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Mavila temperament modal harmony: Difference between revisions

VisualWikitext
Wikispaces>Natebedell
**Imported revision 250975218 - Original comment: **
 
got rid of the horrifically idiosyncratic "patet" stuff and used a more proper mode name system
 
(40 intermediate revisions by 15 users not shown)
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
== Introduction ==
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:Natebedell|Natebedell]] and made on <tt>2011-09-05 19:25:51 UTC</tt>.<br>
: The original revision id was <tt>250975218</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>
<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">==Heptatonic MOS==  


Anti-Lydian
Mavila is the regular temperament eliminating [[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]]) 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].
Anti-Ionian
Anti-Mixolydian
Anti-Dorian
Anti-Aeolian
Anti-Phrygian
Anti-Locrian


==Nonatonic MOS== </pre></div>
=== How to read these charts ===
<h4>Original HTML content:</h4>
* The 6|0, 5|1, 4|2 markings are an instance of [[Modal UDP Notation]].
<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;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-Heptatonic MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Heptatonic MOS&lt;/h2&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;br /&gt;
* Additionally, "diatonic" names make use of the following abbreviations:
Anti-Lydian&lt;br /&gt;
** SM - Supermajor
Anti-Ionian&lt;br /&gt;
** M - Major
Anti-Mixolydian&lt;br /&gt;
** N - Neutral
Anti-Dorian&lt;br /&gt;
** m - Minor
Anti-Aeolian&lt;br /&gt;
** sm - Subminor
Anti-Phrygian&lt;br /&gt;
 
Anti-Locrian&lt;br /&gt;
== 2L 3s Pentatonic MOS: Pentic ==
&lt;br /&gt;
4|0 - LsLss - Jue
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Nonatonic MOS"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Nonatonic MOS&lt;/h2&gt;
 
&lt;/body&gt;&lt;/html&gt;</pre></div>
3|1 - LssLs - Yu
 
2|2 - sLsLs - Shang
 
3|1 - sLssL - Zhi
 
0|4 - ssLsL - Gong
 
In cyclic permutational order: Gong, Shang, Jue, Zhi, Yu
 
=== Transversal ===
 
{| class="wikitable center-all"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
|-
| 4|0
| LsLss
| Jue
| 1/1
| <span style="color: #3F5CDB;">5/4</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #3F5CDB;">5/3</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 3|1
| LssLs
| Yu
| 1/1
| <span style="color: #3F5CDB;">5/4</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 2|2
| sLsLs
| Shang
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 1|3
| sLssL
| Zhi
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #D84F00;">8/5</span>
|-
| 0|4
| ssLsL
| Gong
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">6/5</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #D84F00;">8/5</span>
|}
 
=== Antidiatonic Names ===
 
{| class="wikitable center-all"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
|-
| 4|0
| LsLss
| Jue
| P1
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 3|1
| LssLs
| Yu
| P1
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 2|2
| sLsLs
| Shang
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 1|3
| sLssL
| Zhi
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
|-
| 0|4
| ssLsL
| Gong
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
|}
 
=== Qualities ===
{| class="wikitable center-all"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
|-
| <nowiki>4|0</nowiki>
| LsLss
| Jue
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #3F5CDB;">A</span>
| <span style="color: #3F5CDB;">M</span>
|-
| <nowiki>3|1</nowiki>
| LssLs
| Yu
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">M</span>
|-
| <nowiki>2|2</nowiki>
| sLsLs
| Shang
| P
| <span style="color: #D84F00;">m</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">M</span>
|-
| <nowiki>1|3</nowiki>
| sLssL
| Zhi
| P
| <span style="color: #D84F00;">m</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #D84F00;">m</span>
|-
| <nowiki>0|4</nowiki>
| ssLsL
| Gong
| P
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">d</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #D84F00;">m</span>
|}
 
== 2L 5s Heptatonic MOS: Antidiatonic ==
 
{| class="wikitable"
|-
| 6|0 - LssLsss - Antilocrian
| [[File:MavilaAntidiatonic16edo.mp3]]
|-
| 5|1 - LsssLss - Antiphrygian ("major")
|
|-
| 4|2 - sLssLss - Antiaeolian
|
|-
| 3|3 - sLsssLs - Antidorian
|
|-
| 2|4 - ssLssLs - Antimixolydian ("minor")
|
|-
| 1|5 - ssLsssL - Antiionian
|
|-
| 0|6 - sssLssL - Antiphrygian
|
|}
<span style="line-height: 1.5;">In cyclic permutational order: Ionian | Dorian | Phrygian | Lydian | Mixolydian | Aeolian | Locrian</span>
 
=== Transversal ===
 
{| class="wikitable center-all"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
| 6|0
| LssLsss
| Antilocrian
| 1/1
| <span style="color: #3F5CDB;">8/7</span>
| <span style="color: #3F5CDB;">5/4</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #3F5CDB;">14/9</span>
| <span style="color: #3F5CDB;">5/3</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 5|1
| LsssLss
| Antiphrygian
| 1/1
| <span style="color: #3F5CDB;">8/7</span>
| <span style="color: #3F5CDB;">5/4</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #3F5CDB;">5/3</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 4|2
| sLssLss
| Antiaeolian
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #3F5CDB;">5/4</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #3F5CDB;">5/3</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 3|3
| sLsssLs
| Antidorian
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #3F5CDB;">5/4</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #D84F00;">8/5</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 2|4
| ssLssLs
| Antimixolydian
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">6/5</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #D84F00;">8/5</span>
| <span style="color: #3F5CDB;">11/6</span>
|-
| 1|5
| ssLsssL
| Antiionian
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">6/5</span>
| <span style="color: #3F5CDB;">4/3</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #D84F00;">8/5</span>
| <span style="color: #D84F00;">7/4</span>
|-
| 0|6
| sssLssL
| Antilydian
| 1/1
| <span style="color: #D84F00;">12/11</span>
| <span style="color: #D84F00;">6/5</span>
| <span style="color: #D84F00;">9/7</span>
| <span style="color: #D84F00;">3/2</span>
| <span style="color: #D84F00;">8/5</span>
| <span style="color: #D84F00;">7/4</span>
|}
 
=== Antidiatonic Names ===
 
{| class="wikitable center-all"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
! 6
! 7
|-
| 6|0
| LssLsss
| Antilocrian
| P1
| <span style="color: #3F5CDB;">M2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #3F5CDB;">A5</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 5|1
| LsssLss
| Antiphrygian
| P1
| <span style="color: #3F5CDB;">M2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 4|2
| sLssLss
| Antiaeolian
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #3F5CDB;">M6</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 3|3
| sLsssLs
| Antidorian
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #3F5CDB;">M3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 2|4
| ssLssLs
| Antimixolydian
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #3F5CDB;">M7</span>
|-
| 1|5
| ssLsssL
| Antiionian
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #3F5CDB;">P4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">m7</span>
|-
| 0|6
| sssLssL
| Antilydian
| P1
| <span style="color: #D84F00;">m2</span>
| <span style="color: #D84F00;">m3</span>
| <span style="color: #D84F00;">d4</span>
| <span style="color: #D84F00;">P5</span>
| <span style="color: #D84F00;">m6</span>
| <span style="color: #D84F00;">m7</span>
|}
 
== 7L 2s Nonatonic MOS: Superdiatonic ==
 
{| class="wikitable"
|-
| <nowiki>8|0 - LLLLsLLLs - Superlydian</nowiki>
|
|-
| <nowiki>7|1 - LLLsLLLLs - Adlocrian</nowiki>
|
|-
| <nowiki>6|2 - LLLsLLLsL - Adphrygian</nowiki>
|
|-
| <nowiki>5|3 - LLsLLLLsL - Adaeolian</nowiki>
|
|-
| <nowiki>4|4 - LLsLLLsLL - Addorian</nowiki>
| [[File:MavilaOlympian16edo.mp3]]
|-
| <nowiki>3|5 - LsLLLLsLL - Admixolydian</nowiki>
|
|-
| <nowiki>2|6 - LsLLLsLLL - Adionian</nowiki>
|
|-
| <nowiki>1|7 - sLLLLsLLL - Adlydian</nowiki>
|
|-
| <nowiki>0|8 - sLLLsLLLL - Superlocrian</nowiki>
| [[File:MavilaSuperdiatonic16edo.mp3]]
|}
 
In cyclic permutational order: Adlocrian - Adaeolian - Admixolydian - Adlydian - Superlydian - Adphrygian - Addorian - Adionian - Superlocrian
 
=== Transversal ===
 
{| class="wikitable"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
|-
| <nowiki>8|0</nowiki>
| LLLLsLLLs
| Superlydian
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">6/5</span>
| <span style="color: #3F5CDB;">9/7</span>
| <span style="color: #3F5CDB;">7/5</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #3F5CDB;">8/5</span>
| <span style="color: #3F5CDB;">7/4</span>
| <span style="color: #3F5CDB;">21/11</span>
|-
| <nowiki>7|1</nowiki>
| LLLsLLLLs
| Adlocrian
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">6/5</span>
| <span style="color: #3F5CDB;">9/7</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #3F5CDB;">8/5</span>
| <span style="color: #3F5CDB;">7/4</span>
| <span style="color: #3F5CDB;">21/11</span>
|-
| <nowiki>6|2</nowiki>
| LLLsLLLsL
| Adphrygian
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">6/5</span>
| <span style="color: #3F5CDB;">9/7</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #3F5CDB;">8/5</span>
| <span style="color: #3F5CDB;">7/4</span>
| <span style="color: #D84F00;">11/6</span>
|-
| <nowiki>5|3</nowiki>
| LLsLLLLsL
| Adaeolian
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">6/5</span>
| <span style="color: #D84F00;">5/4</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #3F5CDB;">8/5</span>
| <span style="color: #3F5CDB;">7/4</span>
| <span style="color: #D84F00;">11/6</span>
|-
| <nowiki>4|4</nowiki>
| LLsLLLsLL
| Addorian
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #3F5CDB;">6/5</span>
| <span style="color: #D84F00;">5/4</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #3F5CDB;">8/5</span>
| <span style="color: #D84F00;">5/3</span>
| <span style="color: #D84F00;">11/6</span>
|-
| <nowiki>3|5</nowiki>
| LsLLLLsLL
| Admixolydian
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #D84F00;">8/7</span>
| <span style="color: #D84F00;">5/4</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #3F5CDB;">8/5</span>
| <span style="color: #D84F00;">5/3</span>
| <span style="color: #D84F00;">11/6</span>
|-
| <nowiki>2|6</nowiki>
| LsLLLsLLL
| Adionian
| 1/1
| <span style="color: #3F5CDB;">12/11</span>
| <span style="color: #D84F00;">8/7</span>
| <span style="color: #D84F00;">5/4</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #D84F00;">14/9</span>
| <span style="color: #D84F00;">5/3</span>
| <span style="color: #D84F00;">11/6</span>
|-
| <nowiki>1|7</nowiki>
| sLLLLsLLL
| Adlydian
| 1/1
| <span style="color: #D84F00;">22/21</span>
| <span style="color: #D84F00;">8/7</span>
| <span style="color: #D84F00;">5/4</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #3F5CDB;">3/2</span>
| <span style="color: #D84F00;">14/9</span>
| <span style="color: #D84F00;">5/3</span>
| <span style="color: #D84F00;">11/6</span>
|-
| <nowiki>0|8</nowiki>
| sLLLsLLLL
| Superlocrian
| 1/1
| <span style="color: #D84F00;">22/21</span>
| <span style="color: #D84F00;">8/7</span>
| <span style="color: #D84F00;">5/4</span>
| <span style="color: #D84F00;">4/3</span>
| <span style="color: #D84F00;">10/7</span>
| <span style="color: #D84F00;">14/9</span>
| <span style="color: #D84F00;">5/3</span>
| <span style="color: #D84F00;">11/6</span>
|}
 
=== "Diatonic" Names ===
 
{| class="wikitable center-all"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
|-
| <nowiki>8|0</nowiki>
| LLLLsLLLs
| Superlydian
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">m3</span>
| <span style="color: #3F5CDB;">SM3</span>
| <span style="color: #3F5CDB;">A4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #3F5CDB;">m6</span>
| <span style="color: #3F5CDB;">(s)m7</span>
| <span style="color: #3F5CDB;">(S)M7</span>
|-
| <nowiki>7|1</nowiki>
| LLLsLLLLs
| Adlocrian
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">m3</span>
| <span style="color: #3F5CDB;">SM3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #3F5CDB;">m6</span>
| <span style="color: #3F5CDB;">(s)m7</span>
| <span style="color: #3F5CDB;">(S)M7</span>
|-
| <nowiki>6|2</nowiki>
| LLLsLLLsL
| Adphrygian
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">m3</span>
| <span style="color: #3F5CDB;">SM3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #3F5CDB;">m6</span>
| <span style="color: #3F5CDB;">(s)m7</span>
| <span style="color: #D84F00;">N7</span>
|-
| <nowiki>5|3</nowiki>
| LLsLLLLsL
| Adaeolian
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">m3</span>
| <span style="color: #D84F00;">M3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #3F5CDB;">m6</span>
| <span style="color: #3F5CDB;">(s)m7</span>
| <span style="color: #D84F00;">N7</span>
|-
| <nowiki>4|4</nowiki>
| LLsLLLsLL
| Addorian
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #3F5CDB;">m3</span>
| <span style="color: #D84F00;">M3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #3F5CDB;">m6</span>
| <span style="color: #D84F00;">M6</span>
| <span style="color: #D84F00;">N7</span>
|-
| <nowiki>3|5</nowiki>
| LsLLLLsLL
| Admixolydian
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #D84F00;">(S)M2</span>
| <span style="color: #D84F00;">M3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #3F5CDB;">m6</span>
| <span style="color: #D84F00;">M6</span>
| <span style="color: #D84F00;">N7</span>
|-
| <nowiki>2|6</nowiki>
| LsLLLsLLL
| Adionian
| P1
| <span style="color: #3F5CDB;">N2</span>
| <span style="color: #D84F00;">(S)M2</span>
| <span style="color: #D84F00;">M3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #D84F00;">sm6</span>
| <span style="color: #D84F00;">M6</span>
| <span style="color: #D84F00;">N7</span>
|-
| <nowiki>1|7</nowiki>
| sLLLLsLLL
| Adlydian
| P1
| <span style="color: #D84F00;">(s)m2</span>
| <span style="color: #D84F00;">(S)M2</span>
| <span style="color: #D84F00;">M3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #3F5CDB;">P5</span>
| <span style="color: #D84F00;">sm6</span>
| <span style="color: #D84F00;">M6</span>
| <span style="color: #D84F00;">N7</span>
|-
| <nowiki>0|8</nowiki>
| sLLLsLLLL
| Superlocrian
| P1
| <span style="color: #D84F00;">(s)m2</span>
| <span style="color: #D84F00;">(S)M2</span>
| <span style="color: #D84F00;">M3</span>
| <span style="color: #D84F00;">P4</span>
| <span style="color: #D84F00;">d5</span>
| <span style="color: #D84F00;">sm6</span>
| <span style="color: #D84F00;">M6</span>
| <span style="color: #D84F00;">N7</span>
|}
 
=== Superdiatonic Qualities ===
{| class="wikitable center-all"
|-
! UDP
! Imprint
! Name
! 1
! 2
! 3
! 4
! 5
! 6
! 7
! 8
! 9
|-
| <nowiki>8|0</nowiki>
|  LLLLsLLLs
| Superlydian
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">A</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
|-
| <nowiki>7|1</nowiki>
| LLLsLLLLs
|  Adlocrian
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
|-
| <nowiki>6|2</nowiki>
| LLLsLLLsL
|  Adphrygian
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
|-
| <nowiki>5|3</nowiki>
| LLsLLLLsL
| Adaeolian
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
|-
| <nowiki>4|4</nowiki>
| LLsLLLsLL
| Addorian
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
|-
| <nowiki>3|5</nowiki>
| LsLLLLsLL
| Admixolydian
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
|-
| <nowiki>2|6</nowiki>
| LsLLLsLLL
| Adionian
| P
| <span style="color: #3F5CDB;">M</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
|-
| <nowiki>1|7</nowiki>
| sLLLLsLLL
| Adlydian
| P
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #3F5CDB;">P</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
|-
| <nowiki>0|8</nowiki>
| sLLLsLLLL
| Superlocrian
| P
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">P</span>
| <span style="color: #D84F00;">d</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
| <span style="color: #D84F00;">m</span>
|}
 
== Notes on Naming ==
 
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 LLsLLLs 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-Locrian 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. 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.
 
[[Category:Mavila]]
[[Category:Modes]]
[[Category:Essays]]
Retrieved from "https://en.xen.wiki/w/Mavila_temperament_modal_harmony"