Mavila temperament modal harmony: Difference between revisions

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**Imported revision 284062080 - Original comment: **
Wikispaces>mbattaglia1
**Imported revision 284063100 - 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:mbattaglia1|mbattaglia1]] and made on <tt>2011-12-09 02:34:45 UTC</tt>.<br>
: This revision was by author [[User:mbattaglia1|mbattaglia1]] and made on <tt>2011-12-09 02:43:09 UTC</tt>.<br>
: The original revision id was <tt>284062080</tt>.<br>
: The original revision id was <tt>284063100</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<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">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].
<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=


The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
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].
 
Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLLsLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.
 
Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.
 
As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&gt; Corinthian -&gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.


===How to read these charts===  
===How to read these charts===  
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** m - Minor
** m - Minor
** sm - Subminor
** sm - Subminor


=2L3s Pentatonic MOS: Pelogic=  
=2L3s Pentatonic MOS: Pelogic=  
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||= 1|5 ||= ssLsssL ||= Ionian ||= 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: #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; ||= &lt;span style="color: #ff0000;"&gt;sm7&lt;/span&gt; ||
||= 1|5 ||= ssLsssL ||= Ionian ||= 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: #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; ||= &lt;span style="color: #ff0000;"&gt;sm7&lt;/span&gt; ||
||= 0|6 ||= sssLssL ||= Lydian ||= 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;SM3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm7&lt;/span&gt; ||
||= 0|6 ||= sssLssL ||= Lydian ||= 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;SM3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;m6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm7&lt;/span&gt; ||


=7L2s Nonatonic MOS: Superdiatonic=  
=7L2s Nonatonic MOS: Superdiatonic=  
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||= 2|6 ||= LsLLLsLLL ||= Aeolian ||= P1 ||= &lt;span style="color: #0000ff;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;SM2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;N7&lt;/span&gt; ||
||= 2|6 ||= LsLLLsLLL ||= Aeolian ||= P1 ||= &lt;span style="color: #0000ff;"&gt;N2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;SM2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;N7&lt;/span&gt; ||
||= 1|7 ||= sLLLLsLLL ||= Phrygian ||= P1 ||= &lt;span style="color: #ff0000;"&gt;sm2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;SM2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;N7&lt;/span&gt; ||
||= 1|7 ||= sLLLLsLLL ||= Phrygian ||= P1 ||= &lt;span style="color: #ff0000;"&gt;sm2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;SM2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #0000ff;"&gt;P5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;N7&lt;/span&gt; ||
||= 0|8 ||= sLLLsLLLL ||= Locrian ||= P1 ||= &lt;span style="color: #ff0000;"&gt;sm2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;SM2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;d5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;N7&lt;/span&gt; ||</pre></div>
||= 0|8 ||= sLLLsLLLL ||= Locrian ||= P1 ||= &lt;span style="color: #ff0000;"&gt;sm2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;SM2&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M3&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;P4&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;d5&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;sm6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;M6&lt;/span&gt; ||= &lt;span style="color: #ff0000;"&gt;N7&lt;/span&gt; ||
 
=Notes on Naming=
 
The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.
 
Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLLsLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.
 
Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.
 
As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&gt; Corinthian -&gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML 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;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;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;
<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:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Introduction"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Introduction&lt;/h1&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;
&lt;br /&gt;
&lt;br /&gt;
The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the &amp;quot;Anti-&amp;quot; prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the &amp;quot;Super&amp;quot; prefix (e.g. Superionian, Superaeolian, etc.). The &amp;quot;anti&amp;quot; and &amp;quot;super&amp;quot; prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&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:2 --&gt;How to read these charts&lt;/h3&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"&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;
Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the &amp;quot;shape&amp;quot; of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLLsLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.&lt;br /&gt;
&lt;br /&gt;
Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as &amp;quot;mixed&amp;quot; modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.&lt;br /&gt;
&lt;br /&gt;
As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&amp;gt; Corinthian -&amp;gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc0"&gt;&lt;a name="x--How to read these charts"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;How to read these charts&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&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:4 --&gt;2L3s Pentatonic MOS: Pelogic&lt;/h1&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;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="x2L3s Pentatonic MOS: Pelogic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;2L3s Pentatonic MOS: Pelogic&lt;/h1&gt;
  4|0 - LsLss - Patet deng&lt;br /&gt;
  4|0 - LsLss - Patet deng&lt;br /&gt;
3|1 - LssLs - Patet dang&lt;br /&gt;
3|1 - LssLs - Patet dang&lt;br /&gt;
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In cyclic permutational order: Patet ding | Patet dong | Patet deng | Patet dung | Patet dang&lt;br /&gt;
In cyclic permutational order: Patet ding | Patet dong | Patet deng | Patet dung | Patet dang&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc2"&gt;&lt;a name="x2L3s Pentatonic MOS: Pelogic--Transversal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Transversal&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x2L3s Pentatonic MOS: Pelogic--Transversal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Transversal&lt;/h3&gt;
   
   


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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="x2L3s Pentatonic MOS: Pelogic--&amp;quot;Diatonic&amp;quot; Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;&amp;quot;Diatonic&amp;quot; Names&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc4"&gt;&lt;a name="x2L3s Pentatonic MOS: Pelogic--&amp;quot;Diatonic&amp;quot; Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&amp;quot;Diatonic&amp;quot; Names&lt;/h3&gt;
   
   


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&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;a name="x2L5s Heptatonic MOS: Antidiatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;2L5s Heptatonic MOS: Antidiatonic&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="x2L5s Heptatonic MOS: Antidiatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;2L5s Heptatonic MOS: Antidiatonic&lt;/h1&gt;
  6|0 - LssLsss - (Anti)Locrian&lt;br /&gt;
  6|0 - LssLsss - (Anti)Locrian&lt;br /&gt;
5|1 - LsssLss - (Anti)Phrygian&lt;br /&gt;
5|1 - LsssLss - (Anti)Phrygian&lt;br /&gt;
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In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian&lt;br /&gt;
In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x2L5s Heptatonic MOS: Antidiatonic--Transversal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Transversal&lt;/h3&gt;
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&lt;br /&gt;
&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x2L5s Heptatonic MOS: Antidiatonic--&amp;quot;Diatonic&amp;quot; Names"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&amp;quot;Diatonic&amp;quot; Names&lt;/h3&gt;
   
   


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&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="x7L2s Nonatonic MOS: Superdiatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;7L2s Nonatonic MOS: Superdiatonic&lt;/h1&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc8"&gt;&lt;a name="x7L2s Nonatonic MOS: Superdiatonic"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;7L2s Nonatonic MOS: Superdiatonic&lt;/h1&gt;
  8|0 - LLLLsLLLs - (Super)Lydian&lt;br /&gt;
  8|0 - LLLLsLLLs - (Super)Lydian&lt;br /&gt;
7|1 - LLLsLLLLs - (Super)Ionian&lt;br /&gt;
7|1 - LLLsLLLLs - (Super)Ionian&lt;br /&gt;
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In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian&lt;br /&gt;
In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x7L2s Nonatonic MOS: Superdiatonic--Transversal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Transversal&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x7L2s Nonatonic MOS: Superdiatonic--Transversal"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Transversal&lt;/h3&gt;
   
   


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&lt;br /&gt;
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&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc11"&gt;&lt;a name="Notes on Naming"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Notes on Naming&lt;/h1&gt;
&lt;br /&gt;
The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the &amp;quot;Anti-&amp;quot; prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the &amp;quot;Super&amp;quot; prefix (e.g. Superionian, Superaeolian, etc.). The &amp;quot;anti&amp;quot; and &amp;quot;super&amp;quot; prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.&lt;br /&gt;
&lt;br /&gt;
Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the &amp;quot;shape&amp;quot; of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLLsLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.&lt;br /&gt;
&lt;br /&gt;
Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as &amp;quot;mixed&amp;quot; modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.&lt;br /&gt;
&lt;br /&gt;
As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&amp;gt; Corinthian -&amp;gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.&lt;/body&gt;&lt;/html&gt;</pre></div>

Revision as of 02:43, 9 December 2011

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=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].

===How to read these charts=== 
* 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.
* Additionally, "diatonic" names make use of the following abbreviations:
** SM - Supermajor
** M - Major
** N - Neutral
** m - Minor
** sm - Subminor


=2L3s Pentatonic MOS: Pelogic= 
4|0 - LsLss - Patet deng
3|1 - LssLs - Patet dang
2|2 - sLsLs - Patet dong
3|1 - sLssL - Patet dung
0|4 - ssLsL - Patet ding

In cyclic permutational order: Patet ding | Patet dong | Patet deng | Patet dung | Patet dang

===Transversal=== 
||= **UDP** ||= **Imprint** ||= **(Patet) Name** ||= **1** ||= **2** ||= **3** ||= **4** ||= **5** ||
||= 4|0 ||= LsLss ||= deng ||= 1/1 ||= <span style="color: #0000ff;">5/4</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #0000ff;">5/3</span> ||= <span style="color: #0000ff;">11/6</span> ||
||= 3|1 ||= LssLs ||= dang ||= 1/1 ||= <span style="color: #0000ff;">5/4</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> ||
||= 0|0 ||= 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=== 
||= **UDP** ||= **Imprint** ||= **(Patet) Name** ||= **1** ||= **2** ||= **3** ||= **4** ||= **5** ||
||= 4|0 ||= LsLss ||= deng ||= P1 ||= <span style="color: #0000ff;">M3</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #0000ff;">M6</span> ||= <span style="color: #0000ff;">N7</span> ||
||= 3|1 ||= LssLs ||= dang ||= P1 ||= <span style="color: #0000ff;">M3</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> ||
||= 0|0 ||= 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> ||


=2L5s Heptatonic MOS: Antidiatonic= 
6|0 - LssLsss - (Anti)Locrian
5|1 - LsssLss - (Anti)Phrygian
4|2 - sLssLss - (Anti)Aeolian ("major")
3|3 - sLsssLs - (Anti)Dorian
2|4 - ssLssLs - (Anti)Mixolydian ("harmonic minor")
1|5 - ssLsssL - (Anti)Ionian ("minor")
0|6 - sssLssL - (Anti)Lydian

In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian

===Transversal=== 
||= **UDP** ||= **Imprint** ||= **(Anti)Name** ||= **1** ||= **2** ||= **3** ||= **4** ||= **5** ||= **6** ||= **7** ||
||= 6|0 ||= LssLsss ||= Locrian ||= 1/1 ||= <span style="color: #0000ff;">8/7</span> ||= <span style="color: #0000ff;">5/4</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #0000ff;">14/9</span> ||= <span style="color: #0000ff;">5/3</span> ||= <span style="color: #0000ff;">11/6</span> ||
||= 5|1 ||= LsssLss ||= Phrygian ||= 1/1 ||= <span style="color: #0000ff;">8/7</span> ||= <span style="color: #0000ff;">5/4</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #0000ff;">5/3</span> ||= <span style="color: #0000ff;">11/6</span> ||
||= 4|2 ||= sLssLss ||= Aeolian ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #0000ff;">5/4</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #0000ff;">5/3</span> ||= <span style="color: #0000ff;">11/6</span> ||
||= 3|3 ||= sLsssLs ||= Dorian ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #0000ff;">5/4</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #ff0000;">8/5</span> ||= <span style="color: #0000ff;">11/6</span> ||
||= 2|4 ||= ssLssLs ||= Mixolydian ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #ff0000;">6/5</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #ff0000;">8/5</span> ||= <span style="color: #0000ff;">11/6</span> ||
||= 1|5 ||= ssLsssL ||= Ionian ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #ff0000;">6/5</span> ||= <span style="color: #0000ff;">4/3</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #ff0000;">8/5</span> ||= <span style="color: #ff0000;">7/4</span> ||
||= 0|6 ||= sssLssL ||= Lydian ||= 1/1 ||= <span style="color: #ff0000;">12/11</span> ||= <span style="color: #ff0000;">6/5</span> ||= <span style="color: #ff0000;">9/7</span> ||= <span style="color: #ff0000;">3/2</span> ||= <span style="color: #ff0000;">8/5</span> ||= <span style="color: #ff0000;">7/4</span> ||

==="Diatonic" Names=== 
||= **UDP** ||= **Imprint** ||= **(Anti)Name** ||= **1** ||= **2** ||= **3** ||= **4** ||= **5** ||= **6** ||= **7** ||
||= 6|0 ||= LssLsss ||= Locrian ||= P1 ||= <span style="color: #0000ff;">SM2</span> ||= <span style="color: #0000ff;">M3</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #0000ff;">sm6</span> ||= <span style="color: #0000ff;">M6</span> ||= <span style="color: #0000ff;">N7</span> ||
||= 5|1 ||= LsssLss ||= Phrygian ||= P1 ||= <span style="color: #0000ff;">SM2</span> ||= <span style="color: #0000ff;">M3</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #0000ff;">M6</span> ||= <span style="color: #0000ff;">N7</span> ||
||= 4|2 ||= sLssLss ||= Aeolian ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #0000ff;">M3</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #0000ff;">M6</span> ||= <span style="color: #0000ff;">N7</span> ||
||= 3|3 ||= sLsssLs ||= Dorian ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #0000ff;">M3</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #ff0000;">m6</span> ||= <span style="color: #0000ff;">N7</span> ||
||= 2|4 ||= ssLssLs ||= Mixolydian ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #ff0000;">m3</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #ff0000;">m6</span> ||= <span style="color: #0000ff;">N7</span> ||
||= 1|5 ||= ssLsssL ||= Ionian ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #ff0000;">m3</span> ||= <span style="color: #0000ff;">P4</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #ff0000;">m6</span> ||= <span style="color: #ff0000;">sm7</span> ||
||= 0|6 ||= sssLssL ||= Lydian ||= P1 ||= <span style="color: #ff0000;">N2</span> ||= <span style="color: #ff0000;">m3</span> ||= <span style="color: #ff0000;">SM3</span> ||= <span style="color: #ff0000;">P5</span> ||= <span style="color: #ff0000;">m6</span> ||= <span style="color: #ff0000;">sm7</span> ||


=7L2s Nonatonic MOS: Superdiatonic= 
8|0 - LLLLsLLLs - (Super)Lydian
7|1 - LLLsLLLLs - (Super)Ionian
6|2 - LLLsLLLsL - (Super)Mixolydian
5|3 - LLsLLLLsL - (Super)Corinthian
4|4 - LLsLLLsLL - (Super)Olympian
3|5 - LsLLLLsLL - (Super)Dorian
2|6 - LsLLLsLLL - (Super)Aeolian
1|7 - sLLLLsLLL - (Super)Phrygian
0|8 - sLLLsLLLL - (Super)Locrian

In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian

===Transversal=== 
||= **UDP** ||= **Imprint** ||= **(Super)Name** ||= **1** ||= **2** ||= **3** ||= **4** ||= **5** ||= **6** ||= **7** ||= **8** ||= **9** ||
||= 8|0 ||= LLLLsLLLs ||= Lydian ||= 1/1 ||= <span style="color: #0000ff;">12/11</span> ||= <span style="color: #0000ff;">6/5</span> ||= <span style="color: #0000ff;">9/7</span> ||= <span style="color: #0000ff;">7/5</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #0000ff;">8/5</span> ||= <span style="color: #0000ff;">7/4</span> ||= <span style="color: #0000ff;">21/11</span> ||
||= 7|1 ||= LLLsLLLLs ||= Ionian ||= 1/1 ||= <span style="color: #0000ff;">12/11</span> ||= <span style="color: #0000ff;">6/5</span> ||= <span style="color: #0000ff;">9/7</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #0000ff;">8/5</span> ||= <span style="color: #0000ff;">7/4</span> ||= <span style="color: #0000ff;">21/11</span> ||
||= 6|2 ||= LLLsLLLsL ||= Mixolydian ||= 1/1 ||= <span style="color: #0000ff;">12/11</span> ||= <span style="color: #0000ff;">6/5</span> ||= <span style="color: #0000ff;">9/7</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #0000ff;">8/5</span> ||= <span style="color: #0000ff;">7/4</span> ||= <span style="color: #ff0000;">11/6</span> ||
||= 5|3 ||= LLsLLLLsL ||= Corinthian ||= 1/1 ||= <span style="color: #0000ff;">12/11</span> ||= <span style="color: #0000ff;">6/5</span> ||= <span style="color: #ff0000;">5/4</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #0000ff;">8/5</span> ||= <span style="color: #0000ff;">7/4</span> ||= <span style="color: #ff0000;">11/6</span> ||
||= 4|4 ||= LLsLLLsLL ||= Olympian ||= 1/1 ||= <span style="color: #0000ff;">12/11</span> ||= <span style="color: #0000ff;">6/5</span> ||= <span style="color: #ff0000;">5/4</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #0000ff;">8/5</span> ||= <span style="color: #ff0000;">5/3</span> ||= <span style="color: #ff0000;">11/6</span> ||
||= 3|5 ||= LsLLLLsLL ||= Dorian ||= 1/1 ||= <span style="color: #0000ff;">12/11</span> ||= <span style="color: #ff0000;">8/7</span> ||= <span style="color: #ff0000;">5/4</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #0000ff;">8/5</span> ||= <span style="color: #ff0000;">5/3</span> ||= <span style="color: #ff0000;">11/6</span> ||
||= 2|6 ||= LsLLLsLLL ||= Aeolian ||= 1/1 ||= <span style="color: #0000ff;">12/11</span> ||= <span style="color: #ff0000;">8/7</span> ||= <span style="color: #ff0000;">5/4</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #ff0000;">14/9</span> ||= <span style="color: #ff0000;">5/3</span> ||= <span style="color: #ff0000;">11/6</span> ||
||= 1|7 ||= sLLLLsLLL ||= Phrygian ||= 1/1 ||= <span style="color: #ff0000;">22/21</span> ||= <span style="color: #ff0000;">8/7</span> ||= <span style="color: #ff0000;">5/4</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #0000ff;">3/2</span> ||= <span style="color: #ff0000;">14/9</span> ||= <span style="color: #ff0000;">5/3</span> ||= <span style="color: #ff0000;">11/6</span> ||
||= 0|8 ||= sLLLsLLLL ||= Locrian ||= 1/1 ||= <span style="color: #ff0000;">22/21</span> ||= <span style="color: #ff0000;">8/7</span> ||= <span style="color: #ff0000;">5/4</span> ||= <span style="color: #ff0000;">4/3</span> ||= <span style="color: #ff0000;">10/7</span> ||= <span style="color: #ff0000;">14/9</span> ||= <span style="color: #ff0000;">5/3</span> ||= <span style="color: #ff0000;">11/6</span> ||

==="Diatonic" Names=== 
||= **UDP** ||= **Imprint** ||= **(Super)Name** ||= **1** ||= **2** ||= **3** ||= **4** ||= **5** ||= **6** ||= **7** ||= **8** ||= **9** ||
||= 8|0 ||= LLLLsLLLs ||= Lydian ||= P1 ||= <span style="color: #0000ff;">N2</span> ||= <span style="color: #0000ff;">m3</span> ||= <span style="color: #0000ff;">SM3</span> ||= <span style="color: #0000ff;">A4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #0000ff;">m6</span> ||= <span style="color: #0000ff;">sm7</span> ||= <span style="color: #0000ff;">SM7</span> ||
||= 7|1 ||= LLLsLLLLs ||= Ionian ||= P1 ||= <span style="color: #0000ff;">N2</span> ||= <span style="color: #0000ff;">m3</span> ||= <span style="color: #0000ff;">SM3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #0000ff;">m6</span> ||= <span style="color: #0000ff;">sm7</span> ||= <span style="color: #0000ff;">SM7</span> ||
||= 6|2 ||= LLLsLLLsL ||= Mixolydian ||= P1 ||= <span style="color: #0000ff;">N2</span> ||= <span style="color: #0000ff;">m3</span> ||= <span style="color: #0000ff;">SM3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #0000ff;">m6</span> ||= <span style="color: #0000ff;">sm7</span> ||= <span style="color: #ff0000;">N7</span> ||
||= 5|3 ||= LLsLLLLsL ||= Corinthian ||= P1 ||= <span style="color: #0000ff;">N2</span> ||= <span style="color: #0000ff;">m3</span> ||= <span style="color: #ff0000;">M3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #0000ff;">m6</span> ||= <span style="color: #0000ff;">sm7</span> ||= <span style="color: #ff0000;">N7</span> ||
||= 4|4 ||= LLsLLLsLL ||= Olympian ||= P1 ||= <span style="color: #0000ff;">N2</span> ||= <span style="color: #0000ff;">m3</span> ||= <span style="color: #ff0000;">M3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #0000ff;">m6</span> ||= <span style="color: #ff0000;">M6</span> ||= <span style="color: #ff0000;">N7</span> ||
||= 3|5 ||= LsLLLLsLL ||= Dorian ||= P1 ||= <span style="color: #0000ff;">N2</span> ||= <span style="color: #ff0000;">SM2</span> ||= <span style="color: #ff0000;">M3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #0000ff;">m6</span> ||= <span style="color: #ff0000;">M6</span> ||= <span style="color: #ff0000;">N7</span> ||
||= 2|6 ||= LsLLLsLLL ||= Aeolian ||= P1 ||= <span style="color: #0000ff;">N2</span> ||= <span style="color: #ff0000;">SM2</span> ||= <span style="color: #ff0000;">M3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #ff0000;">sm6</span> ||= <span style="color: #ff0000;">M6</span> ||= <span style="color: #ff0000;">N7</span> ||
||= 1|7 ||= sLLLLsLLL ||= Phrygian ||= P1 ||= <span style="color: #ff0000;">sm2</span> ||= <span style="color: #ff0000;">SM2</span> ||= <span style="color: #ff0000;">M3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #0000ff;">P5</span> ||= <span style="color: #ff0000;">sm6</span> ||= <span style="color: #ff0000;">M6</span> ||= <span style="color: #ff0000;">N7</span> ||
||= 0|8 ||= sLLLsLLLL ||= Locrian ||= P1 ||= <span style="color: #ff0000;">sm2</span> ||= <span style="color: #ff0000;">SM2</span> ||= <span style="color: #ff0000;">M3</span> ||= <span style="color: #ff0000;">P4</span> ||= <span style="color: #ff0000;">d5</span> ||= <span style="color: #ff0000;">sm6</span> ||= <span style="color: #ff0000;">M6</span> ||= <span style="color: #ff0000;">N7</span> ||

=Notes on Naming= 

The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the "Anti-" prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the "Super" prefix (e.g. Superionian, Superaeolian, etc.). The "anti" and "super" prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.

Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the "shape" of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLLsLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.

Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.

As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -> Corinthian -> Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.

Original HTML content:

<html><head><title>Mavila Temperament Modal Harmony</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Introduction"></a><!-- ws:end:WikiTextHeadingRule:0 -->Introduction</h1>
 <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 />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h3&gt; --><h3 id="toc1"><a name="Introduction--How to read these charts"></a><!-- ws:end:WikiTextHeadingRule:2 -->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 />
<br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="x2L3s Pentatonic MOS: Pelogic"></a><!-- ws:end:WikiTextHeadingRule:4 -->2L3s Pentatonic MOS: Pelogic</h1>
 4|0 - LsLss - Patet deng<br />
3|1 - LssLs - Patet dang<br />
2|2 - sLsLs - Patet dong<br />
3|1 - sLssL - Patet dung<br />
0|4 - ssLsL - Patet ding<br />
<br />
In cyclic permutational order: Patet ding | Patet dong | Patet deng | Patet dung | Patet dang<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="x2L3s Pentatonic MOS: Pelogic--Transversal"></a><!-- ws:end:WikiTextHeadingRule:6 -->Transversal</h3>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>UDP</strong><br />
</td>
        <td style="text-align: center;"><strong>Imprint</strong><br />
</td>
        <td style="text-align: center;"><strong>(Patet) Name</strong><br />
</td>
        <td style="text-align: center;"><strong>1</strong><br />
</td>
        <td style="text-align: center;"><strong>2</strong><br />
</td>
        <td style="text-align: center;"><strong>3</strong><br />
</td>
        <td style="text-align: center;"><strong>4</strong><br />
</td>
        <td style="text-align: center;"><strong>5</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4|0<br />
</td>
        <td style="text-align: center;">LsLss<br />
</td>
        <td style="text-align: center;">deng<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3|1<br />
</td>
        <td style="text-align: center;">LssLs<br />
</td>
        <td style="text-align: center;">dang<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2|2<br />
</td>
        <td style="text-align: center;">sLsLs<br />
</td>
        <td style="text-align: center;">dong<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1|3<br />
</td>
        <td style="text-align: center;">sLssL<br />
</td>
        <td style="text-align: center;">dung<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/5</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0|0<br />
</td>
        <td style="text-align: center;">ssLsL<br />
</td>
        <td style="text-align: center;">ding<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/5</span><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="x2L3s Pentatonic MOS: Pelogic--&quot;Diatonic&quot; Names"></a><!-- ws:end:WikiTextHeadingRule:8 -->&quot;Diatonic&quot; Names</h3>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>UDP</strong><br />
</td>
        <td style="text-align: center;"><strong>Imprint</strong><br />
</td>
        <td style="text-align: center;"><strong>(Patet) Name</strong><br />
</td>
        <td style="text-align: center;"><strong>1</strong><br />
</td>
        <td style="text-align: center;"><strong>2</strong><br />
</td>
        <td style="text-align: center;"><strong>3</strong><br />
</td>
        <td style="text-align: center;"><strong>4</strong><br />
</td>
        <td style="text-align: center;"><strong>5</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4|0<br />
</td>
        <td style="text-align: center;">LsLss<br />
</td>
        <td style="text-align: center;">deng<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3|1<br />
</td>
        <td style="text-align: center;">LssLs<br />
</td>
        <td style="text-align: center;">dang<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2|2<br />
</td>
        <td style="text-align: center;">sLsLs<br />
</td>
        <td style="text-align: center;">dong<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1|3<br />
</td>
        <td style="text-align: center;">sLssL<br />
</td>
        <td style="text-align: center;">dung<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0|0<br />
</td>
        <td style="text-align: center;">ssLsL<br />
</td>
        <td style="text-align: center;">ding<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m6</span><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:&lt;h1&gt; --><h1 id="toc5"><a name="x2L5s Heptatonic MOS: Antidiatonic"></a><!-- ws:end:WikiTextHeadingRule:10 -->2L5s Heptatonic MOS: Antidiatonic</h1>
 6|0 - LssLsss - (Anti)Locrian<br />
5|1 - LsssLss - (Anti)Phrygian<br />
4|2 - sLssLss - (Anti)Aeolian (&quot;major&quot;)<br />
3|3 - sLsssLs - (Anti)Dorian<br />
2|4 - ssLssLs - (Anti)Mixolydian (&quot;harmonic minor&quot;)<br />
1|5 - ssLsssL - (Anti)Ionian (&quot;minor&quot;)<br />
0|6 - sssLssL - (Anti)Lydian<br />
<br />
In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="x2L5s Heptatonic MOS: Antidiatonic--Transversal"></a><!-- ws:end:WikiTextHeadingRule:12 -->Transversal</h3>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>UDP</strong><br />
</td>
        <td style="text-align: center;"><strong>Imprint</strong><br />
</td>
        <td style="text-align: center;"><strong>(Anti)Name</strong><br />
</td>
        <td style="text-align: center;"><strong>1</strong><br />
</td>
        <td style="text-align: center;"><strong>2</strong><br />
</td>
        <td style="text-align: center;"><strong>3</strong><br />
</td>
        <td style="text-align: center;"><strong>4</strong><br />
</td>
        <td style="text-align: center;"><strong>5</strong><br />
</td>
        <td style="text-align: center;"><strong>6</strong><br />
</td>
        <td style="text-align: center;"><strong>7</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6|0<br />
</td>
        <td style="text-align: center;">LssLsss<br />
</td>
        <td style="text-align: center;">Locrian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">14/9</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5|1<br />
</td>
        <td style="text-align: center;">LsssLss<br />
</td>
        <td style="text-align: center;">Phrygian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4|2<br />
</td>
        <td style="text-align: center;">sLssLss<br />
</td>
        <td style="text-align: center;">Aeolian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3|3<br />
</td>
        <td style="text-align: center;">sLsssLs<br />
</td>
        <td style="text-align: center;">Dorian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2|4<br />
</td>
        <td style="text-align: center;">ssLssLs<br />
</td>
        <td style="text-align: center;">Mixolydian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1|5<br />
</td>
        <td style="text-align: center;">ssLsssL<br />
</td>
        <td style="text-align: center;">Ionian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">7/4</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0|6<br />
</td>
        <td style="text-align: center;">sssLssL<br />
</td>
        <td style="text-align: center;">Lydian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">9/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">7/4</span><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h3&gt; --><h3 id="toc7"><a name="x2L5s Heptatonic MOS: Antidiatonic--&quot;Diatonic&quot; Names"></a><!-- ws:end:WikiTextHeadingRule:14 -->&quot;Diatonic&quot; Names</h3>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>UDP</strong><br />
</td>
        <td style="text-align: center;"><strong>Imprint</strong><br />
</td>
        <td style="text-align: center;"><strong>(Anti)Name</strong><br />
</td>
        <td style="text-align: center;"><strong>1</strong><br />
</td>
        <td style="text-align: center;"><strong>2</strong><br />
</td>
        <td style="text-align: center;"><strong>3</strong><br />
</td>
        <td style="text-align: center;"><strong>4</strong><br />
</td>
        <td style="text-align: center;"><strong>5</strong><br />
</td>
        <td style="text-align: center;"><strong>6</strong><br />
</td>
        <td style="text-align: center;"><strong>7</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6|0<br />
</td>
        <td style="text-align: center;">LssLsss<br />
</td>
        <td style="text-align: center;">Locrian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">SM2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">sm6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5|1<br />
</td>
        <td style="text-align: center;">LsssLss<br />
</td>
        <td style="text-align: center;">Phrygian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">SM2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4|2<br />
</td>
        <td style="text-align: center;">sLssLss<br />
</td>
        <td style="text-align: center;">Aeolian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3|3<br />
</td>
        <td style="text-align: center;">sLsssLs<br />
</td>
        <td style="text-align: center;">Dorian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2|4<br />
</td>
        <td style="text-align: center;">ssLssLs<br />
</td>
        <td style="text-align: center;">Mixolydian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1|5<br />
</td>
        <td style="text-align: center;">ssLsssL<br />
</td>
        <td style="text-align: center;">Ionian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">sm7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0|6<br />
</td>
        <td style="text-align: center;">sssLssL<br />
</td>
        <td style="text-align: center;">Lydian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">SM3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">sm7</span><br />
</td>
    </tr>
</table>

<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="x7L2s Nonatonic MOS: Superdiatonic"></a><!-- ws:end:WikiTextHeadingRule:16 -->7L2s Nonatonic MOS: Superdiatonic</h1>
 8|0 - LLLLsLLLs - (Super)Lydian<br />
7|1 - LLLsLLLLs - (Super)Ionian<br />
6|2 - LLLsLLLsL - (Super)Mixolydian<br />
5|3 - LLsLLLLsL - (Super)Corinthian<br />
4|4 - LLsLLLsLL - (Super)Olympian<br />
3|5 - LsLLLLsLL - (Super)Dorian<br />
2|6 - LsLLLsLLL - (Super)Aeolian<br />
1|7 - sLLLLsLLL - (Super)Phrygian<br />
0|8 - sLLLsLLLL - (Super)Locrian<br />
<br />
In cyclic permutational order: Ionian | Corinthian | Dorian | Phrygian | Lydian | Mixolydian | Olympian | Aeolian | Locrian<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h3&gt; --><h3 id="toc9"><a name="x7L2s Nonatonic MOS: Superdiatonic--Transversal"></a><!-- ws:end:WikiTextHeadingRule:18 -->Transversal</h3>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>UDP</strong><br />
</td>
        <td style="text-align: center;"><strong>Imprint</strong><br />
</td>
        <td style="text-align: center;"><strong>(Super)Name</strong><br />
</td>
        <td style="text-align: center;"><strong>1</strong><br />
</td>
        <td style="text-align: center;"><strong>2</strong><br />
</td>
        <td style="text-align: center;"><strong>3</strong><br />
</td>
        <td style="text-align: center;"><strong>4</strong><br />
</td>
        <td style="text-align: center;"><strong>5</strong><br />
</td>
        <td style="text-align: center;"><strong>6</strong><br />
</td>
        <td style="text-align: center;"><strong>7</strong><br />
</td>
        <td style="text-align: center;"><strong>8</strong><br />
</td>
        <td style="text-align: center;"><strong>9</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8|0<br />
</td>
        <td style="text-align: center;">LLLLsLLLs<br />
</td>
        <td style="text-align: center;">Lydian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">9/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">7/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">7/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">21/11</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7|1<br />
</td>
        <td style="text-align: center;">LLLsLLLLs<br />
</td>
        <td style="text-align: center;">Ionian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">9/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">7/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">21/11</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6|2<br />
</td>
        <td style="text-align: center;">LLLsLLLsL<br />
</td>
        <td style="text-align: center;">Mixolydian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">9/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">7/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5|3<br />
</td>
        <td style="text-align: center;">LLsLLLLsL<br />
</td>
        <td style="text-align: center;">Corinthian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">7/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4|4<br />
</td>
        <td style="text-align: center;">LLsLLLsLL<br />
</td>
        <td style="text-align: center;">Olympian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">6/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3|5<br />
</td>
        <td style="text-align: center;">LsLLLLsLL<br />
</td>
        <td style="text-align: center;">Dorian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">8/5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2|6<br />
</td>
        <td style="text-align: center;">LsLLLsLLL<br />
</td>
        <td style="text-align: center;">Aeolian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">12/11</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">14/9</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1|7<br />
</td>
        <td style="text-align: center;">sLLLLsLLL<br />
</td>
        <td style="text-align: center;">Phrygian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">22/21</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">3/2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">14/9</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">11/6</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0|8<br />
</td>
        <td style="text-align: center;">sLLLsLLLL<br />
</td>
        <td style="text-align: center;">Locrian<br />
</td>
        <td style="text-align: center;">1/1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">22/21</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">8/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">4/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">10/7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">14/9</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">5/3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">11/6</span><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h3&gt; --><h3 id="toc10"><a name="x7L2s Nonatonic MOS: Superdiatonic--&quot;Diatonic&quot; Names"></a><!-- ws:end:WikiTextHeadingRule:20 -->&quot;Diatonic&quot; Names</h3>
 

<table class="wiki_table">
    <tr>
        <td style="text-align: center;"><strong>UDP</strong><br />
</td>
        <td style="text-align: center;"><strong>Imprint</strong><br />
</td>
        <td style="text-align: center;"><strong>(Super)Name</strong><br />
</td>
        <td style="text-align: center;"><strong>1</strong><br />
</td>
        <td style="text-align: center;"><strong>2</strong><br />
</td>
        <td style="text-align: center;"><strong>3</strong><br />
</td>
        <td style="text-align: center;"><strong>4</strong><br />
</td>
        <td style="text-align: center;"><strong>5</strong><br />
</td>
        <td style="text-align: center;"><strong>6</strong><br />
</td>
        <td style="text-align: center;"><strong>7</strong><br />
</td>
        <td style="text-align: center;"><strong>8</strong><br />
</td>
        <td style="text-align: center;"><strong>9</strong><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">8|0<br />
</td>
        <td style="text-align: center;">LLLLsLLLs<br />
</td>
        <td style="text-align: center;">Lydian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">SM3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">A4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">sm7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">SM7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">7|1<br />
</td>
        <td style="text-align: center;">LLLsLLLLs<br />
</td>
        <td style="text-align: center;">Ionian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">SM3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">sm7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">SM7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">6|2<br />
</td>
        <td style="text-align: center;">LLLsLLLsL<br />
</td>
        <td style="text-align: center;">Mixolydian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">SM3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">sm7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">5|3<br />
</td>
        <td style="text-align: center;">LLsLLLLsL<br />
</td>
        <td style="text-align: center;">Corinthian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">sm7</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">4|4<br />
</td>
        <td style="text-align: center;">LLsLLLsLL<br />
</td>
        <td style="text-align: center;">Olympian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">3|5<br />
</td>
        <td style="text-align: center;">LsLLLLsLL<br />
</td>
        <td style="text-align: center;">Dorian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">SM2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">m6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">2|6<br />
</td>
        <td style="text-align: center;">LsLLLsLLL<br />
</td>
        <td style="text-align: center;">Aeolian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">N2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">SM2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">sm6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">1|7<br />
</td>
        <td style="text-align: center;">sLLLLsLLL<br />
</td>
        <td style="text-align: center;">Phrygian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">sm2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">SM2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #0000ff;">P5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">sm6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N7</span><br />
</td>
    </tr>
    <tr>
        <td style="text-align: center;">0|8<br />
</td>
        <td style="text-align: center;">sLLLsLLLL<br />
</td>
        <td style="text-align: center;">Locrian<br />
</td>
        <td style="text-align: center;">P1<br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">sm2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">SM2</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M3</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">P4</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">d5</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">sm6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">M6</span><br />
</td>
        <td style="text-align: center;"><span style="color: #ff0000;">N7</span><br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h1&gt; --><h1 id="toc11"><a name="Notes on Naming"></a><!-- ws:end:WikiTextHeadingRule:22 -->Notes on Naming</h1>
 <br />
The modes of the antidiatonic scale are simply named after the existing diatonic scale modes, but with the &quot;Anti-&quot; prefix (e.g. Anti-ionian, Anti-aeolian, etc). The modes of the superdiatonic scale are also named after the existing modes, but contain the &quot;Super&quot; prefix (e.g. Superionian, Superaeolian, etc.). The &quot;anti&quot; and &quot;super&quot; prefixes can be left in to explicitly distinguish which MOS's modes you're talking about, or can be omitted for convention.<br />
<br />
Each superdiatonic mode contains its corresponding mode in the antidiatonic scale. Additionally, the superdiatonic modes also resemble the &quot;shape&quot; of their meantone diatonic counterparts. This leads to a pattern: LLLsLLLLs both resembles the meantone LLLsLLs Ionian mode, and contains the mavila ssLsssL anti-Ionian mode as well. Additionally, sLLLsLLLL resembles the diatonic sLLsLLL Locrian mode, and also contains the mavila LssLsss anti-Ionian mode. Furthermore, every mavila mode contains a tonic triad of the -opposite- quality as the corresponding diatonic mode, so that Superionian and Anti-ionian contain a minor triad, and Superphrygian and Antiphrygian contain a major triad.<br />
<br />
Since there are only seven diatonic modes, two of the superdiatonic modes need additional names and cannot reference any mode of the diatonic scale. These two modes present themselves as &quot;mixed&quot; modes, which begin with the LLs tetrachord, and so contain both the ~300 cent minor third and the ~375 cent major third (and hence both minor and major triads). These are the only two modes to exhibit this behavior. They're interspersed on the rotational continuum between Ionian and Dorian, and Mixolydian and Aeolian.<br />
<br />
As were the original modes named after regions of ancient Greece, so are these new superdiatonic extensions. The one between Ionian and Dorian is called Corinthian, after the Greek island of Corinth, set up so that the Ionian -&gt; Corinthian -&gt; Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The mode cyclically placed between Mixolydian and Aeolian, which is the symmetrical LLsLLLsLL scale, has a number of noteworthy theoretical properties, in that it contains every modal rotation of mavila[5], and hence the entire mavila-tempered 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.</body></html>
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