Tuning systems for qanun: Difference between revisions

Wikispaces>hstraub
**Imported revision 247434221 - Original comment: **
Wikispaces>hstraub
**Imported revision 247611167 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-21 15:51:34 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-22 05:47:48 UTC</tt>.<br>
: The original revision id was <tt>247434221</tt>.<br>
: The original revision id was <tt>247611167</tt>.<br>
: The revision comment was: <tt></tt><br>
: The revision comment was: <tt></tt><br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
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Interval table XXX
Interval table XXX


==Symmetrical model==  
==Symmetrical and super-symmetrical models==
Characteristics: XXX
 
===Symmetrical model===  
J.J. Weiss
J.J. Weiss
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.
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Interval table XXX
Interval table XXX


==Super-symmetrical model==  
===Super-symmetrical model===  
J.J. Weiss
J.J. Weiss
XXX
XXX
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Interval table XXX
Interval table XXX


==Super-symmetrical model, variant==  
===Unequal division of 65/54===  
J.J. Weiss
J.J. Weiss
Unequal division of 65/54 (320.98 cents)
Unequal division of 65/54 (320.98 cents)
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XXX
XXX


==Equal division of the Zarlinian semitone==  
===Equal division of the Zarlinian semitone===  
J.J. Weiss
J.J. Weiss
Equal division of [[25_24|25/24 (70.67 cents)]] into 5 parts (to make it easier for luthiers)
Equal division of [[25_24|25/24 (70.67 cents)]] into 5 parts (to make it easier for luthiers)
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Interval table XXX
Interval table XXX


==Super-symmetrical system, ascending/descending with 54/49==  
===Ascending/descending with 54/49===  
J.J. Weiss
J.J. Weiss
XXX
XXX
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Interval table XXX
Interval table XXX


==Super-symmetrical system, ascending/descending with 14/13==  
===Ascending/descending with 14/13===
 
J.J. Weiss
J.J. Weiss
&lt;span style="color: #00000a; font-family: Tahoma;"&gt;XXX&lt;/span&gt;
&lt;span style="color: #00000a; font-family: Tahoma;"&gt;XXX&lt;/span&gt;
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Interval table XXX
Interval table XXX


==Super-symmetrical system, ascening/descending with 11/10==  
===Ascending/descending with 11/10===  
J.J. Weiss
J.J. Weiss
XXX
XXX
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Interval table XXX
Interval table XXX


==Super-symmetrical system, ascending/descending with 35/32==  
===Ascending/descending with 35/32===  
J.J. Weiss
J.J. Weiss
XXX
XXX
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Interval table XXX
Interval table XXX


==Arithmetic system, Jacques Dudon==  
===Arithmetic system===  


Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 &lt;/span&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 &lt;/span&gt;
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<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;tuning systems for qanun&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 150%;"&gt;&lt;strong&gt;Tuning systems for the qanun&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;tuning systems for qanun&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="font-size: 150%;"&gt;&lt;strong&gt;Tuning systems for the qanun&lt;/strong&gt;&lt;/span&gt;&lt;br /&gt;
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&lt;!-- ws:start:WikiTextTocRule:38:&amp;lt;img id=&amp;quot;wikitext@@toc@@normal&amp;quot; class=&amp;quot;WikiMedia WikiMediaToc&amp;quot; title=&amp;quot;Table of Contents&amp;quot; src=&amp;quot;/site/embedthumbnail/toc/normal?w=225&amp;amp;h=100&amp;quot;/&amp;gt; --&gt;&lt;div id="toc"&gt;&lt;h1 class="nopad"&gt;Table of Contents&lt;/h1&gt;&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Explanation"&gt;Explanation&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Older systems"&gt;Older systems&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Older systems"&gt;Older systems&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-First System J.J.Weiss"&gt;First System J.J.Weiss&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-First System J.J.Weiss"&gt;First System J.J.Weiss&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-Variant with 128/119"&gt;Variant with 128/119&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-Variant with 128/119"&gt;Variant with 128/119&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:40 --&gt;&lt;!-- ws:start:WikiTextTocRule:41: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-Variant with 128/119 ascending/descending"&gt;Variant with 128/119 ascending/descending&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-Variant with 128/119 ascending/descending"&gt;Variant with 128/119 ascending/descending&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:41 --&gt;&lt;!-- ws:start:WikiTextTocRule:42: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-Variant with 43/40 ascending/descending"&gt;Variant with 43/40 ascending/descending&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Older systems-Variant with 43/40 ascending/descending"&gt;Variant with 43/40 ascending/descending&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:42 --&gt;&lt;!-- ws:start:WikiTextTocRule:43: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Newer systems"&gt;Newer systems&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;div style="margin-left: 1em;"&gt;&lt;a href="#Newer systems"&gt;Newer systems&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:43 --&gt;&lt;!-- ws:start:WikiTextTocRule:44: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-System 2, better suited for ottoman maqams"&gt;System 2, better suited for ottoman maqams&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-System 2, better suited for ottoman maqams"&gt;System 2, better suited for ottoman maqams&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:44 --&gt;&lt;!-- ws:start:WikiTextTocRule:45: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Symmetrical model"&gt;Symmetrical model&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models"&gt;Symmetrical and super-symmetrical models&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:45 --&gt;&lt;!-- ws:start:WikiTextTocRule:46: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Super-symmetrical model"&gt;Super-symmetrical model&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Symmetrical model"&gt;Symmetrical model&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:46 --&gt;&lt;!-- ws:start:WikiTextTocRule:47: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Super-symmetrical model, variant"&gt;Super-symmetrical model, variant&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Super-symmetrical model"&gt;Super-symmetrical model&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:47 --&gt;&lt;!-- ws:start:WikiTextTocRule:48: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Equal division of the Zarlinian semitone"&gt;Equal division of the Zarlinian semitone&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Unequal division of 65/54"&gt;Unequal division of 65/54&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Super-symmetrical system, ascending/descending with 54/49"&gt;Super-symmetrical system, ascending/descending with 54/49&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Equal division of the Zarlinian semitone"&gt;Equal division of the Zarlinian semitone&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:49 --&gt;&lt;!-- ws:start:WikiTextTocRule:50: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Super-symmetrical system, ascending/descending with 14/13"&gt;Super-symmetrical system, ascending/descending with 14/13&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 54/49"&gt;Ascending/descending with 54/49&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:50 --&gt;&lt;!-- ws:start:WikiTextTocRule:51: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Super-symmetrical system, ascening/descending with 11/10"&gt;Super-symmetrical system, ascening/descending with 11/10&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 14/13"&gt;Ascending/descending with 14/13&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:51 --&gt;&lt;!-- ws:start:WikiTextTocRule:52: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Super-symmetrical system, ascending/descending with 35/32"&gt;Super-symmetrical system, ascending/descending with 35/32&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 11/10"&gt;Ascending/descending with 11/10&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:52 --&gt;&lt;!-- ws:start:WikiTextTocRule:53: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-System Jacques Dudon (2006)"&gt;System Jacques Dudon (2006)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 35/32"&gt;Ascending/descending with 35/32&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:53 --&gt;&lt;!-- ws:start:WikiTextTocRule:54: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-Arithmetic system, Jacques Dudon"&gt;Arithmetic system, Jacques Dudon&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:55 --&gt;&lt;!-- ws:start:WikiTextTocRule:56: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-System Jacques Dudon (2006)"&gt;System Jacques Dudon (2006)&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:56 --&gt;&lt;!-- ws:start:WikiTextTocRule:57: --&gt;&lt;div style="margin-left: 3em;"&gt;&lt;a href="#Newer systems-System Jacques Dudon (2006)-Arithmetic system"&gt;Arithmetic system&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:55 --&gt;Julien Jalaleddine Weiss, used with permission.&lt;br /&gt;
&lt;!-- ws:end:WikiTextTocRule:57 --&gt;&lt;!-- ws:start:WikiTextTocRule:58: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:58 --&gt;Julien Jalaleddine Weiss, used with permission.&lt;br /&gt;
Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance&lt;br /&gt;
Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance&lt;br /&gt;
Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical&lt;br /&gt;
Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical&lt;br /&gt;
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Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Newer systems-Symmetrical model"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Symmetrical model&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Symmetrical and super-symmetrical models&lt;/h2&gt;
Characteristics: XXX&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="Newer systems-Symmetrical and super-symmetrical models-Symmetrical model"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Symmetrical model&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.&lt;br /&gt;
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.&lt;br /&gt;
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Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Newer systems-Super-symmetrical model"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Super-symmetrical model&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc10"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Super-symmetrical model"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Super-symmetrical model&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
XXX&lt;br /&gt;
XXX&lt;br /&gt;
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Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Newer systems-Super-symmetrical model, variant"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Super-symmetrical model, variant&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc11"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Unequal division of 65/54"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Unequal division of 65/54&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
Unequal division of 65/54 (320.98 cents)&lt;br /&gt;
Unequal division of 65/54 (320.98 cents)&lt;br /&gt;
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XXX&lt;br /&gt;
XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Newer systems-Equal division of the Zarlinian semitone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;Equal division of the Zarlinian semitone&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc12"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Equal division of the Zarlinian semitone"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Equal division of the Zarlinian semitone&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
Equal division of &lt;a class="wiki_link" href="/25_24"&gt;25/24 (70.67 cents)&lt;/a&gt; into 5 parts (to make it easier for luthiers)&lt;br /&gt;
Equal division of &lt;a class="wiki_link" href="/25_24"&gt;25/24 (70.67 cents)&lt;/a&gt; into 5 parts (to make it easier for luthiers)&lt;br /&gt;
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Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:24:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc12"&gt;&lt;a name="Newer systems-Super-symmetrical system, ascending/descending with 54/49"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Super-symmetrical system, ascending/descending with 54/49&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc13"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 54/49"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Ascending/descending with 54/49&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
XXX&lt;br /&gt;
XXX&lt;br /&gt;
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Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
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&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:26:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc13"&gt;&lt;a name="Newer systems-Super-symmetrical system, ascending/descending with 14/13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Super-symmetrical system, ascending/descending with 14/13&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc14"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 14/13"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Ascending/descending with 14/13&lt;/h3&gt;
  &lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
J.J. Weiss&lt;br /&gt;
&lt;span style="color: #00000a; font-family: Tahoma;"&gt;XXX&lt;/span&gt;&lt;br /&gt;
&lt;span style="color: #00000a; font-family: Tahoma;"&gt;XXX&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Line 454: Line 459:
Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:28:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc14"&gt;&lt;a name="Newer systems-Super-symmetrical system, ascening/descending with 11/10"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Super-symmetrical system, ascening/descending with 11/10&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc15"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 11/10"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Ascending/descending with 11/10&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
XXX&lt;br /&gt;
XXX&lt;br /&gt;
Line 462: Line 467:
Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:30:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc15"&gt;&lt;a name="Newer systems-Super-symmetrical system, ascending/descending with 35/32"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Super-symmetrical system, ascending/descending with 35/32&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc16"&gt;&lt;a name="Newer systems-Symmetrical and super-symmetrical models-Ascending/descending with 35/32"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;Ascending/descending with 35/32&lt;/h3&gt;
  J.J. Weiss&lt;br /&gt;
  J.J. Weiss&lt;br /&gt;
XXX&lt;br /&gt;
XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:32:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc16"&gt;&lt;a name="Newer systems-System Jacques Dudon (2006)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:32 --&gt;System Jacques Dudon (2006)&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Newer systems-System Jacques Dudon (2006)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;System Jacques Dudon (2006)&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5&lt;/span&gt;&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5&lt;/span&gt;&lt;br /&gt;
Line 472: Line 477:
Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:34:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc17"&gt;&lt;a name="Newer systems-Arithmetic system, Jacques Dudon"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:34 --&gt;Arithmetic system, Jacques Dudon&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:36:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc18"&gt;&lt;a name="Newer systems-System Jacques Dudon (2006)-Arithmetic system"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:36 --&gt;Arithmetic system&lt;/h3&gt;
  &lt;br /&gt;
  &lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 &lt;/span&gt;&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 &lt;/span&gt;&lt;br /&gt;