39edo: Difference between revisions

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<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:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-28 13:13:53 UTC</tt>.<br>

: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-28 21:29:20 UTC</tt>.<br>

: The original revision id was <tt>~~576072691~~</tt>.<br>

: The original revision id was <tt>576100823</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>

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**2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/10L 19s|10L 19s]]

2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/8L 23s|8L 23s]]

2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)</pre></div>

2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)

==**__39edo and world music:__**==

39edo is a good candidate for a "universal tuning" in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.

===Western:===

39edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: **7 7 2 7 7 7 2**). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since "minor" and "major" triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.

Another option is to use a MODMOS, such as **7 6 3 7 6 7 3**; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth can be avoided by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in //many// different ways, acquiring a distinctly different but still harmonious character each time.

The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.

===**Indian:**===

A similar situation arises with Indian music since the sruti system, like the Western system, also has multiple possible mappings in 39edo. Many of these are modified versions of the 17L 5s MOS (where the generator is a perfect fifth).

===**[[Arabic, Turkish, Persian]]:**===

While middle-eastern music is commonly approximated using 24edo, 39edo offers a potentially better alternative. 17edo and 24edo both satisfy the "Level 1" requirements for maqam tuning sytems. 39edo is a Level 2 system because:

* It has two types of "neutral" seconds (154 and 185 cents)

* It has two minor seconds (92 and 123 cents), which when added together give a whole tone (215 cents)

whereas neither 17edo nor 24edo satisfy these properties.

39edo will likely be more suited to some middle-eastern scales than others. Specifically, Turkish music (in which the Rast makam has a "major-like" wide neutral third and a wide "neutral" second approaching 10/9), will likely be especially well suited to 39edo.

===**Blues / Jazz / African-American:**===

The harmonic seventh ("barbershop seventh") tetrad is reasonably well approximated in 39edo, and some temperaments (augene in particular) are liberally supplied with them. John Coltrane [[https://en.wikipedia.org/wiki/Coltrane_changes|would have loved augene]].

Tritone substitution, which is a major part of jazz and blues harmony, is more complicated in 39edo because there are two types of tritones. Therefore the tritone substitution of one seventh chord will need to be a different type of seventh chord. However, this also opens new possibilities; if the substituted chord is of a more consonant type than the original, then the tritone substitution may function as a //resolution// rather than a suspension.

Blue notes, rather than being considered inflections, can be notated as accidentals instead; for example, a "blue major third" can be identified as either of the two neutral thirds. There are two possible mappings for 7:4 which are about equal in closeness. The sharp mapping is the normal one because it works better with the 5:4 and 3:2, but using the flat one instead (as an accidental) allows for another type of blue note.

===Other:===

39edo offers a good approximation of pelog / mavila using the flat fifth as a generator.

It also offers //many// possible pentatonic scales, including the 2L+3S MOS (which is **9 7 7 9 7**). Slendro can be approximated using this scale or using something like the quasi-equal **8 8 8 8 7**. A more expressive pentatonic scale is the oneirotonic subset **9 6 9 9 6**. Many Asian and African musical styles can thus be accomodated.</pre></div>

<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>39edo</title></head><body><h1 id="toc0"><a name="x39 tone equal temperament"></a><span style="color: #9900ab; font-family: 'Times New Roman',Times,serif; font-size: 113%;">39 tone equal temperament</span></h1>

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<h2 id="toc2"><a name="x39 tone equal temperament-Instruments (prototypes):"></a><u>Instruments (prototypes):</u></h2>

<br />

<img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /><br />

<img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /><br />

<em>An illustrative image of a 39-ED2 keyboard</em><br />

<table class="captionBox"><tr><td class="captionedImage"><img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /></td></tr><tr><td class="imageCaption">39-EDD fretboard visualization</td></tr></table><br />

<table class="captionBox"><tr><td class="captionedImage"><img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /></td></tr><tr><td class="imageCaption">39-EDD fretboard visualization</td></tr></table><br />

<br />

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2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - <a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales">MOS</a> of type <a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%2023s">8L 23s</a><br />

2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)</body></html></pre></div>

2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)<br />

<br />

<h2 id="toc4"><a name="x39 tone equal temperament-39edo and world music:"></a><strong><u>39edo and world music:</u></strong></h2>

<br />

39edo is a good candidate for a &quot;universal tuning&quot; in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.<br />

<br />

<h3 id="toc5"><a name="x39 tone equal temperament-39edo and world music:-Western:"></a>Western:</h3>

<br />

39edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: <strong>7 7 2 7 7 7 2</strong>). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since &quot;minor&quot; and &quot;major&quot; triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.<br />

<br />

Another option is to use a MODMOS, such as <strong>7 6 3 7 6 7 3</strong>; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth can be avoided by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in <em>many</em> different ways, acquiring a distinctly different but still harmonious character each time.<br />

<br />

The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.<br />

<br />

<h3 id="toc6"><a name="x39 tone equal temperament-39edo and world music:-Indian:"></a><strong>Indian:</strong></h3>

<br />

A similar situation arises with Indian music since the sruti system, like the Western system, also has multiple possible mappings in 39edo. Many of these are modified versions of the 17L 5s MOS (where the generator is a perfect fifth).<br />

<br />

<h3 id="toc7"><a name="x39 tone equal temperament-39edo and world music:-Arabic, Turkish, Persian:"></a><strong><a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, Persian</a>:</strong></h3>

<br />

While middle-eastern music is commonly approximated using 24edo, 39edo offers a potentially better alternative. 17edo and 24edo both satisfy the &quot;Level 1&quot; requirements for maqam tuning sytems. 39edo is a Level 2 system because:<br />

<br />

<ul><li>It has two types of &quot;neutral&quot; seconds (154 and 185 cents)</li><li>It has two minor seconds (92 and 123 cents), which when added together give a whole tone (215 cents)</li></ul><br />

whereas neither 17edo nor 24edo satisfy these properties.<br />

<br />

39edo will likely be more suited to some middle-eastern scales than others. Specifically, Turkish music (in which the Rast makam has a &quot;major-like&quot; wide neutral third and a wide &quot;neutral&quot; second approaching 10/9), will likely be especially well suited to 39edo.<br />

<br />

<h3 id="toc8"><a name="x39 tone equal temperament-39edo and world music:-Blues / Jazz / African-American:"></a><strong>Blues / Jazz / African-American:</strong></h3>

<br />

The harmonic seventh (&quot;barbershop seventh&quot;) tetrad is reasonably well approximated in 39edo, and some temperaments (augene in particular) are liberally supplied with them. John Coltrane <a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Coltrane_changes" rel="nofollow">would have loved augene</a>.<br />

<br />

Tritone substitution, which is a major part of jazz and blues harmony, is more complicated in 39edo because there are two types of tritones. Therefore the tritone substitution of one seventh chord will need to be a different type of seventh chord. However, this also opens new possibilities; if the substituted chord is of a more consonant type than the original, then the tritone substitution may function as a <em>resolution</em> rather than a suspension.<br />

<br />

Blue notes, rather than being considered inflections, can be notated as accidentals instead; for example, a &quot;blue major third&quot; can be identified as either of the two neutral thirds. There are two possible mappings for 7:4 which are about equal in closeness. The sharp mapping is the normal one because it works better with the 5:4 and 3:2, but using the flat one instead (as an accidental) allows for another type of blue note.<br />

<br />

<h3 id="toc9"><a name="x39 tone equal temperament-39edo and world music:-Other:"></a>Other:</h3>

<br />

39edo offers a good approximation of pelog / mavila using the flat fifth as a generator.<br />

<br />

It also offers <em>many</em> possible pentatonic scales, including the 2L+3S MOS (which is <strong>9 7 7 9 7</strong>). Slendro can be approximated using this scale or using something like the quasi-equal <strong>8 8 8 8 7</strong>. A more expressive pentatonic scale is the oneirotonic subset <strong>9 6 9 9 6</strong>. Many Asian and African musical styles can thus be accomodated.</body></html></pre></div>

@@ 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:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-28 13:13:53 UTC</tt>.<br>
+: This revision was by author [[User:MasonGreen1|MasonGreen1]] and made on <tt>2016-02-28 21:29:20 UTC</tt>.<br>
-: The original revision id was <tt>576072691</tt>.<br>
+: The original revision id was <tt>576100823</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 120: / Line 120: @@
 **2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1** - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/10L 19s|10L 19s]]
 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - [[xenharmonic/MOSScales|MOS]] of type [[xenharmonic/8L 23s|8L 23s]]
-1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)</pre></div>
+1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)
+==**__39edo and world music:__**==
+edo is a good candidate for a "universal tuning" in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.
+===Western:===
+edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: **7 7 2 7 7 7 2**). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since "minor" and "major" triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.
+Another option is to use a MODMOS, such as **7 6 3 7 6 7 3**; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth can be avoided by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in //many// different ways, acquiring a distinctly different but still harmonious character each time.
+The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.
+===**Indian:**===
+A similar situation arises with Indian music since the sruti system, like the Western system, also has multiple possible mappings in 39edo. Many of these are modified versions of the 17L 5s MOS (where the generator is a perfect fifth).
+===**[[Arabic, Turkish, Persian]]:**===
+While middle-eastern music is commonly approximated using 24edo, 39edo offers a potentially better alternative. 17edo and 24edo both satisfy the "Level 1" requirements for maqam tuning sytems. 39edo is a Level 2 system because:
+* It has two types of "neutral" seconds (154 and 185 cents)
+* It has two minor seconds (92 and 123 cents), which when added together give a whole tone (215 cents)
+whereas neither 17edo nor 24edo satisfy these properties.
+edo will likely be more suited to some middle-eastern scales than others. Specifically, Turkish music (in which the Rast makam has a "major-like" wide neutral third and a wide "neutral" second approaching 10/9), will likely be especially well suited to 39edo.
+===**Blues / Jazz / African-American:**===
+The harmonic seventh ("barbershop seventh") tetrad is reasonably well approximated in 39edo, and some temperaments (augene in particular) are liberally supplied with them. John Coltrane [[https://en.wikipedia.org/wiki/Coltrane_changes|would have loved augene]].
+Tritone substitution, which is a major part of jazz and blues harmony, is more complicated in 39edo because there are two types of tritones. Therefore the tritone substitution of one seventh chord will need to be a different type of seventh chord. However, this also opens new possibilities; if the substituted chord is of a more consonant type than the original, then the tritone substitution may function as a //resolution// rather than a suspension.
+Blue notes, rather than being considered inflections, can be notated as accidentals instead; for example, a "blue major third" can be identified as either of the two neutral thirds. There are two possible mappings for 7:4 which are about equal in closeness. The sharp mapping is the normal one because it works better with the 5:4 and 3:2, but using the flat one instead (as an accidental) allows for another type of blue note.
+===Other:===
+edo offers a good approximation of pelog / mavila using the flat fifth as a generator.
+It also offers //many// possible pentatonic scales, including the 2L+3S MOS (which is **9 7 7 9 7**). Slendro can be approximated using this scale or using something like the quasi-equal **8 8 8 8 7**. A more expressive pentatonic scale is the oneirotonic subset **9 6 9 9 6**. Many Asian and African musical styles can thus be accomodated.</pre></div>
 <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;39edo&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="x39 tone equal temperament"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;&lt;span style="color: #9900ab; font-family: 'Times New Roman',Times,serif; font-size: 113%;"&gt;39 tone equal temperament&lt;/span&gt;&lt;/h1&gt;
@@ Line 812: / Line 853: @@
 &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x39 tone equal temperament-Instruments (prototypes):"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;u&gt;Instruments (prototypes):&lt;/u&gt;&lt;/h2&gt;
   &lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:686:&amp;lt;img src=&amp;quot;/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 467px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:686 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:704:&amp;lt;img src=&amp;quot;/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG&amp;quot; alt=&amp;quot;&amp;quot; title=&amp;quot;&amp;quot; style=&amp;quot;height: 467px; width: 800px;&amp;quot; /&amp;gt; --&gt;&lt;img src="/file/view/TECLADO%2039-EDD.PNG/390052498/800x467/TECLADO%2039-EDD.PNG" alt="TECLADO 39-EDD.PNG" title="TECLADO 39-EDD.PNG" style="height: 467px; width: 800px;" /&gt;&lt;!-- ws:end:WikiTextLocalImageRule:704 --&gt;&lt;br /&gt;
 &lt;em&gt;An illustrative image of a 39-ED2 keyboard&lt;/em&gt;&lt;br /&gt;
-&lt;!-- ws:start:WikiTextLocalImageRule:687:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;39-EDD fretboard visualization&amp;quot; title=&amp;quot;39-EDD fretboard visualization&amp;quot; style=&amp;quot;height: 203px; width: 826px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDD fretboard visualization&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:687 --&gt;&lt;br /&gt;
+&lt;!-- ws:start:WikiTextLocalImageRule:705:&amp;lt;img src=&amp;quot;http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png&amp;quot; alt=&amp;quot;39-EDD fretboard visualization&amp;quot; title=&amp;quot;39-EDD fretboard visualization&amp;quot; style=&amp;quot;height: 203px; width: 826px;&amp;quot; /&amp;gt; --&gt;&lt;table class="captionBox"&gt;&lt;tr&gt;&lt;td class="captionedImage"&gt;&lt;img src="http://xenharmonic.wikispaces.com/file/view/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png/258445130/826x203/Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" alt="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" title="Custom_700mm_5-str_Tricesanonaphonic_Guitar.png" style="height: 203px; width: 826px;" /&gt;&lt;/td&gt;&lt;/tr&gt;&lt;tr&gt;&lt;td class="imageCaption"&gt;39-EDD fretboard visualization&lt;/td&gt;&lt;/tr&gt;&lt;/table&gt;&lt;!-- ws:end:WikiTextLocalImageRule:705 --&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
@@ Line 863: / Line 904: @@
 &lt;strong&gt;2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1 1 2 1&lt;/strong&gt; - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/10L%2019s"&gt;10L 19s&lt;/a&gt;&lt;br /&gt;
 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 1 2 1 1 - &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/MOSScales"&gt;MOS&lt;/a&gt; of type &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/8L%2023s"&gt;8L 23s&lt;/a&gt;&lt;br /&gt;
-1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)&lt;/body&gt;&lt;/html&gt;</pre></div>
+1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 2 1 2 1 2 1 2 1 2 1 1 - 3MOS of type 18L 21s (augene)&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="x39 tone equal temperament-39edo and world music:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;&lt;strong&gt;&lt;u&gt;39edo and world music:&lt;/u&gt;&lt;/strong&gt;&lt;/h2&gt;
+ &lt;br /&gt;
+edo is a good candidate for a &amp;quot;universal tuning&amp;quot; in that it offers reasonable approximations of many different world music traditions; it is one of the simplest edos that can make this claim. Because of this, composers wishing to combine multiple world music traditions (for example, gamelan with maqam singing) within one unified framework would find 39edo an interesting possibility.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc5"&gt;&lt;a name="x39 tone equal temperament-39edo and world music:-Western:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Western:&lt;/h3&gt;
+ &lt;br /&gt;
+edo offers not one, but several different ways to realize the traditional Western diatonic scale. One way is to simply take a chain of fifths (the diatonic MOS: &lt;strong&gt;7 7 2 7 7 7 2&lt;/strong&gt;). Because 39edo is a superpyth rather than a meantone system, this means that the harmonic quality of its diatonic scale will differ somewhat, since &amp;quot;minor&amp;quot; and &amp;quot;major&amp;quot; triads now approximate 6:7:9 and 14:18:21 respectively, rather than 10:12:15 and 4:5:6 as in meantone diatonic systems. Diatonic compositions translated onto this scale thus acquire a wildly different harmonic character, albeit still very pleasing.&lt;br /&gt;
+&lt;br /&gt;
+Another option is to use a MODMOS, such as &lt;strong&gt;7 6 3 7 6 7 3&lt;/strong&gt;; this scale enables us to continue using pental rather than septimal thirds, but it has a false (wolf) fifth. When translating diatonic compositions into this scale, the wolf fifth can be avoided by introducing accidental notes when necessary. There are other MODMOS's that combine both pental and septimal harmonies. As such, a single Western classical or pop composition can be translated into 39edo in &lt;em&gt;many&lt;/em&gt; different ways, acquiring a distinctly different but still harmonious character each time.&lt;br /&gt;
+&lt;br /&gt;
+The MOS and the MODMOS's all have smaller-than-usual semitones, which makes them more effective for melody than their counterparts in 12edo or meantone systems.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc6"&gt;&lt;a name="x39 tone equal temperament-39edo and world music:-Indian:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;strong&gt;Indian:&lt;/strong&gt;&lt;/h3&gt;
+ &lt;br /&gt;
+A similar situation arises with Indian music since the sruti system, like the Western system, also has multiple possible mappings in 39edo. Many of these are modified versions of the 17L 5s MOS (where the generator is a perfect fifth).&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc7"&gt;&lt;a name="x39 tone equal temperament-39edo and world music:-Arabic, Turkish, Persian:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;&lt;strong&gt;&lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic, Turkish, Persian&lt;/a&gt;:&lt;/strong&gt;&lt;/h3&gt;
+ &lt;br /&gt;
+While middle-eastern music is commonly approximated using 24edo, 39edo offers a potentially better alternative. 17edo and 24edo both satisfy the &amp;quot;Level 1&amp;quot; requirements for maqam tuning sytems. 39edo is a Level 2 system because:&lt;br /&gt;
+&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;It has two types of &amp;quot;neutral&amp;quot; seconds (154 and 185 cents)&lt;/li&gt;&lt;li&gt;It has two minor seconds (92 and 123 cents), which when added together give a whole tone (215 cents)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
+whereas neither 17edo nor 24edo satisfy these properties.&lt;br /&gt;
+&lt;br /&gt;
+edo will likely be more suited to some middle-eastern scales than others. Specifically, Turkish music (in which the Rast makam has a &amp;quot;major-like&amp;quot; wide neutral third and a wide &amp;quot;neutral&amp;quot; second approaching 10/9), will likely be especially well suited to 39edo.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc8"&gt;&lt;a name="x39 tone equal temperament-39edo and world music:-Blues / Jazz / African-American:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;strong&gt;Blues / Jazz / African-American:&lt;/strong&gt;&lt;/h3&gt;
+ &lt;br /&gt;
+The harmonic seventh (&amp;quot;barbershop seventh&amp;quot;) tetrad is reasonably well approximated in 39edo, and some temperaments (augene in particular) are liberally supplied with them. John Coltrane &lt;a class="wiki_link_ext" href="https://en.wikipedia.org/wiki/Coltrane_changes" rel="nofollow"&gt;would have loved augene&lt;/a&gt;.&lt;br /&gt;
+&lt;br /&gt;
+Tritone substitution, which is a major part of jazz and blues harmony, is more complicated in 39edo because there are two types of tritones. Therefore the tritone substitution of one seventh chord will need to be a different type of seventh chord. However, this also opens new possibilities; if the substituted chord is of a more consonant type than the original, then the tritone substitution may function as a &lt;em&gt;resolution&lt;/em&gt; rather than a suspension.&lt;br /&gt;
+&lt;br /&gt;
+Blue notes, rather than being considered inflections, can be notated as accidentals instead; for example, a &amp;quot;blue major third&amp;quot; can be identified as either of the two neutral thirds. There are two possible mappings for 7:4 which are about equal in closeness. The sharp mapping is the normal one because it works better with the 5:4 and 3:2, but using the flat one instead (as an accidental) allows for another type of blue note.&lt;br /&gt;
+&lt;br /&gt;
+&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc9"&gt;&lt;a name="x39 tone equal temperament-39edo and world music:-Other:"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Other:&lt;/h3&gt;
+ &lt;br /&gt;
+edo offers a good approximation of pelog / mavila using the flat fifth as a generator.&lt;br /&gt;
+&lt;br /&gt;
+It also offers &lt;em&gt;many&lt;/em&gt; possible pentatonic scales, including the 2L+3S MOS (which is &lt;strong&gt;9 7 7 9 7&lt;/strong&gt;). Slendro can be approximated using this scale or using something like the quasi-equal &lt;strong&gt;8 8 8 8 7&lt;/strong&gt;. A more expressive pentatonic scale is the oneirotonic subset &lt;strong&gt;9 6 9 9 6&lt;/strong&gt;. Many Asian and African musical styles can thus be accomodated.&lt;/body&gt;&lt;/html&gt;</pre></div>