Mavila temperament modal harmony: Difference between revisions

Wikispaces>hstraub
**Imported revision 445260816 - Original comment: **
Wikispaces>JosephRuhf
**Imported revision 509642410 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2013-08-17 16:29:06 UTC</tt>.<br>
: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2014-05-18 12:11:13 UTC</tt>.<br>
: The original revision id was <tt>445260816</tt>.<br>
: The original revision id was <tt>509642410</tt>.<br>
: The revision comment was: <tt></tt><br>
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<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">=Introduction=  
<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">=Introduction=  


Mavila is the regular temperament eliminating [[135_128|135/128]]. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an "antidiatonic" 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see [[2L 5s]]) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note "superdiatonic" MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see[[7L 2s| 7L 2s]]) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].
Mavila is the regular temperament eliminating [[@135_128|135/128]]. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an "antidiatonic" 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see [[@2L 5s]]) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note "superdiatonic" MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see[[@7L 2s| 7L 2s]]) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].


===How to read these charts===  
===How to read these charts===  
* The 6|0, 5|1, 4|2 markings are an instance of [[Modal UDP Notation]].
* The 6|0, 5|1, 4|2 markings are an instance of [[@Modal UDP Notation]].
* Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.
* Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.
* Additionally, "diatonic" names make use of the following abbreviations:
* Additionally, "diatonic" names make use of the following abbreviations:
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||= 2|2 ||= sLsLs ||= dong ||= 1/1 ||= &lt;span style="color: #ff0000;"&gt;12/11&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;4/3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;3/2&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;11/6&lt;/span&gt; ||
||= 2|2 ||= sLsLs ||= dong ||= 1/1 ||= &lt;span style="color: #ff0000;"&gt;12/11&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;4/3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;3/2&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;11/6&lt;/span&gt; ||
||= 1|3 ||= sLssL ||= dung ||= 1/1 ||= &lt;span style="color: #ff0000;"&gt;12/11&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;4/3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;3/2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;8/5&lt;/span&gt; ||
||= 1|3 ||= sLssL ||= dung ||= 1/1 ||= &lt;span style="color: #ff0000;"&gt;12/11&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;4/3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;3/2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;8/5&lt;/span&gt; ||
||= 0|0 ||= ssLsL ||= ding ||= 1/1 ||= &lt;span style="color: #ff0000;"&gt;12/11&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;6/5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;3/2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;8/5&lt;/span&gt; ||
||= 0|4 ||= ssLsL ||= ding ||= 1/1 ||= &lt;span style="color: #ff0000;"&gt;12/11&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;6/5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;3/2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;8/5&lt;/span&gt; ||


==="Diatonic" Names===  
==="Diatonic" Names===  
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||= 2|2 ||= sLsLs ||= dong ||= P1 ||= &lt;span style="color: #ff0000;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;N7&lt;/span&gt; ||
||= 2|2 ||= sLsLs ||= dong ||= P1 ||= &lt;span style="color: #ff0000;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;N7&lt;/span&gt; ||
||= 1|3 ||= sLssL ||= dung ||= P1 ||= &lt;span style="color: #ff0000;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m6&lt;/span&gt; ||
||= 1|3 ||= sLssL ||= dung ||= P1 ||= &lt;span style="color: #ff0000;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m6&lt;/span&gt; ||
||= 0|0 ||= ssLsL ||= ding ||= P1 ||= &lt;span style="color: #ff0000;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m6&lt;/span&gt; ||
||= 0|4 ||= ssLsL ||= ding ||= P1 ||= &lt;span style="color: #ff0000;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m6&lt;/span&gt; ||




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|| 2|6 - LsLLLsLLL - (Super)Aeolian ||  ||
|| 2|6 - LsLLLsLLL - (Super)Aeolian ||  ||
|| 1|7 - sLLLLsLLL - (Super)Phrygian ||  ||
|| 1|7 - sLLLLsLLL - (Super)Phrygian ||  ||
|| 0|8 - sLLLsLLLL - (Super)Locrian || [[media type="file" key="MavilaSuperdiatonic16edo.mp3"]] ||
|| 0|8 - sLLLsLLLL - (Super)Locrian || [[media type="file" key="MavilaSuperdiatonic16edo.mp3" width="240" height="20"]] ||


In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian
In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian
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<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;Mavila Temperament Modal Harmony&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Introduction&lt;/h1&gt;
<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;Mavila Temperament Modal Harmony&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Introduction&lt;/h1&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Mavila is the regular temperament eliminating &lt;a class="wiki_link" href="/135_128"&gt;135/128&lt;/a&gt;. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an &amp;quot;antidiatonic&amp;quot; 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see &lt;a class="wiki_link" href="/2L%205s"&gt;2L 5s&lt;/a&gt;) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note &amp;quot;superdiatonic&amp;quot; MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see&lt;a class="wiki_link" href="/7L%202s"&gt; 7L 2s&lt;/a&gt;) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].&lt;br /&gt;
Mavila is the regular temperament eliminating &lt;a class="wiki_link" href="/135_128" target="_blank"&gt;135/128&lt;/a&gt;. As a consequence, this means that it will have a generator significantly flat of 3/2 so that 4 of them add up to a minor third. For any decent tuning of mavila, another consequence of this tempering is that we end up with an &amp;quot;antidiatonic&amp;quot; 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see &lt;a class="wiki_link" href="/2L%205s" target="_blank"&gt;2L 5s&lt;/a&gt;) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note &amp;quot;superdiatonic&amp;quot; MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see&lt;a class="wiki_link" href="/7L%202s" target="_blank"&gt; 7L 2s&lt;/a&gt;) These correspondences can be harnessed to create an intuitive naming system for the modes of mavila[7] and mavila[9] which reference the names of the existing familiar modes of meantone[7].&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="Introduction--How to read these charts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;How to read these charts&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc1"&gt;&lt;a name="Introduction--How to read these charts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;How to read these charts&lt;/h3&gt;
  &lt;ul&gt;&lt;li&gt;The 6|0, 5|1, 4|2 markings are an instance of &lt;a class="wiki_link" href="/Modal%20UDP%20Notation"&gt;Modal UDP Notation&lt;/a&gt;.&lt;/li&gt;&lt;li&gt;Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.&lt;/li&gt;&lt;li&gt;Additionally, &amp;quot;diatonic&amp;quot; names make use of the following abbreviations:&lt;ul&gt;&lt;li&gt;SM - Supermajor&lt;/li&gt;&lt;li&gt;M - Major&lt;/li&gt;&lt;li&gt;N - Neutral&lt;/li&gt;&lt;li&gt;m - Minor&lt;/li&gt;&lt;li&gt;sm - Subminor&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;The 6|0, 5|1, 4|2 markings are an instance of &lt;a class="wiki_link" href="/Modal%20UDP%20Notation" target="_blank"&gt;Modal UDP Notation&lt;/a&gt;.&lt;/li&gt;&lt;li&gt;Unless otherwise specified, all transversals occur in the 2.3.5.7.11 extension of Mavila which tempers out 135/128, 36/35, 45/44, 33/32, called 11-limit Armodue temperament.&lt;/li&gt;&lt;li&gt;Additionally, &amp;quot;diatonic&amp;quot; names make use of the following abbreviations:&lt;ul&gt;&lt;li&gt;SM - Supermajor&lt;/li&gt;&lt;li&gt;M - Major&lt;/li&gt;&lt;li&gt;N - Neutral&lt;/li&gt;&lt;li&gt;m - Minor&lt;/li&gt;&lt;li&gt;sm - Subminor&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x2L3s Pentatonic MOS: Pelogic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;2L3s Pentatonic MOS: Pelogic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="x2L3s Pentatonic MOS: Pelogic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;2L3s Pentatonic MOS: Pelogic&lt;/h1&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;0|0&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;0|4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;ssLsL&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;ssLsL&lt;br /&gt;
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     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td style="text-align: center;"&gt;0|0&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;0|4&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td style="text-align: center;"&gt;ssLsL&lt;br /&gt;
         &lt;td style="text-align: center;"&gt;ssLsL&lt;br /&gt;
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         &lt;td&gt;0|8 - sLLLsLLLL - (Super)Locrian&lt;br /&gt;
         &lt;td&gt;0|8 - sLLLsLLLL - (Super)Locrian&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/MavilaSuperdiatonic16edo.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;MavilaSuperdiatonic16edo.mp3&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FMavilaSuperdiatonic16edo.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;&lt;br /&gt;
         &lt;td&gt;&lt;!-- ws:start:WikiTextMediaRule:1:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/MavilaSuperdiatonic16edo.mp3?h=20&amp;amp;w=240&amp;quot; class=&amp;quot;WikiMedia WikiMediaFile&amp;quot; id=&amp;quot;wikitext@@media@@type=&amp;amp;quot;file&amp;amp;quot; key=&amp;amp;quot;MavilaSuperdiatonic16edo.mp3&amp;amp;quot; width=&amp;amp;quot;240&amp;amp;quot; height=&amp;amp;quot;20&amp;amp;quot;&amp;quot; title=&amp;quot;Local Media File&amp;quot;height=&amp;quot;20&amp;quot; width=&amp;quot;240&amp;quot;/&amp;gt; --&gt;&lt;embed src="/s/mediaplayer.swf" pluginspage="http://www.macromedia.com/go/getflashplayer" type="application/x-shockwave-flash" quality="high" width="240" height="20" wmode="transparent" flashvars="file=http%253A%252F%252Fxenharmonic.wikispaces.com%252Ffile%252Fview%252FMavilaSuperdiatonic16edo.mp3?file_extension=mp3&amp;autostart=false&amp;repeat=false&amp;showdigits=true&amp;showfsbutton=false&amp;width=240&amp;height=20"&gt;&lt;/embed&gt;&lt;!-- ws:end:WikiTextMediaRule:1 --&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;