Maqamat in maqamic temperament: Difference between revisions

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D Ev F G A Bb C D

Maqam Bayati and Makam Uşşak can both be identified with maqamic[7] 2|4 b3 b6 (ssLLdLL).

===Potential for 11-limit harmony===

Ev is the only "quarter tone", so the only 11-limit chords are those that include Ev.

* Ev is the 12/11~11/10 of D, so on D there is a nice 10:11:12:15:18 chord (a minor chord where Ev is a neutral second)

* Ev is the 11/6 of F, so on F there are interesting chords like 6:9:11 or 6:9:10:11.

* Ev is the 13/8 of G (in mohoho temperament), so on G there is a 8:9:12:13 chord and also the chord G Bb D Ev (minor w/ neutral sixth)

* Ev is the half-diminished fifth of A, so the chords on A are quite dissonant.

* Ev is the 11/8 of Bb, so on Bb there is a complete 8:9:10:11:12(:15) otonality. Obviously this could be quite a powerful chord.

* Ev is the 11/9 of C, so there are neutral chords on C (between major and minor).

==Hijaz==

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D Eb F# G A Bb C D

Maqam Hijaz has two forms, one which can be identified with meantone[7] 1|5 #3 (meantone phrygian dominant), and another which differs by having a neutral sixth degree instead of a minor sixth.

===Potential for 11-limit harmony===

Bv is the only "quarter tone", so the only 11-limit chords are those that include Bv.

* Bv is the 13/8 of D (in mohoho temperament), and there is a 8:10:12:13 chord on D.

* Bv is the half-augmented fifth of Eb, so the chords on Eb are quite dissonant.

* Bv is the half-diminished fourth of F#, which is fairly dissonant (it represents 13/10 in mohoho).

* Bv is the 11/9 of G, so there are neutral chords on G.

* Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).

* Bv is the 11/6 of C, so there are 6:9:11 and 6:9:10:11 chords on C.

==Hijaz Kar==

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C D Ev F G A Bb C

Maqam Rast has two forms, one that can be identified with maqamic[7] 2|4 #6 (equivalently maqamic[7] 0|6 b4), and another form with a minor seventh degree rather than a neutral seventh.

===Potential for 11-limit harmony===

Ev and Bv are both "quarter tones" so 11-limit chords could include either of them.

* Ev is the 11/9 of C, so the tonic chord is neutral (neither major nor minor). There is also a neutral seventh chord, C Ev G Bv.

* Ev is the 12/11~11/10 of D, so there is a nice 10:11:12:15:18 chord on D.

* Ev is the 11/6 of F, so there are 6:9:11 and 6:9:10:11 chords on F.

* Ev is the 13/8 of G (in mohoho temperament), and there is a 8:9:12:13 chord on G. There is also a neutral sixth chord, G Bv D Ev.

* Ev is the half-diminished fifth of A, so chords on A are quite dissonant.

* Ev is the 11/8 of Bb, and there is a complete 8:9:10:11:12(:15) otonality on Bb.

* Chords with Ev and Bv as the root and fifth are very interesting because the root is on a "quarter tone". There is a neutral triad, and a nice 8:11:12:13 chord on Ev.

* Bv is the 11/6 of C, and there are 6:9:11 and 6:9:10:11 chords on C as well as the neutral seventh chord.

* Bv is the 13/8 of D (in mohoho temperament) and there is a 8:12:13 chord on D as well as D F A Bv which is a minor w/ neutral sixth.

* Bv is the 11/8 of F, and there is a complete 8:9:10:11:12 otonality on F.

* Bv is the 11/9 of G, so there are neutral chords on G.

* Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).

==Saba==

D Ev F Gb A Bb C D

Maqam Saba can be identified with maqamic[7] 0|6 bb4 #5 b6, or equivalently maqamic[7] 2|4 b3 bb4 b6. This is a rather complex MODMOS (but it sounds awesome).

===Weird form of Saba===

D Ev F Gb A Bb C Db E F

This alternate form of Saba "doesn't include the octave of the tonic", and includes another non-octave as well (Ev-E). It could possibly be thought of as a scale with more than 7 notes, but it's unclear to what extent it's used this way in traditional music.

===Potential for 11-limit harmony===

==Sikah==

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Maqam Sikah has by far the largest number of neutral scale degrees relative to the tonic.

===Potential for 11-limit harmony===

=UNDER CONSTRUCTION=

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<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"><html><head><title>Maqamat in maqamic temperament</title></head><body><h1 id="toc0"><a name="Introduction"></a>Introduction</h1>

Maqamat (singular &quot;maqam&quot;) are scale-like abstractions in <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, and Persian</a> music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the &quot;central&quot; or &quot;canonical&quot; pitches for each note of a maqam. See <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/101523" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/101523</a> for an explanation of the level of abstraction being used here.<br />

Maqamat (singular &quot;maqam&quot;) are scale-like abstractions in <a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, and Persian</a> music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the &quot;central&quot; or &quot;canonical&quot; pitches for each note of a maqam. See <a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/101523" rel="nofollow">http://launch.groups.yahoo.com/group/tuning/message/101523</a> for an explanation of the level of abstraction being used here.<br />

<br />

Other theorists have developed completely different and often very complicated regular temperament structures to accomodate maqamat. This article is based on a simple rank-2 temperament known variously as &quot;2.3.5.11 <a class="wiki_link" href="/maqamic">maqamic</a>&quot;, or &quot;2.3.5.11 <a class="wiki_link" href="/Meantone%20family#Mohajira">mohajira</a>&quot;, or &quot;<a class="wiki_link" href="/Chromatic%20pairs#Mohaha">mohaha</a>&quot;. Whatever its name, it is the 2.3.5.11 temperament that tempers out 81/80, 121/120, and 243/242. This means that every other note in the generator chain is meantone, and the fifth generator is split into two equal &quot;neutral thirds&quot; that represent 11/9. An interval is 5-limit if and only if the number of generators needed to reach it is even. Therefore &quot;quarter tones&quot; (i.e. intervals outside meantone) and &quot;intervals outside the 5 limit&quot; are identified in this temperament. See <a class="wiki_link" href="/Neutral%20third%20scales">Neutral third scales</a> for more information.<br />

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D Ev F G A Bb C D<br />

Maqam Bayati and Makam Uşşak can both be identified with maqamic[7] 2|4 b3 b6 (ssLLdLL).<br />

<br />

<h3 id="toc18"><a name="Maqamat-Bayati/Uşşak-Potential for 11-limit harmony"></a>Potential for 11-limit harmony</h3>

<h2 id="~~toc18~~"><a name="Maqamat-Hijaz"></a>Hijaz</h2>

Ev is the only &quot;quarter tone&quot;, so the only 11-limit chords are those that include Ev.<br />

<ul><li>Ev is the 12/11~11/10 of D, so on D there is a nice 10:11:12:15:18 chord (a minor chord where Ev is a neutral second)</li><li>Ev is the 11/6 of F, so on F there are interesting chords like 6:9:11 or 6:9:10:11.</li><li>Ev is the 13/8 of G (in mohoho temperament), so on G there is a 8:9:12:13 chord and also the chord G Bb D Ev (minor w/ neutral sixth)</li><li>Ev is the half-diminished fifth of A, so the chords on A are quite dissonant.</li><li>Ev is the 11/8 of Bb, so on Bb there is a complete 8:9:10:11:12(:15) otonality. Obviously this could be quite a powerful chord.</li><li>Ev is the 11/9 of C, so there are neutral chords on C (between major and minor).</li></ul><br />

<h2 id="toc19"><a name="Maqamat-Hijaz"></a>Hijaz</h2>

D Eb F# G A Bv C D<br />

D Eb F# G A Bb C D<br />

Maqam Hijaz has two forms, one which can be identified with meantone[7] 1|5 #3 (meantone phrygian dominant), and another which differs by having a neutral sixth degree instead of a minor sixth.<br />

<br />

<h3 id="toc20"><a name="Maqamat-Hijaz-Potential for 11-limit harmony"></a>Potential for 11-limit harmony</h3>

<h2 id="~~toc19~~"><a name="Maqamat-Hijaz Kar"></a>Hijaz Kar</h2>

Bv is the only &quot;quarter tone&quot;, so the only 11-limit chords are those that include Bv.<br />

<ul><li>Bv is the 13/8 of D (in mohoho temperament), and there is a 8:10:12:13 chord on D.</li><li>Bv is the half-augmented fifth of Eb, so the chords on Eb are quite dissonant.</li><li>Bv is the half-diminished fourth of F#, which is fairly dissonant (it represents 13/10 in mohoho).</li><li>Bv is the 11/9 of G, so there are neutral chords on G.</li><li>Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).</li><li>Bv is the 11/6 of C, so there are 6:9:11 and 6:9:10:11 chords on C.</li></ul><br />

<h2 id="toc21"><a name="Maqamat-Hijaz Kar"></a>Hijaz Kar</h2>

C Db E F G Ab B C<br />

Maqam Hijaz Kar can be identified with meantone[7] 5|1 b2 b6 (equivalently meantone[7] 1|5 #3 #7). This is also known as the meantone &quot;double harmonic scale&quot; or simply &quot;Arabic scale&quot;.<br />

<br />

<h2 id="~~toc20~~"><a name="Maqamat-Kurd"></a>Kurd</h2>

<h2 id="toc22"><a name="Maqamat-Kurd"></a>Kurd</h2>

D Eb F G A Bb C D<br />

Maqam Kurd can be identified with the meantone Phrygian scale, meantone[7] 1|5.<br />

<br />

<h2 id="~~toc21~~"><a name="Maqamat-Nahawand"></a>Nahawand</h2>

<h2 id="toc23"><a name="Maqamat-Nahawand"></a>Nahawand</h2>

C D Eb F G Ab B C<br />

C D Eb F G Ab Bb C<br />

Almost exactly like the meantone natural minor / harmonic minor scale pair, Maqam Nahawand has two forms, meantone aeolian (meantone[7] 4|2) and meantone harmonic minor (meantone[7] 4|2 #7). In other words Maqam Nahawand is the same as meantone natural minor with a major seventh as an alternate.<br />

<br />

<h2 id="~~toc22~~"><a name="Maqamat-Rast"></a>Rast</h2>

<h2 id="toc24"><a name="Maqamat-Rast"></a>Rast</h2>

C D Ev F G A Bv C<br />

C D Ev F G A Bb C<br />

Maqam Rast has two forms, one that can be identified with maqamic[7] 2|4 #6 (equivalently maqamic[7] 0|6 b4), and another form with a minor seventh degree rather than a neutral seventh.<br />

<br />

<h3 id="toc25"><a name="Maqamat-Rast-Potential for 11-limit harmony"></a>Potential for 11-limit harmony</h3>

<h2 id="~~toc23~~"><a name="Maqamat-Saba"></a>Saba</h2>

Ev and Bv are both &quot;quarter tones&quot; so 11-limit chords could include either of them.<br />

<ul><li>Ev is the 11/9 of C, so the tonic chord is neutral (neither major nor minor). There is also a neutral seventh chord, C Ev G Bv.</li><li>Ev is the 12/11~11/10 of D, so there is a nice 10:11:12:15:18 chord on D.</li><li>Ev is the 11/6 of F, so there are 6:9:11 and 6:9:10:11 chords on F.</li><li>Ev is the 13/8 of G (in mohoho temperament), and there is a 8:9:12:13 chord on G. There is also a neutral sixth chord, G Bv D Ev.</li><li>Ev is the half-diminished fifth of A, so chords on A are quite dissonant.</li><li>Ev is the 11/8 of Bb, and there is a complete 8:9:10:11:12(:15) otonality on Bb.</li><li>Chords with Ev and Bv as the root and fifth are very interesting because the root is on a &quot;quarter tone&quot;. There is a neutral triad, and a nice 8:11:12:13 chord on Ev.</li><li>Bv is the 11/6 of C, and there are 6:9:11 and 6:9:10:11 chords on C as well as the neutral seventh chord.</li><li>Bv is the 13/8 of D (in mohoho temperament) and there is a 8:12:13 chord on D as well as D F A Bv which is a minor w/ neutral sixth.</li><li>Bv is the 11/8 of F, and there is a complete 8:9:10:11:12 otonality on F.</li><li>Bv is the 11/9 of G, so there are neutral chords on G.</li><li>Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).</li></ul><br />

<h2 id="toc26"><a name="Maqamat-Saba"></a>Saba</h2>

D Ev F Gb A Bb C D<br />

Maqam Saba can be identified with maqamic[7] 0|6 bb4 #5 b6, or equivalently maqamic[7] 2|4 b3 bb4 b6. This is a rather complex MODMOS (but it sounds awesome).<br />

~~<br />~~

<h3 id="toc27"><a name="Maqamat-Saba-Weird form of Saba"></a>Weird form of Saba</h3>

<h3 id="~~toc24~~"><a name="Maqamat-Saba-Weird form of Saba"></a>Weird form of Saba</h3>

D Ev F Gb A Bb C Db E F<br />

This alternate form of Saba &quot;doesn't include the octave of the tonic&quot;, and includes another non-octave as well (Ev-E). It could possibly be thought of as a scale with more than 7 notes, but it's unclear to what extent it's used this way in traditional music.<br />

<h3 id="toc28"><a name="Maqamat-Saba-Potential for 11-limit harmony"></a>Potential for 11-limit harmony</h3>

<br />

<h2 id="~~toc25~~"><a name="Maqamat-Sikah"></a>Sikah</h2>

<h2 id="toc29"><a name="Maqamat-Sikah"></a>Sikah</h2>

Ev F G A Bv C D Ev<br />

Ev F G A Bb C D Ev<br />

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<br />

Maqam Sikah has by far the largest number of neutral scale degrees relative to the tonic.<br />

<h3 id="toc30"><a name="Maqamat-Sikah-Potential for 11-limit harmony"></a>Potential for 11-limit harmony</h3>

<br />

<h1 id="~~toc26~~"><a name="UNDER CONSTRUCTION"></a>UNDER CONSTRUCTION</h1>

<h1 id="toc31"><a name="UNDER CONSTRUCTION"></a>UNDER CONSTRUCTION</h1>

<br />

d (minor), s (neutral), L (major), ? (half-augmented), A (augmented)<br />

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2012-12-15 11:18:43 UTC</tt>.<br>
+: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2012-12-15 16:37:22 UTC</tt>.<br>
-: The original revision id was <tt>392560624</tt>.<br>
+: The original revision id was <tt>392603912</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>
@@ Line 87: / Line 87: @@
 D Ev F G A Bb C D
 Maqam Bayati and Makam Uşşak can both be identified with maqamic[7] 2|4 b3 b6 (ssLLdLL).
+===Potential for 11-limit harmony===
+Ev is the only "quarter tone", so the only 11-limit chords are those that include Ev.
+* Ev is the 12/11~11/10 of D, so on D there is a nice 10:11:12:15:18 chord (a minor chord where Ev is a neutral second)
+* Ev is the 11/6 of F, so on F there are interesting chords like 6:9:11 or 6:9:10:11.
+* Ev is the 13/8 of G (in mohoho temperament), so on G there is a 8:9:12:13 chord and also the chord G Bb D Ev (minor w/ neutral sixth)
+* Ev is the half-diminished fifth of A, so the chords on A are quite dissonant.
+* Ev is the 11/8 of Bb, so on Bb there is a complete 8:9:10:11:12(:15) otonality. Obviously this could be quite a powerful chord.
+* Ev is the 11/9 of C, so there are neutral chords on C (between major and minor).
 ==Hijaz==
@@ Line 92: / Line 100: @@
 D Eb F# G A Bb C D
 Maqam Hijaz has two forms, one which can be identified with meantone[7] 1|5 #3 (meantone phrygian dominant), and another which differs by having a neutral sixth degree instead of a minor sixth.
+===Potential for 11-limit harmony===
+Bv is the only "quarter tone", so the only 11-limit chords are those that include Bv.
+* Bv is the 13/8 of D (in mohoho temperament), and there is a 8:10:12:13 chord on D.
+* Bv is the half-augmented fifth of Eb, so the chords on Eb are quite dissonant.
+* Bv is the half-diminished fourth of F#, which is fairly dissonant (it represents 13/10 in mohoho).
+* Bv is the 11/9 of G, so there are neutral chords on G.
+* Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).
+* Bv is the 11/6 of C, so there are 6:9:11 and 6:9:10:11 chords on C.
 ==Hijaz Kar==
@@ Line 110: / Line 126: @@
 C D Ev F G A Bb C
 Maqam Rast has two forms, one that can be identified with maqamic[7] 2|4 #6 (equivalently maqamic[7] 0|6 b4), and another form with a minor seventh degree rather than a neutral seventh.
+===Potential for 11-limit harmony===
+Ev and Bv are both "quarter tones" so 11-limit chords could include either of them.
+* Ev is the 11/9 of C, so the tonic chord is neutral (neither major nor minor). There is also a neutral seventh chord, C Ev G Bv.
+* Ev is the 12/11~11/10 of D, so there is a nice 10:11:12:15:18 chord on D.
+* Ev is the 11/6 of F, so there are 6:9:11 and 6:9:10:11 chords on F.
+* Ev is the 13/8 of G (in mohoho temperament), and there is a 8:9:12:13 chord on G. There is also a neutral sixth chord, G Bv D Ev.
+* Ev is the half-diminished fifth of A, so chords on A are quite dissonant.
+* Ev is the 11/8 of Bb, and there is a complete 8:9:10:11:12(:15) otonality on Bb.
+* Chords with Ev and Bv as the root and fifth are very interesting because the root is on a "quarter tone". There is a neutral triad, and a nice 8:11:12:13 chord on Ev.
+* Bv is the 11/6 of C, and there are 6:9:11 and 6:9:10:11 chords on C as well as the neutral seventh chord.
+* Bv is the 13/8 of D (in mohoho temperament) and there is a 8:12:13 chord on D as well as D F A Bv which is a minor w/ neutral sixth.
+* Bv is the 11/8 of F, and there is a complete 8:9:10:11:12 otonality on F.
+* Bv is the 11/9 of G, so there are neutral chords on G.
+* Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).
 ==Saba==
 D Ev F Gb A Bb C D
 Maqam Saba can be identified with maqamic[7] 0|6 bb4 #5 b6, or equivalently maqamic[7] 2|4 b3 bb4 b6. This is a rather complex MODMOS (but it sounds awesome).
 ===Weird form of Saba===
 D Ev F Gb A Bb C Db E F
 This alternate form of Saba "doesn't include the octave of the tonic", and includes another non-octave as well (Ev-E). It could possibly be thought of as a scale with more than 7 notes, but it's unclear to what extent it's used this way in traditional music.
+===Potential for 11-limit harmony===
 ==Sikah==
@@ Line 125: / Line 155: @@
 Maqam Sikah has by far the largest number of neutral scale degrees relative to the tonic.
+===Potential for 11-limit harmony===
 =UNDER CONSTRUCTION=
@@ Line 141: / Line 172: @@
 <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;Maqamat in maqamic temperament&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;
-  Maqamat (singular &amp;quot;maqam&amp;quot;) are scale-like abstractions in &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic, Turkish, and Persian&lt;/a&gt; music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the &amp;quot;central&amp;quot; or &amp;quot;canonical&amp;quot; pitches for each note of a maqam. See &lt;!-- ws:start:WikiTextUrlRule:174:http://launch.groups.yahoo.com/group/tuning/message/101523 --&gt;&lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/101523" rel="nofollow"&gt;http://launch.groups.yahoo.com/group/tuning/message/101523&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:174 --&gt; for an explanation of the level of abstraction being used here.&lt;br /&gt;
+  Maqamat (singular &amp;quot;maqam&amp;quot;) are scale-like abstractions in &lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic, Turkish, and Persian&lt;/a&gt; music. This article, for the most part, treats maqamat simply as scales and disregards everything else about them (emotional connotation, melodic idioms, emphasized pitches...). Also note that in performance, depending on the instrument, a wide variety of subtle microtonal inflections may be used, rather than sticking rigidly to the pitches of a scale. This article deals with only the &amp;quot;central&amp;quot; or &amp;quot;canonical&amp;quot; pitches for each note of a maqam. See &lt;!-- ws:start:WikiTextUrlRule:240:http://launch.groups.yahoo.com/group/tuning/message/101523 --&gt;&lt;a class="wiki_link_ext" href="http://launch.groups.yahoo.com/group/tuning/message/101523" rel="nofollow"&gt;http://launch.groups.yahoo.com/group/tuning/message/101523&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:240 --&gt; for an explanation of the level of abstraction being used here.&lt;br /&gt;
 &lt;br /&gt;
 Other theorists have developed completely different and often very complicated regular temperament structures to accomodate maqamat. This article is based on a simple rank-2 temperament known variously as &amp;quot;2.3.5.11 &lt;a class="wiki_link" href="/maqamic"&gt;maqamic&lt;/a&gt;&amp;quot;, or &amp;quot;2.3.5.11 &lt;a class="wiki_link" href="/Meantone%20family#Mohajira"&gt;mohajira&lt;/a&gt;&amp;quot;, or &amp;quot;&lt;a class="wiki_link" href="/Chromatic%20pairs#Mohaha"&gt;mohaha&lt;/a&gt;&amp;quot;. Whatever its name, it is the 2.3.5.11 temperament that tempers out 81/80, 121/120, and 243/242. This means that every other note in the generator chain is meantone, and the fifth generator is split into two equal &amp;quot;neutral thirds&amp;quot; that represent 11/9. An interval is 5-limit if and only if the number of generators needed to reach it is even. Therefore &amp;quot;quarter tones&amp;quot; (i.e. intervals outside meantone) and &amp;quot;intervals outside the 5 limit&amp;quot; are identified in this temperament. See &lt;a class="wiki_link" href="/Neutral%20third%20scales"&gt;Neutral third scales&lt;/a&gt; for more information.&lt;br /&gt;
@@ Line 218: / Line 249: @@
   D Ev F G A Bb C D&lt;br /&gt;
 Maqam Bayati and Makam Uşşak can both be identified with maqamic[7] 2|4 b3 b6 (ssLLdLL).&lt;br /&gt;
-&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Maqamat-Bayati/Uşşak-Potential for 11-limit harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Potential for 11-limit harmony&lt;/h3&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc18"&gt;&lt;a name="Maqamat-Hijaz"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Hijaz&lt;/h2&gt;
+ Ev is the only &amp;quot;quarter tone&amp;quot;, so the only 11-limit chords are those that include Ev.&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Ev is the 12/11~11/10 of D, so on D there is a nice 10:11:12:15:18 chord (a minor chord where Ev is a neutral second)&lt;/li&gt;&lt;li&gt;Ev is the 11/6 of F, so on F there are interesting chords like 6:9:11 or 6:9:10:11.&lt;/li&gt;&lt;li&gt;Ev is the 13/8 of G (in mohoho temperament), so on G there is a 8:9:12:13 chord and also the chord G Bb D Ev (minor w/ neutral sixth)&lt;/li&gt;&lt;li&gt;Ev is the half-diminished fifth of A, so the chords on A are quite dissonant.&lt;/li&gt;&lt;li&gt;Ev is the 11/8 of Bb, so on Bb there is a complete 8:9:10:11:12(:15) otonality. Obviously this could be quite a powerful chord.&lt;/li&gt;&lt;li&gt;Ev is the 11/9 of C, so there are neutral chords on C (between major and minor).&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Maqamat-Hijaz"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Hijaz&lt;/h2&gt;
   D Eb F# G A Bv C D&lt;br /&gt;
 D Eb F# G A Bb C D&lt;br /&gt;
 Maqam Hijaz has two forms, one which can be identified with meantone[7] 1|5 #3 (meantone phrygian dominant), and another which differs by having a neutral sixth degree instead of a minor sixth.&lt;br /&gt;
-&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc20"&gt;&lt;a name="Maqamat-Hijaz-Potential for 11-limit harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Potential for 11-limit harmony&lt;/h3&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:38:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc19"&gt;&lt;a name="Maqamat-Hijaz Kar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:38 --&gt;Hijaz Kar&lt;/h2&gt;
+ Bv is the only &amp;quot;quarter tone&amp;quot;, so the only 11-limit chords are those that include Bv.&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Bv is the 13/8 of D (in mohoho temperament), and there is a 8:10:12:13 chord on D.&lt;/li&gt;&lt;li&gt;Bv is the half-augmented fifth of Eb, so the chords on Eb are quite dissonant.&lt;/li&gt;&lt;li&gt;Bv is the half-diminished fourth of F#, which is fairly dissonant (it represents 13/10 in mohoho).&lt;/li&gt;&lt;li&gt;Bv is the 11/9 of G, so there are neutral chords on G.&lt;/li&gt;&lt;li&gt;Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).&lt;/li&gt;&lt;li&gt;Bv is the 11/6 of C, so there are 6:9:11 and 6:9:10:11 chords on C.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Maqamat-Hijaz Kar"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Hijaz Kar&lt;/h2&gt;
   C Db E F G Ab B C&lt;br /&gt;
 Maqam Hijaz Kar can be identified with meantone[7] 5|1 b2 b6 (equivalently meantone[7] 1|5 #3 #7). This is also known as the meantone &amp;quot;double harmonic scale&amp;quot; or simply &amp;quot;Arabic scale&amp;quot;.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:40:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc20"&gt;&lt;a name="Maqamat-Kurd"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:40 --&gt;Kurd&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Maqamat-Kurd"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Kurd&lt;/h2&gt;
   D Eb F G A Bb C D&lt;br /&gt;
 Maqam Kurd can be identified with the meantone Phrygian scale, meantone[7] 1|5.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:42:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc21"&gt;&lt;a name="Maqamat-Nahawand"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:42 --&gt;Nahawand&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Maqamat-Nahawand"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Nahawand&lt;/h2&gt;
   C D Eb F G Ab B C&lt;br /&gt;
 C D Eb F G Ab Bb C&lt;br /&gt;
 Almost exactly like the meantone natural minor / harmonic minor scale pair, Maqam Nahawand has two forms, meantone aeolian (meantone[7] 4|2) and meantone harmonic minor (meantone[7] 4|2 #7). In other words Maqam Nahawand is the same as meantone natural minor with a major seventh as an alternate.&lt;br /&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:44:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc22"&gt;&lt;a name="Maqamat-Rast"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:44 --&gt;Rast&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc24"&gt;&lt;a name="Maqamat-Rast"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Rast&lt;/h2&gt;
   C D Ev F G A Bv C&lt;br /&gt;
 C D Ev F G A Bb C&lt;br /&gt;
 Maqam Rast has two forms, one that can be identified with maqamic[7] 2|4 #6 (equivalently maqamic[7] 0|6 b4), and another form with a minor seventh degree rather than a neutral seventh.&lt;br /&gt;
-&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc25"&gt;&lt;a name="Maqamat-Rast-Potential for 11-limit harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Potential for 11-limit harmony&lt;/h3&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:46:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc23"&gt;&lt;a name="Maqamat-Saba"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:46 --&gt;Saba&lt;/h2&gt;
+Ev and Bv are both &amp;quot;quarter tones&amp;quot; so 11-limit chords could include either of them.&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Ev is the 11/9 of C, so the tonic chord is neutral (neither major nor minor). There is also a neutral seventh chord, C Ev G Bv.&lt;/li&gt;&lt;li&gt;Ev is the 12/11~11/10 of D, so there is a nice 10:11:12:15:18 chord on D.&lt;/li&gt;&lt;li&gt;Ev is the 11/6 of F, so there are 6:9:11 and 6:9:10:11 chords on F.&lt;/li&gt;&lt;li&gt;Ev is the 13/8 of G (in mohoho temperament), and there is a 8:9:12:13 chord on G. There is also a neutral sixth chord, G Bv D Ev.&lt;/li&gt;&lt;li&gt;Ev is the half-diminished fifth of A, so chords on A are quite dissonant.&lt;/li&gt;&lt;li&gt;Ev is the 11/8 of Bb, and there is a complete 8:9:10:11:12(:15) otonality on Bb.&lt;/li&gt;&lt;li&gt;Chords with Ev and Bv as the root and fifth are very interesting because the root is on a &amp;quot;quarter tone&amp;quot;. There is a neutral triad, and a nice 8:11:12:13 chord on Ev.&lt;/li&gt;&lt;li&gt;Bv is the 11/6 of C, and there are 6:9:11 and 6:9:10:11 chords on C as well as the neutral seventh chord.&lt;/li&gt;&lt;li&gt;Bv is the 13/8 of D (in mohoho temperament) and there is a 8:12:13 chord on D as well as D F A Bv which is a minor w/ neutral sixth.&lt;/li&gt;&lt;li&gt;Bv is the 11/8 of F, and there is a complete 8:9:10:11:12 otonality on F.&lt;/li&gt;&lt;li&gt;Bv is the 11/9 of G, so there are neutral chords on G.&lt;/li&gt;&lt;li&gt;Bv is the 12/11~11/10 of A, and there is a 10:11:12:18 chord on A (no fifth though).&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc26"&gt;&lt;a name="Maqamat-Saba"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;Saba&lt;/h2&gt;
   D Ev F Gb A Bb C D&lt;br /&gt;
 Maqam Saba can be identified with maqamic[7] 0|6 bb4 #5 b6, or equivalently maqamic[7] 2|4 b3 bb4 b6. This is a rather complex MODMOS (but it sounds awesome).&lt;br /&gt;
-&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:54:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc27"&gt;&lt;a name="Maqamat-Saba-Weird form of Saba"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:54 --&gt;Weird form of Saba&lt;/h3&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:48:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc24"&gt;&lt;a name="Maqamat-Saba-Weird form of Saba"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:48 --&gt;Weird form of Saba&lt;/h3&gt;
   D Ev F Gb A Bb C Db E F&lt;br /&gt;
 This alternate form of Saba &amp;quot;doesn't include the octave of the tonic&amp;quot;, and includes another non-octave as well (Ev-E). It could possibly be thought of as a scale with more than 7 notes, but it's unclear to what extent it's used this way in traditional music.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:56:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc28"&gt;&lt;a name="Maqamat-Saba-Potential for 11-limit harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:56 --&gt;Potential for 11-limit harmony&lt;/h3&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:50:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc25"&gt;&lt;a name="Maqamat-Sikah"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:50 --&gt;Sikah&lt;/h2&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:58:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc29"&gt;&lt;a name="Maqamat-Sikah"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:58 --&gt;Sikah&lt;/h2&gt;
   Ev F G A Bv C D Ev&lt;br /&gt;
 Ev F G A Bb C D Ev&lt;br /&gt;
@@ Line 256: / Line 293: @@
 &lt;br /&gt;
 Maqam Sikah has by far the largest number of neutral scale degrees relative to the tonic.&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:60:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc30"&gt;&lt;a name="Maqamat-Sikah-Potential for 11-limit harmony"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:60 --&gt;Potential for 11-limit harmony&lt;/h3&gt;
 &lt;br /&gt;
-&lt;!-- ws:start:WikiTextHeadingRule:52:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc26"&gt;&lt;a name="UNDER CONSTRUCTION"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:52 --&gt;UNDER CONSTRUCTION&lt;/h1&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:62:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc31"&gt;&lt;a name="UNDER CONSTRUCTION"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:62 --&gt;UNDER CONSTRUCTION&lt;/h1&gt;
   &lt;br /&gt;
 d (minor), s (neutral), L (major), ? (half-augmented), A (augmented)&lt;br /&gt;