Carlos Gamma: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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{{Wikipedia|Gamma scale}}
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
'''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]].
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">=Carlos Gamma (equal division of the [[perfect fifth]] into 20 equal parts)=
==Theory==
[[http://www.wendycarlos.com/resources/pitch.html|Article by Wendy Carlos]]


Closely related to Gamma is [[Gammic family|gammic temperament]].
== Theory ==
Lookalikes: [[34edo]]
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
==Compositions==  
 
[[http://www.seraph.it/dep/det/AdagioGamma.mp3|Adagio Gamma]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/140006ae42b0d87bb0903cdd857fa62c-24.html|blog entry]])
<math>\displaystyle
[[http://www.seraph.it/dep/det/Gammalan.mp3|Gammalan]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/ef1a7e2088ff6ad32fc50cbd4b2a601d-25.html|blog entry]])
\frac{20^2 + 11^2 + 9^2}{20\log_2(3/2) + 11\log_2(5/4) + 9\log_2(6/5)} ≃ 34.189454
[[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]])
</math>
[[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]])
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.
[[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]])
 
[[http://www.seraph.it/dep/det/GammaElegy.mp3|Gamma Elegy]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/dada89373d85adfc7c01a844eb0d4693-46.html|blog entry]])
Carlos Gamma is closely related to the [[gammic]] temperament.
[[http://www.seraph.it/dep/det/GloriousGuitars.mp3|Glorious Guitars]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/e8a36018d6b782c8ff7bc2416fa7ea5b-47.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]])
Lookalikes: [[34edo]], [[54edt]], [[96ed7]], [[171edo]]
[[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.youtube.com/watch?v=o8dIJmpt8IY|East Of The Moon (video)]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/5dfe4aeb16f360dd16dd93bada02c021-53.html|blog entry]])
== Intervals ==
[[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]])
The first steps up to two perfect fifths should give a feeling of the granularity of this system…
[[http://www.youtube.com/watch?v=r3xMmAI_DgM&amp;feature=player_embedded|Micro Vocoder 1 (video)]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/b7fcede2a50aa768948bf462836670d6-56.html|blog entry]])
{| class="wikitable"
[[http://www.seraph.it/dep/det/Namul1.mp3|Namul1]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/a71f095266803b874c26f7b13c3bd20b-58.html|blog entry]])
!Degrees
[[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/DeltaGammaBlues.mp3|Delta Gamma Blues]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/90950fe2c088f39d304b8c4f2f1d0c3e-60.html|blog entry]])
|-
[[http://www.seraph.it/dep/det/HalTrumpetti.mp3|Hal Trumpetti]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/7dc6017950283556600a376bec4dd354-62.html|blog entry]])
|1
[[http://www.youtube.com/watch?v=FyZUMqQzIZA&amp;feature=player_embedded|Talking Gamma In Your Sleep (video)]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/39c23a1e5e5bdeb4e0fd2c574a21ca58-63.html|blog entry]])
|35.098542
[[http://www.seraph.it/dep/det/GammaRaga.mp3|Gamma Raga]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/cc6f0d7f9c85257c843f6a5990a8beff-64.html|blog entry]])
|-
[[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]])
| |2
[[http://www.seraph.it/dep/det/GammaBreezin.mp3|Gamma Breezin']] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/e4692c0e583f1f86d8efdc705e5d0b0c-67.html|blog entry]])
| |70.197085
[[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]])
| |3
[[http://www.youtube.com/watch?v=uEQTzRVZWkE&amp;feature=player_embedded|Elba Gamma (video)]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/ce09fb08fffa7470ebb4200702129edf-75.html|blog entry]])
| | 105.295627
[[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.youtube.com/watch?v=dNNJ1hoQkhw&amp;feature=related|Double Trouble 2 (video)]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html|blog entry]])
| |4
[[http://www.seraph.it/dep/det/AutumnalModulations.mp3|Autumnal Modulations]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/15eb9cc6a8a58abab04319e332ac65d5-81.html|blog entry]])
| |140.394169
[[http://www.youtube.com/watch?v=s7pcu8U7BAU|Invocation (video)]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/cba5fea101e97ae6e80d4fcafeff5564-83.html|blog entry]])
|-
[[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]])
| |5
[[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]])
| |175.492711
[[http://split-notes.com/spnt006.php|Gammatar (the album)]] by [[Carlo Serafini]] ([[http://www.seraph.it/blog_files/9a58ec270939f33b70f9db0d76cabfae-90.html|blog entry]])</pre></div>
|-
<h4>Original HTML content:</h4>
| |6
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Carlos Gamma&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Carlos Gamma (equal division of the perfect fifth into 20 equal parts)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Carlos Gamma (equal division of the &lt;a class="wiki_link" href="/perfect%20fifth"&gt;perfect fifth&lt;/a&gt; into 20 equal parts)&lt;/h1&gt;
| |210.591254
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="Carlos Gamma (equal division of the perfect fifth into 20 equal parts)-Theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory&lt;/h2&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.wendycarlos.com/resources/pitch.html" rel="nofollow"&gt;Article by Wendy Carlos&lt;/a&gt;&lt;br /&gt;
| |7
&lt;br /&gt;
| |245.689796
Closely related to Gamma is &lt;a class="wiki_link" href="/Gammic%20family"&gt;gammic temperament&lt;/a&gt;.&lt;br /&gt;
|-
Lookalikes: &lt;a class="wiki_link" href="/34edo"&gt;34edo&lt;/a&gt;&lt;br /&gt;
| |8
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Carlos Gamma (equal division of the perfect fifth into 20 equal parts)-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Compositions&lt;/h2&gt;
| | 280.788338
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/AdagioGamma.mp3" rel="nofollow"&gt;Adagio Gamma&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/140006ae42b0d87bb0903cdd857fa62c-24.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Gammalan.mp3" rel="nofollow"&gt;Gammalan&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/ef1a7e2088ff6ad32fc50cbd4b2a601d-25.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |9
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/moonlightgammaserenade.mp3" rel="nofollow"&gt;Moonlight Gamma Serenade&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/91c9f8975a11199a130e18bbc1c436ae-31.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |315.886881
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/BixInTheSkyWithGamma.mp3" rel="nofollow"&gt;Bix In The Sky With Gamma&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/3be0c8f6ba38f8985d0d33aa529f51cd-40.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/AnIrishmanInGuangdong.mp3" rel="nofollow"&gt;An Irishman In Guangdong&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/eea975e524f69f869408c8fccc3ff274-41.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |10
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/ChameleonsInTheDark.mp3" rel="nofollow"&gt;Chameleons In The Dark&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/f743270786dc14253dae1d90fd827c5a-43.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |350.985423
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/GammaElegy.mp3" rel="nofollow"&gt;Gamma Elegy&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/dada89373d85adfc7c01a844eb0d4693-46.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/GloriousGuitars.mp3" rel="nofollow"&gt;Glorious Guitars&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/e8a36018d6b782c8ff7bc2416fa7ea5b-47.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |11
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/ChameleonsInTheSun.mp3" rel="nofollow"&gt;Chameleons In The Sun&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/5b5e9af886df068be22fdfe37523eba3-48.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |386.083965
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/GammaMonk.mp3" rel="nofollow"&gt;Gamma Monk&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/c883c0c218b0e1a9767e1ae71d700e8f-49.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=o8dIJmpt8IY" rel="nofollow"&gt;East Of The Moon (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/5dfe4aeb16f360dd16dd93bada02c021-53.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |12
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/TheSingingAlchemist.mp3" rel="nofollow"&gt;The Singing Alchemist&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/dc22d50ef807215177743a8c0adb6e8b-55.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |421.182507
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=r3xMmAI_DgM&amp;amp;feature=player_embedded" rel="nofollow"&gt;Micro Vocoder 1 (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/b7fcede2a50aa768948bf462836670d6-56.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Namul1.mp3" rel="nofollow"&gt;Namul1&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/a71f095266803b874c26f7b13c3bd20b-58.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |13
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/Namul2.mp3" rel="nofollow"&gt;Namul 2&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/21e1fd914125f5840789ab05eda26643-59.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |456.281050
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/DeltaGammaBlues.mp3" rel="nofollow"&gt;Delta Gamma Blues&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/90950fe2c088f39d304b8c4f2f1d0c3e-60.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/HalTrumpetti.mp3" rel="nofollow"&gt;Hal Trumpetti&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/7dc6017950283556600a376bec4dd354-62.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |14
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=FyZUMqQzIZA&amp;amp;feature=player_embedded" rel="nofollow"&gt;Talking Gamma In Your Sleep (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/39c23a1e5e5bdeb4e0fd2c574a21ca58-63.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |491.379592
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/GammaRaga.mp3" rel="nofollow"&gt;Gamma Raga&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/cc6f0d7f9c85257c843f6a5990a8beff-64.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/sol/SolsticeSongP5.mp3" rel="nofollow"&gt;The Solstice Song - Part 5&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/b7d1e65adf0e9d93eeed220bea2d4479-66.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |15
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/GammaBreezin.mp3" rel="nofollow"&gt;Gamma Breezin'&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/e4692c0e583f1f86d8efdc705e5d0b0c-67.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |526.478134
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/ConferenceOfFlutes.mp3" rel="nofollow"&gt;Conference of Flutes&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/e9b86c48d498ced631139e0af8f20a5a-69.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/BicyclesAndBowls.mp3" rel="nofollow"&gt;Bicycles and Bowls&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/931ae9c9f594da7bcead8d69300349f1-73.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |16
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=uEQTzRVZWkE&amp;amp;feature=player_embedded" rel="nofollow"&gt;Elba Gamma (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/ce09fb08fffa7470ebb4200702129edf-75.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |561.576676
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=iI8qoM_7KNA" rel="nofollow"&gt;Double Trouble 1 (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=dNNJ1hoQkhw&amp;amp;feature=related" rel="nofollow"&gt;Double Trouble 2 (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |17
&lt;a class="wiki_link_ext" href="http://www.seraph.it/dep/det/AutumnalModulations.mp3" rel="nofollow"&gt;Autumnal Modulations&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/15eb9cc6a8a58abab04319e332ac65d5-81.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |596.675219
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=s7pcu8U7BAU" rel="nofollow"&gt;Invocation (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/cba5fea101e97ae6e80d4fcafeff5564-83.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
|-
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=cY6S-Gc7joM" rel="nofollow"&gt;KYMI #1 (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/9487bd24fa4b8670cb306e57069cf328-84.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |18
&lt;a class="wiki_link_ext" href="http://www.youtube.com/watch?v=QHrESeeUEGk" rel="nofollow"&gt;Jingle Gamma Bells (video)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/93d1553538122dc28f0bb1f5a46fedeb-86.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;br /&gt;
| |631.773761
&lt;a class="wiki_link_ext" href="http://split-notes.com/spnt006.php" rel="nofollow"&gt;Gammatar (the album)&lt;/a&gt; by &lt;a class="wiki_link" href="/Carlo%20Serafini"&gt;Carlo Serafini&lt;/a&gt; (&lt;a class="wiki_link_ext" href="http://www.seraph.it/blog_files/9a58ec270939f33b70f9db0d76cabfae-90.html" rel="nofollow"&gt;blog entry&lt;/a&gt;)&lt;/body&gt;&lt;/html&gt;</pre></div>
|-
| |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]]
* [https://www.youtube.com/watch?v=MCNtpptAgLE ''180db_{{lbrack}}130{{rbrack}} - Aphex Twin''] (2022)
* [https://www.youtube.com/shorts/f-d_RMhgLOE ''Microtonal Improvisation in Carlos Gamma''] (2023)
 
; [[James Mulvale]]
* [https://youtu.be/2MseEBUhZBQ ''SpeedRun''] (2021) – 11ed5/4 tuning, microtonal chiptune
 
; [[Carlo Serafini]]
* ''Adagio Gamma'' (2009) – [http://www.seraph.it/dep/det/AdagioGamma.mp3 play] | [http://www.seraph.it/blog_files/140006ae42b0d87bb0903cdd857fa62c-24.html blog]
* ''Gammalan'' (2009) – [http://www.seraph.it/dep/det/Gammalan.mp3 play] | [http://www.seraph.it/blog_files/ef1a7e2088ff6ad32fc50cbd4b2a601d-25.html blog]
* ''Moonlight Gamma Serenade'' (2009) – [http://www.seraph.it/dep/det/moonlightgammaserenade.mp3 play] | [http://www.seraph.it/blog_files/91c9f8975a11199a130e18bbc1c436ae-31.html blog]
* ''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]
* ''An Irishman in Guangdong'' (2009) – [http://www.seraph.it/dep/det/AnIrishmanInGuangdong.mp3 play] | [http://www.seraph.it/blog_files/eea975e524f69f869408c8fccc3ff274-41.html blog]
* ''Chameleons in the Dark'' (2009) – [http://www.seraph.it/dep/det/ChameleonsInTheDark.mp3 play] | [http://www.seraph.it/blog_files/f743270786dc14253dae1d90fd827c5a-43.html blog]
* ''East Of The Moon'' (2010) – [http://www.seraph.it/blog_files/5dfe4aeb16f360dd16dd93bada02c021-53.html blog] | [https://www.youtube.com/watch?v=o8dIJmpt8IY YouTube]
* ''The Singing Alchemist'' (2010) – [http://www.seraph.it/dep/det/TheSingingAlchemist.mp3 play] | [http://www.seraph.it/blog_files/dc22d50ef807215177743a8c0adb6e8b-55.html blog]
* ''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]
* ''Namul1'' (2010) – [http://www.seraph.it/dep/det/Namul1.mp3 play] | [http://www.seraph.it/blog_files/a71f095266803b874c26f7b13c3bd20b-58.html blog]
* ''Namul2'' (2010) – [http://www.seraph.it/dep/det/Namul2.mp3 play] | [http://www.seraph.it/blog_files/21e1fd914125f5840789ab05eda26643-59.html blog]
* ''Hal Trumpetti'' (2010) – [http://www.seraph.it/dep/det/HalTrumpetti.mp3 play] | [http://www.seraph.it/blog_files/7dc6017950283556600a376bec4dd354-62.html blog]
* ''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]
* ''Gamma Raga'' (2010) – [http://www.seraph.it/dep/det/GammaRaga.mp3 play] | [http://www.seraph.it/blog_files/cc6f0d7f9c85257c843f6a5990a8beff-64.html blog]
* from [http://www.seraph.it/blog_files/b7d1e65adf0e9d93eeed220bea2d4479-66.html ''The Solstice Song''] (2010)
** [http://www.seraph.it/dep/sol/SolsticeSongP1.mp3 "Part 1"]
** [http://www.seraph.it/dep/sol/SolsticeSongP1.mp3 "Part 3"] – 12et and Carlos gamma polysystemic
** [http://www.seraph.it/dep/sol/SolsticeSongP5.mp3 "Part 5"] – 12et and Carlos gamma polysystemic
* ''Conference of Flutes'' (2010) – [http://www.seraph.it/dep/det/ConferenceOfFlutes.mp3 play] | [http://www.seraph.it/blog_files/e9b86c48d498ced631139e0af8f20a5a-69.html blog]
* ''Bicycles and Bowls'' (2010) – [http://www.seraph.it/dep/det/BicyclesAndBowls.mp3 play] | [http://www.seraph.it/blog_files/931ae9c9f594da7bcead8d69300349f1-73.html blog]
* ''Elba Gamma'' (2010) – [http://www.seraph.it/blog_files/ce09fb08fffa7470ebb4200702129edf-75.html blog] | [https://www.youtube.com/watch?v=uEQTzRVZWkE&feature=player_embedded YouTube]
* ''Double Trouble 1'' (2010) – [http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html blog] | [https://www.youtube.com/watch?v=iI8qoM_7KNA YouTube]
* ''Double Trouble 2'' (2010) – [http://www.seraph.it/blog_files/10c767fd3bd1cadf413da8be511c10fa-77.html blog] | [https://www.youtube.com/watch?v=dNNJ1hoQkhw&feature=related YouTube]
* ''Invocation'' (2010) – [http://www.seraph.it/blog_files/cba5fea101e97ae6e80d4fcafeff5564-83.html blog] | [https://www.youtube.com/watch?v=s7pcu8U7BAU YouTube]
* ''KYMI Exercise #1'' (2010) – [http://www.seraph.it/blog_files/9487bd24fa4b8670cb306e57069cf328-84.html blog] | [https://www.youtube.com/watch?v=cY6S-Gc7joM YouTube]
* ''Gammatar'' (2011) [http://www.seraph.it/blog_files/9a58ec270939f33b70f9db0d76cabfae-90.html blog] | [http://split-notes.com/spnt006.php split-notes] – 9-piece album
** "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]
** "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]
** "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]
** "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]
** "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]
** "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]
** "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]
** "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]
** "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]
* ''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 ==
<references/>
 
== 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:Equal-step tuning]]
[[Category:Listen]]
 
{{Todo| cleanup | expand }}

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"