-133.14 | 137.78 | 138.96 | 139.2 | 139.64 | 140 | 140.39 | 140.72 | 141.17 | 141.6 | 141.81 | 143.16 | 148-149 |
| 5 | 165.18-166.43 | 172.22 | 173.7 | 174 | 174.545 | 175 | 175.49 | 175.91 | 176.46 | 177 | 177.27 | 178.95 | 185-186.25 |
| 6 | 198.21-199.71 | 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 | 231.25-233 | 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 | 264.29-266.29 | 275.56 | 277.93 | 278.4 | 279.27 | 280 | 280.78 | 281.45 | 282.34 | 283.2 | 283.63 | 286.32 | 296-298 |
| 9 | 297.32-299.57 | 310 | 312.67 | 313.2 | 314.18 | 315 | 315.88 | 316.64 | 317.635 | 318.6 | 319.08 | 322.105 | 333-335.25 |
| 10 | 330.35-332.86 | 344.44 | 347.41 | 348 | 349.09 | 350 | 350.98 | 351.82 | 352.93 | 354 | 354.53 | 357.895 | 370-372.5 |
| 11 | 363.39-366.14 | 378.89 | 382.15 | 382.8 | 384 | 385 | 386.075 | 387 | 388.22 | 389.4 | 389.99 | 393.68 | 407-409.75 |
| 12 | 396.43-399.43 | 413.33 | 416.89 | 417.6 | 418.91 | 420 | 421.17 | 422.18 | 423.51 | 424.8 | 425.44 | 429.47 | 444-447 |
| 13 | 429.46-432.71 | 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 | 462.5-466 | 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 | 495.54-499.29 | 516.67 | 521.11 | 522 | 523.64 | 525 | 526.47 | 527.73 | 529.39 | 531 | 531.8 | 536.84 | 555-558.75 |
| 16 | 528.57-532.57 | 551.11 | 555.85 | 556.8 | 558.545 | 560 | 561.56 | 562.91 | 564.68 | 566.4 | 567.25 | 572.63 | 592-596 |
| 17 | 561.61-565.86 | 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 | 594.64-599.14 | 620 | 625.33 | 626.4 | 628.36 | 630 | 631.76 | 633.27 | 635.27 | 637.2 | 638.16 | 644.21 | 666-670.5 |
| 19 | 627.68-632.43 | 654.44 | 660.075 | 661.2 | 663.27 | 665 | 666.86 | 668.45 | 670.56 | 672.6 | 673.61 | 680 | 703-707.75 |
| 20 | 660.71-665.71 | 688.89 | 694.82 | 696 | 698.18 | 700 | 701.955 | 703.64 | 705.86 | 708 | 709.065 | 715.79 | 740-745 |
| 21 | 693.75-699 | 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 | 726.79-732.29 | 757.78 | 764.3 | 765.6 | 768 | 770 | 772.15 | 774 | 776.44 | 778.8 | 779.97 | 787.37 | 814-819.5 |
| 23 | 759.82-765.57 | 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 | 792.86-798.86 | 826.67 | 833.78 | 835.2 | 837.82 | 840 | 842.35 | 844.36 | 847.03 | 848.6 | 850.88 | 858.95 | 888-894 |
| 25 | 825.89-832.14 | 861.11 | 868.52 | 870 | 872.73 | 875 | 877.44 | 879.545 | 882.32 | 885 | 886.33 | 894.74 | 925-931.25 |
| 26 | 858.93-865.43 | 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 | 891.96-898.71 | 930 | 938 | 939.6 | 942.545 | 945 | 947.64 | 949.91 | 952.905 | 955.8 | 957.24 | 966.32 | 999-1005.75 |
| 28 | 925-932 | 964.4 | 972.74 | 974.4 | 977.455 | 980 | 982.74 | 985.09 | 988.2 | 991.2 | 992.69 | 1002.105 | 1036-1043 |
| 29 | 958.04-965.29 | 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 | 991.07-998.57 | 1033.33 | 1042.22 | 1044 | 1047.27 | 1050 | 1052.93 | 1055.45 | 1058.78 | 1062 | 1063.6 | 1073.68 | 1110-1117.5 |
| 31 | 1024.11-1031.86 | 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 | 1057.14-1065.14 | 1102.22 | 1111.705 | 1113.6 | 1117.09 | 1120 | 1123.13 | 1125.82 | 1129.37 | 1132.8 | 1134.5 | 1145.26 | 1184-1192 |
| 33 | 1090.18-1098.43 | 1136.67 | 1146.45 | 1148.4 | 1152 | 1155 | 1158.23 | 1161 | 1164.66 | 1168.2 | 1169.96 | 1181.05 | 1221-1229.25 |
| 34 | 1123.21-1131.71 | 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 | 1156.25-1165 | 1205.56 | 1215.93 | 1218 | 1221.82 | 1225 | 1228.42 | 1231.36 | 1235.25 | 1239 | 1240.86 | 1252.63 | 1295-1303.75 |
| 36 | 1189.29-1198.29 | 1240 | 1250.67 | 1252.8 | 1256.73 | 1260 | 1263.52 | 1266.545 | 1270.54 | 1274.4 | 1276.32 | 1288.42 | 1332-1341 |
| 37 | 1222.32-1231.57 | 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 | 1255.36-1263.86 | 1308.89 | 1320.15 | 1322.4 | 1326.545 | 1330 | 1333.715 | 1336.91 | 1341.125 | 1345.2 | 1347.22 | 1360 | 1406-1415.5 |
| 39 | 1288.39-1298.14 | 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 | 1321.43-1331.43 | 1377.78 | 1389.6 | 1392 | 1396.36 | 1400 | 1403.91 | 1407.27 | 1411.71 | 1416 | 1418.13 | 1431.6 | 1480-1490 |
Compositions
- Adagio Gamma by Carlo Serafini (blog entry)
- Gammalan by Carlo Serafini (blog entry)
- Moonlight Gamma Serenade by Carlo Serafini (blog entry)
- Bix In The Sky With Gamma by Carlo Serafini (blog entry)
- An Irishman In Guangdong by Carlo Serafini (blog entry)
- Chameleons In The Dark by Carlo Serafini (blog entry)
- Gamma Elegy by Carlo Serafini (blog entry)
- Glorious Guitars by Carlo Serafini (blog entry)
- Chameleons In The Sun by Carlo Serafini (blog entry)
- Gamma Monk by Carlo Serafini (blog entry)
- East Of The Moon (video) by Carlo Serafini (blog entry)
- The Singing Alchemist by Carlo Serafini (blog entry)
- Micro Vocoder 1 (video) by Carlo Serafini (blog entry)
- Namul1 by Carlo Serafini (blog entry)
- Namul 2 by Carlo Serafini (blog entry)
- Delta Gamma Blues by Carlo Serafini (blog entry)
- Hal Trumpetti by Carlo Serafini (blog entry)
- Talking Gamma In Your Sleep by Carlo Serafini (blog entry)
- Gamma Raga by Carlo Serafini (blog entry)
- The Solstice Song - Part 5 by Carlo Serafini (blog entry)
- Gamma Breezin' by Carlo Serafini (blog entry)
- Conference of Flutes by Carlo Serafini (blog entry)
- Bicycles and Bowls by Carlo Serafini (blog entry)
- Elba Gamma (video) by Carlo Serafini (blog entry)
- Double Trouble 1 (video) by Carlo Serafini (blog entry)
- Double Trouble 2 (video) by Carlo Serafini (blog entry)
- Autumnal Modulations by Carlo Serafini (blog entry)
- Invocation (video) by Carlo Serafini (blog entry)
- KYMI #1 (video) by Carlo Serafini (blog entry)
- Jingle Gamma Bells (video) by Carlo Serafini (blog entry)
- Gammatar (the album) by Carlo Serafini (blog entry)
- Out of Gamma Body Experience by Carlo Serafini (blog entry)
- Gamma Meditation by Carlo Serafini (blog entry)
- Sea Of Tranquility by Carlo Serafini (blog entry)
- Organum 1 by Carlo Serafini (blog entry)
- Organum 2 by Carlo Serafini (blog entry)
- Adagio Gamma X (video) by Carlo Serafini (blog entry)
- Far Away From Home (video) by Carlo Serafini (blog entry)
- Lament for Marco (video) by Carlo Serafini (blog entry)
- Forward Gamma March by Carlo Serafini (blog entry)
- J.F.Sebastian's Lullaby by Carlo Serafini (blog entry)
- Gamma Quarantine (video) by Carlo Serafini (blog entry)
- Babylon Gamma by Carlo Serafini (blog entry)
- Gamma Constant Structures by Carlo Serafini (blog entry)
- FASTFAST SpeedRun [Microtonal Chiptune] - Carlos Gamma
See also
Reference
- ↑ Wendy Carlos, "Tuning: At the Crossroads", Computer Music Journal vol. 11 no. 1, 1987, pp. 29-43