Mavila temperament modal harmony: Difference between revisions
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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 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #0000ff;">11/6</span> || | ||= 2|2 ||= sLsLs ||= dong ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #0000ff;">11/6</span> || | ||
||= 1|3 ||= sLssL ||= dung ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #ff0000;">8/5</span> || | ||= 1|3 ||= sLssL ||= dung ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #ff0000;">8/5</span> || | ||
||= 0| | ||= 0|4 ||= ssLsL ||= ding ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #ff0000;">6/5</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #ff0000;">8/5</span> || | ||
==="Diatonic" Names=== | ==="Diatonic" Names=== | ||
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||= 2|2 ||= sLsLs ||= dong ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #0000ff;">N7</span> || | ||= 2|2 ||= sLsLs ||= dong ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #0000ff;">N7</span> || | ||
||= 1|3 ||= sLssL ||= dung ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #ff0000;">m6</span> || | ||= 1|3 ||= sLssL ||= dung ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #ff0000;">m6</span> || | ||
||= 0| | ||= 0|4 ||= ssLsL ||= ding ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #ff0000;">m3</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #ff0000;">m6</span> || | ||
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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"><html><head><title>Mavila Temperament Modal Harmony</title></head><body><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:2 -->Introduction</h1> | <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"><html><head><title>Mavila Temperament Modal Harmony</title></head><body><!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:2 -->Introduction</h1> | ||
<br /> | <br /> | ||
Mavila is the regular temperament eliminating <a class="wiki_link" href="/135_128">135/128</a>. 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 &quot;antidiatonic&quot; 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see <a class="wiki_link" href="/2L%205s">2L 5s</a>) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note &quot;superdiatonic&quot; MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see<a class="wiki_link" href="/7L%202s"> 7L 2s</a>) 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].<br /> | Mavila is the regular temperament eliminating <a class="wiki_link" href="/135_128" target="_blank">135/128</a>. 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 &quot;antidiatonic&quot; 7-note MOS, such that the LLsLLLs melodic pattern becomes inverted into the ssLsssL pattern. (see <a class="wiki_link" href="/2L%205s" target="_blank">2L 5s</a>) Additionally, while mavila supports 5-note and 7-note MOS's like meantone, it has an additional 9-note &quot;superdiatonic&quot; MOS scale as well, in which the LLsLLLs melodic pattern becomes extended into the LLLsLLLLs pattern. (see<a class="wiki_link" href="/7L%202s" target="_blank"> 7L 2s</a>) 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].<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc1"><a name="Introduction--How to read these charts"></a><!-- ws:end:WikiTextHeadingRule:4 -->How to read these charts</h3> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h3&gt; --><h3 id="toc1"><a name="Introduction--How to read these charts"></a><!-- ws:end:WikiTextHeadingRule:4 -->How to read these charts</h3> | ||
<ul><li>The 6|0, 5|1, 4|2 markings are an instance of <a class="wiki_link" href="/Modal%20UDP%20Notation">Modal UDP Notation</a>.</li><li>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.</li><li>Additionally, &quot;diatonic&quot; names make use of the following abbreviations:<ul><li>SM - Supermajor</li><li>M - Major</li><li>N - Neutral</li><li>m - Minor</li><li>sm - Subminor</li></ul></li></ul><br /> | <ul><li>The 6|0, 5|1, 4|2 markings are an instance of <a class="wiki_link" href="/Modal%20UDP%20Notation" target="_blank">Modal UDP Notation</a>.</li><li>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.</li><li>Additionally, &quot;diatonic&quot; names make use of the following abbreviations:<ul><li>SM - Supermajor</li><li>M - Major</li><li>N - Neutral</li><li>m - Minor</li><li>sm - Subminor</li></ul></li></ul><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="x2L3s Pentatonic MOS: Pelogic"></a><!-- ws:end:WikiTextHeadingRule:6 -->2L3s Pentatonic MOS: Pelogic</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc2"><a name="x2L3s Pentatonic MOS: Pelogic"></a><!-- ws:end:WikiTextHeadingRule:6 -->2L3s Pentatonic MOS: Pelogic</h1> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">0| | <td style="text-align: center;">0|4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">ssLsL<br /> | <td style="text-align: center;">ssLsL<br /> | ||
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</tr> | </tr> | ||
<tr> | <tr> | ||
<td style="text-align: center;">0| | <td style="text-align: center;">0|4<br /> | ||
</td> | </td> | ||
<td style="text-align: center;">ssLsL<br /> | <td style="text-align: center;">ssLsL<br /> | ||
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<td>0|8 - sLLLsLLLL - (Super)Locrian<br /> | <td>0|8 - sLLLsLLLL - (Super)Locrian<br /> | ||
</td> | </td> | ||
<td><!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/MavilaSuperdiatonic16edo.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;MavilaSuperdiatonic16edo.mp3&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><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&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:1 --><br /> | <td><!-- ws:start:WikiTextMediaRule:1:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file-audio/MavilaSuperdiatonic16edo.mp3?h=20&amp;w=240&quot; class=&quot;WikiMedia WikiMediaFile&quot; id=&quot;wikitext@@media@@type=&amp;quot;file&amp;quot; key=&amp;quot;MavilaSuperdiatonic16edo.mp3&amp;quot; width=&amp;quot;240&amp;quot; height=&amp;quot;20&amp;quot;&quot; title=&quot;Local Media File&quot;height=&quot;20&quot; width=&quot;240&quot;/&gt; --><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&autostart=false&repeat=false&showdigits=true&showfsbutton=false&width=240&height=20"></embed><!-- ws:end:WikiTextMediaRule:1 --><br /> | ||
</td> | </td> | ||
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