Tuning systems for qanun: Difference between revisions

Wikispaces>hstraub
**Imported revision 247431833 - Original comment: **
Wikispaces>hstraub
**Imported revision 247433417 - 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 15:39:39 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-21 15:47:46 UTC</tt>.<br>
: The original revision id was <tt>247431833</tt>.<br>
: The original revision id was <tt>247433417</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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<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">&lt;span style="font-size: 150%;"&gt;**Tuning systems for the qanun**&lt;/span&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;white-space: pre-wrap ! important" class="old-revision-html">&lt;span style="font-size: 150%;"&gt;**Tuning systems for the qanun**&lt;/span&gt;
[[toc]]
[[toc]]
Julien Jalaleddine Weiss
Julien Jalaleddine Weiss, used with permission.
Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance
Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance
Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical
Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical
Line 68: Line 68:
J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.
J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.


Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;&lt;/span&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;


Interval table XXX
Interval table XXX
Line 76: Line 76:
Equal division of 65/54 (320.98 cents)
Equal division of 65/54 (320.98 cents)


Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13|22&lt;/span&gt;
Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a; font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13|22&lt;/span&gt;


Interval table XXX
Interval table XXX
Line 83: Line 83:
XXX
XXX


Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13&lt;/span&gt;&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;|&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;22&lt;/span&gt;
Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a; font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13&lt;/span&gt;&lt;span style="color: #00000a; font-family: Tahoma;"&gt;|&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;22&lt;/span&gt;


Interval table XXX
Interval table XXX
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Equal division of [[25_24|25/24]] into 5 parts (to make it easier for luthiers)
Equal division of [[25_24|25/24]] into 5 parts (to make it easier for luthiers)


Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;&lt;/span&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;


Interval table XXX
Interval table XXX
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==Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss==  
==Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss==  
XXX
XXX
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|14|17|13|13|13|22&lt;/span&gt;&lt;/span&gt;
Interval table XXX


==Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss==  
==Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss==  
&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;XXX&lt;/span&gt;&lt;/span&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22, 16, 13, 12, 13, 16, 22&lt;/span&gt;&lt;/span&gt;
Interval table XXX
==Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss==
XXX
XXX


==9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss==  
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|16|15|13|13|13|22&lt;/span&gt;&lt;/span&gt;
 
Interval table XXX
 
==Super-symmetrical system, ascening/descending with 35/32, J.J. Weiss==  
XXX
XXX


==System Jacques Dudon (2006)==  
==System Jacques Dudon (2006)==  
XXX</pre></div>
 
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5&lt;/span&gt;&lt;/span&gt;
 
Interval table XXX
 
==Arithmetic system, Jacques Dudon==
 
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 &lt;/span&gt;&lt;/span&gt;
&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;
&lt;/span&gt;&lt;/span&gt;
Interval table XXX
&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;
&lt;/span&gt;&lt;/span&gt;</pre></div>
<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:end:WikiTextTocRule:33 --&gt;&lt;!-- ws:start:WikiTextTocRule:34: --&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: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:34 --&gt;&lt;!-- ws:start:WikiTextTocRule:35: --&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: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:35 --&gt;&lt;!-- ws:start:WikiTextTocRule:36: --&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: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:36 --&gt;&lt;!-- ws:start:WikiTextTocRule:37: --&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: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:37 --&gt;&lt;!-- ws:start:WikiTextTocRule:38: --&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: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:38 --&gt;&lt;!-- ws:start:WikiTextTocRule:39: --&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: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:39 --&gt;&lt;!-- ws:start:WikiTextTocRule:40: --&gt;&lt;div style="margin-left: 2em;"&gt;&lt;a href="#Newer systems-System 2 J.J. Weiss, better suited for ottoman maqams"&gt;System 2 J.J. Weiss, better suited for ottoman maqams&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 J.J. Weiss, better suited for ottoman maqams"&gt;System 2 J.J. Weiss, better suited for ottoman maqams&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="#Newer systems-Symmetrical model J.J. Weiss"&gt;Symmetrical model J.J. Weiss&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 J.J. Weiss"&gt;Symmetrical model J.J. Weiss&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="#Newer systems-Super-symmetrical model J.J. Weiss"&gt;Super-symmetrical model J.J. Weiss&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 J.J. Weiss"&gt;Super-symmetrical model J.J. Weiss&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="#Newer systems-Super-symmetrical model J.J. Weiss, variant"&gt;Super-symmetrical model J.J. Weiss, variant&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 J.J. Weiss, variant"&gt;Super-symmetrical model J.J. Weiss, variant&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-Equal division of the Zarlinian semitone, J.J. Weiss"&gt;Equal division of the Zarlinian semitone, J.J. Weiss&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, J.J. Weiss"&gt;Equal division of the Zarlinian semitone, J.J. Weiss&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-Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss"&gt;Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss&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, J.J. Weiss"&gt;Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss&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 system, ascending/descending with 14/13, J.J. Weiss"&gt;Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss&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, J.J. Weiss"&gt;Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss&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-9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss"&gt;9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss&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, J.J. Weiss"&gt;Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss&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-System Jacques Dudon (2006)"&gt;System Jacques Dudon (2006)&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, ascening/descending with 35/32, J.J. Weiss"&gt;Super-symmetrical system, ascening/descending with 35/32, J.J. Weiss&lt;/a&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:48 --&gt;&lt;!-- ws:start:WikiTextTocRule:49: --&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:49 --&gt;Julien Jalaleddine Weiss&lt;br /&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:54 --&gt;&lt;!-- ws:start:WikiTextTocRule:55: --&gt;&lt;/div&gt;
&lt;!-- ws:end:WikiTextTocRule:55 --&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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  J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.&lt;br /&gt;
  J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
Line 374: Line 403:
Equal division of 65/54 (320.98 cents)&lt;br /&gt;
Equal division of 65/54 (320.98 cents)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13|22&lt;/span&gt;&lt;br /&gt;
Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a; font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13|22&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
Line 381: Line 410:
  XXX&lt;br /&gt;
  XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13&lt;/span&gt;&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;|&lt;/span&gt;&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;22&lt;/span&gt;&lt;br /&gt;
Mandal positions (cents): &lt;span style="font-family: Tahoma;"&gt;22|13|13|1&lt;/span&gt;&lt;span style="color: #00000a; font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13&lt;/span&gt;&lt;span style="color: #00000a; font-family: Tahoma;"&gt;|&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;22&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Interval table XXX&lt;br /&gt;
Interval table XXX&lt;br /&gt;
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  Equal division of &lt;a class="wiki_link" href="/25_24"&gt;25/24&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&lt;/a&gt; into 5 parts (to make it easier for luthiers)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|14|14|14|14|14|22&lt;/span&gt;&lt;br /&gt;
&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, J.J. Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss&lt;/h2&gt;
&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, J.J. Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:24 --&gt;Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss&lt;/h2&gt;
  XXX&lt;br /&gt;
  XXX&lt;br /&gt;
&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|14|17|13|13|13|22&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;br /&gt;
&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, J.J. Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss&lt;/h2&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, J.J. Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:26 --&gt;Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss&lt;/h2&gt;
&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;XXX&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22, 16, 13, 12, 13, 16, 22&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
Interval table XXX&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, J.J. Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss&lt;/h2&gt;
  XXX&lt;br /&gt;
  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-9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:28 --&gt;9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss&lt;/h2&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;22|16|15|13|13|13|22&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
Interval table XXX&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, ascening/descending with 35/32, J.J. Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;Super-symmetrical system, ascening/descending with 35/32, J.J. Weiss&lt;/h2&gt;
  XXX&lt;br /&gt;
  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-System Jacques Dudon (2006)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:30 --&gt;System Jacques Dudon (2006)&lt;/h2&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;
  XXX&lt;/body&gt;&lt;/html&gt;</pre></div>
  &lt;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
Interval table XXX&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;br /&gt;
Mandal positions (cents): &lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 &lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/span&gt;&lt;br /&gt;
Interval table XXX&lt;br /&gt;
&lt;span style="color: #00000a;"&gt;&lt;span style="font-family: Tahoma;"&gt;&lt;br /&gt;
&lt;/span&gt;&lt;/span&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>