Mavila temperament modal harmony
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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]. The "anti" and "super" prefixes can be left in to explicitly distinguish which mode you're talking about, or can be omitted for convention.
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.
==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
==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** ||~ **Name** ||~ **1** ||~ **2** ||~ **3** ||~ **4** ||~ **5** ||~ **6** ||~ **7** ||
|| 6|0 || LssLsss || (Anti)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 ||< (Anti)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 ||< (Anti)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 ||< (Anti)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 ||< (Anti)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 ||< (Anti)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 ||< (Anti)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"-Based Names===
||~ **UDP** ||~ **Imprint** ||~ **Name** ||~ **1** ||~ **2** ||~ **3** ||~ **4** ||~ **5** ||~ **6** ||~ **7** ||
|| 6|0 || LssLsss || (Anti)Locrian || P1 ||= <span style="color: #0000ff;">SM2</span> || <span style="color: #0000ff;">M3</span> || <span style="color: #0000ff;">P4</span> || <span style="color: #0000ff;">14/9</span> || <span style="color: #0000ff;">M6</span> || <span style="color: #0000ff;">N7</span> ||
||= 5|1 ||= LsssLss ||< (Anti)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 ||< (Anti)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 ||< (Anti)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 ||< (Anti)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 ||< (Anti)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 ||< (Anti)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** ||~ **Name** ||~ **1** ||~ **2** ||~ **3** ||~ **4** ||~ **5** ||~ **6** ||~ **7** ||~ **8** ||~ **9** ||
||= 8|0 ||= LLLLsLLLs ||< (Super)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 ||< (Super)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 ||< (Super)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 ||< (Super)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 ||< (Super)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 ||< (Super)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 ||< (Super)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 ||< (Super)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 ||< (Super)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> ||
Each "super" mode contains the corresponding "anti" mode below it, and two adjacent modes as well (though pathological at the extreme ends of the modal continuum). The superdiatonic modes also resemble the shape of the meantone diatonic modes somewhat, so that LLLsLLLLs resembles the meantone LLLsLLs Ionian mode, and also 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.
Since there are only seven diatonic modes, two superdiatonic modes need additional names beyond the usual gamut of options. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and hence contain both the ~300 cent minor third and the ~375 cent major third. 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 one 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 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>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.<br />
<br />
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 <a class="wiki_link" href="/2L%205s">2L 5s</a>)<br />
<br />
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<a class="wiki_link" href="/7L%202s"> 7L 2s</a>)<br />
<br />
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]. The "anti" and "super" prefixes can be left in to explicitly distinguish which mode you're talking about, or can be omitted for convention.<br />
<br />
The 6|0, 5|1, 4|2 markings are an instance of <a class="wiki_link" href="/Modal%20UDP%20Notation">Modal UDP Notation</a>.<br />
<br />
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.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h2> --><h2 id="toc0"><a name="x-2L3s Pentatonic MOS: Pelogic"></a><!-- ws:end:WikiTextHeadingRule:0 -->2L3s Pentatonic MOS: Pelogic</h2>
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 />
<!-- ws:start:WikiTextHeadingRule:2:<h2> --><h2 id="toc1"><a name="x-2L5s Heptatonic MOS: Antidiatonic"></a><!-- ws:end:WikiTextHeadingRule:2 -->2L5s Heptatonic MOS: Antidiatonic</h2>
6|0 - LssLsss - (Anti)Locrian<br />
5|1 - LsssLss - (Anti)Phrygian<br />
4|2 - sLssLss - (Anti)Aeolian ("major")<br />
3|3 - sLsssLs - (Anti)Dorian<br />
2|4 - ssLssLs - (Anti)Mixolydian ("harmonic minor")<br />
1|5 - ssLsssL - (Anti)Ionian ("minor")<br />
0|6 - sssLssL - (Anti)Lydian<br />
<br />
In cyclic permutational order: Ionian Dorian Phrygian Lydian Mixolydian Aeolian Locrian<br />
<br />
<!-- ws:start:WikiTextHeadingRule:4:<h3> --><h3 id="toc2"><a name="x-2L5s Heptatonic MOS: Antidiatonic-Transversal"></a><!-- ws:end:WikiTextHeadingRule:4 -->Transversal</h3>
<table class="wiki_table">
<tr>
<th><strong>UDP</strong><br />
</th>
<th><strong>Imprint</strong><br />
</th>
<th><strong>Name</strong><br />
</th>
<th><strong>1</strong><br />
</th>
<th><strong>2</strong><br />
</th>
<th><strong>3</strong><br />
</th>
<th><strong>4</strong><br />
</th>
<th><strong>5</strong><br />
</th>
<th><strong>6</strong><br />
</th>
<th><strong>7</strong><br />
</th>
</tr>
<tr>
<td>6|0<br />
</td>
<td>LssLsss<br />
</td>
<td>(Anti)Locrian<br />
</td>
<td>1/1<br />
</td>
<td style="text-align: center;"><span style="color: #0000ff;">8/7</span><br />
</td>
<td><span style="color: #0000ff;">5/4</span><br />
</td>
<td><span style="color: #0000ff;">4/3</span><br />
</td>
<td><span style="color: #0000ff;">14/9</span><br />
</td>
<td><span style="color: #0000ff;">5/3</span><br />
</td>
<td><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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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:6:<h3> --><h3 id="toc3"><a name="x-2L5s Heptatonic MOS: Antidiatonic-"Diatonic"-Based Names"></a><!-- ws:end:WikiTextHeadingRule:6 -->"Diatonic"-Based Names</h3>
<table class="wiki_table">
<tr>
<th><strong>UDP</strong><br />
</th>
<th><strong>Imprint</strong><br />
</th>
<th><strong>Name</strong><br />
</th>
<th><strong>1</strong><br />
</th>
<th><strong>2</strong><br />
</th>
<th><strong>3</strong><br />
</th>
<th><strong>4</strong><br />
</th>
<th><strong>5</strong><br />
</th>
<th><strong>6</strong><br />
</th>
<th><strong>7</strong><br />
</th>
</tr>
<tr>
<td>6|0<br />
</td>
<td>LssLsss<br />
</td>
<td>(Anti)Locrian<br />
</td>
<td>P1<br />
</td>
<td style="text-align: center;"><span style="color: #0000ff;">SM2</span><br />
</td>
<td><span style="color: #0000ff;">M3</span><br />
</td>
<td><span style="color: #0000ff;">P4</span><br />
</td>
<td><span style="color: #0000ff;">14/9</span><br />
</td>
<td><span style="color: #0000ff;">M6</span><br />
</td>
<td><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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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: left;">(Anti)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 />
<!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><a name="x7L2s Nonatonic MOS: Superdiatonic"></a><!-- ws:end:WikiTextHeadingRule:8 -->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:10:<h3> --><h3 id="toc5"><a name="x7L2s Nonatonic MOS: Superdiatonic--Transversal"></a><!-- ws:end:WikiTextHeadingRule:10 -->Transversal</h3>
<br />
<table class="wiki_table">
<tr>
<th><strong>UDP</strong><br />
</th>
<th><strong>Imprint</strong><br />
</th>
<th><strong>Name</strong><br />
</th>
<th><strong>1</strong><br />
</th>
<th><strong>2</strong><br />
</th>
<th><strong>3</strong><br />
</th>
<th><strong>4</strong><br />
</th>
<th><strong>5</strong><br />
</th>
<th><strong>6</strong><br />
</th>
<th><strong>7</strong><br />
</th>
<th><strong>8</strong><br />
</th>
<th><strong>9</strong><br />
</th>
</tr>
<tr>
<td style="text-align: center;">8|0<br />
</td>
<td style="text-align: center;">LLLLsLLLs<br />
</td>
<td style="text-align: left;">(Super)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: left;">(Super)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: left;">(Super)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: left;">(Super)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: left;">(Super)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: left;">(Super)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: left;">(Super)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: left;">(Super)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: left;">(Super)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 />
Each "super" mode contains the corresponding "anti" mode below it, and two adjacent modes as well (though pathological at the extreme ends of the modal continuum). The superdiatonic modes also resemble the shape of the meantone diatonic modes somewhat, so that LLLsLLLLs resembles the meantone LLLsLLs Ionian mode, and also 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.<br />
<br />
Since there are only seven diatonic modes, two superdiatonic modes need additional names beyond the usual gamut of options. These two modes present themselves as "mixed" modes, which begin with the LLs tetrachord, and hence contain both the ~300 cent minor third and the ~375 cent major third. 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 -> Corinthian -> Dorian cyclic sequence will resemble the columns of ancient Greek architecture. The one 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 5-limit tonality diamond; it was given the name of Olympian to match its unique status in this regard.</body></html>