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Tuning systems for qanun

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<span style="font-size: 150%;">**Tuning systems for the qanun**</span>
Julien Jalaleddine Weiss
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
University.

[[toc]]
=Explanation= 
The tuning tables on this page are specifically designed for the tuning system of the [[qanun]] (see the link for details on the system of tuning and playing a qanun with "mandals/orabs").

The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.

The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.

Any given configuration of mandal/orab positions, resulting in a certain set of pitches that can be played at a given time
(base for a maqam tetrachord) is represented by a choice of one cell in each row.

=Older systems= 
==First System J.J.Weiss== 
Inequal subdivision of the [[2187_2048|apotome (2187/2048, 113.7 cents)]] into 7 parts (8 mandals/orabs), in the following manner:
* Subdivision into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlinian semitone (25/24, 70.7 cents)]] and another syntonic comma.
* Further subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).
* 65/64 and 55/54 are each split into two.

This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.
Luthier: Ejder Gulec

Interval Table (cents):
|| 0 || 22 || 35 || 48 || 60 || 76 || 92 || 114 ||
|| 90 || 112 || 125 || 138 || 150 || 166 || 182 || 204 ||
|| 294 || 316 || 330 || 342 || 354 || 370 || 386 || 408 ||
|| 384 || 406 || 420 || 432 || 444 || 460 || 476 || 498 ||
|| 498 || 520 || 533 || 546 || 558 || 574 || 590 || 612 ||

Interval table of just intervals (ascending, descending):
|| 1/1 || 81/80 || 49/48 || 1053/1024 || 729/704 || 2673/2560 || 135/128 || 2187/2048 ||
|| 256/243 || 16/15 || 784/729, 128/119, 43/40 (asc.)
320/297 (desc.) || 13/12 (asc.)
88/81 (desc.) || 12/11 (asc.)
128/117 (desc.) || 11/10, 208/189 (asc.)
54/49 (desc.) || 10/9 || 9/8 ||
|| 32/27 || 6/5 || 98/81 (asc.)
40/33 (desc.) || 39/32 (asc.)
XXX || 27/22 (asc.)
XXX || 99/80, 26/21 (asc.)
XXX || 5/4 || 81/64 ||
|| 8192/6581 || XXX || 25088/19683 || 104/81 || XXX || 176/135 || 320/243 || 4/3 ||
|| XXX || 27/20 || 351/258 || XXX || 243/176 || 891/640 || 45/32 || 729/512 ||

==Older system, variant== 
XXX

=Newer systems= 
==System 2 J.J. Weiss, better suited for ottoman maqams== 
XXX

==Symmetrical model J.J. Weiss== 
XXX

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

==Super-symmetrical model J.J. Weiss, variant== 
XXX

==Equal division of the Zarlinian semitone, J.J. Weiss== 
XXX

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

==Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss== 
XXX

==9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss== 
XXX

==System Jacques Dudon (2006)== 
XXX

Original HTML content:

<html><head><title>tuning systems for qanun</title></head><body><span style="font-size: 150%;"><strong>Tuning systems for the qanun</strong></span><br />
Julien Jalaleddine Weiss<br />
Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance<br />
Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical<br />
University.<br />
<br />
<!-- ws:start:WikiTextTocRule:28:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:28 --><!-- ws:start:WikiTextTocRule:29: --><div style="margin-left: 1em;"><a href="#Explanation">Explanation</a></div>
<!-- ws:end:WikiTextTocRule:29 --><!-- ws:start:WikiTextTocRule:30: --><div style="margin-left: 1em;"><a href="#Older systems">Older systems</a></div>
<!-- ws:end:WikiTextTocRule:30 --><!-- ws:start:WikiTextTocRule:31: --><div style="margin-left: 2em;"><a href="#Older systems-First System J.J.Weiss">First System J.J.Weiss</a></div>
<!-- ws:end:WikiTextTocRule:31 --><!-- ws:start:WikiTextTocRule:32: --><div style="margin-left: 2em;"><a href="#Older systems-Older system, variant">Older system, variant</a></div>
<!-- ws:end:WikiTextTocRule:32 --><!-- ws:start:WikiTextTocRule:33: --><div style="margin-left: 1em;"><a href="#Newer systems">Newer systems</a></div>
<!-- ws:end:WikiTextTocRule:33 --><!-- ws:start:WikiTextTocRule:34: --><div style="margin-left: 2em;"><a href="#Newer systems-System 2 J.J. Weiss, better suited for ottoman maqams">System 2 J.J. Weiss, better suited for ottoman maqams</a></div>
<!-- ws:end:WikiTextTocRule:34 --><!-- ws:start:WikiTextTocRule:35: --><div style="margin-left: 2em;"><a href="#Newer systems-Symmetrical model J.J. Weiss">Symmetrical model J.J. Weiss</a></div>
<!-- ws:end:WikiTextTocRule:35 --><!-- ws:start:WikiTextTocRule:36: --><div style="margin-left: 2em;"><a href="#Newer systems-Super-symmetrical model J.J. Weiss">Super-symmetrical model J.J. Weiss</a></div>
<!-- ws:end:WikiTextTocRule:36 --><!-- ws:start:WikiTextTocRule:37: --><div style="margin-left: 2em;"><a href="#Newer systems-Super-symmetrical model J.J. Weiss, variant">Super-symmetrical model J.J. Weiss, variant</a></div>
<!-- ws:end:WikiTextTocRule:37 --><!-- ws:start:WikiTextTocRule:38: --><div style="margin-left: 2em;"><a href="#Newer systems-Equal division of the Zarlinian semitone, J.J. Weiss">Equal division of the Zarlinian semitone, J.J. Weiss</a></div>
<!-- ws:end:WikiTextTocRule:38 --><!-- ws:start:WikiTextTocRule:39: --><div style="margin-left: 2em;"><a href="#Newer systems-Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss">Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss</a></div>
<!-- ws:end:WikiTextTocRule:39 --><!-- ws:start:WikiTextTocRule:40: --><div style="margin-left: 2em;"><a href="#Newer systems-Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss">Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss</a></div>
<!-- ws:end:WikiTextTocRule:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 2em;"><a href="#Newer systems-9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss">9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss</a></div>
<!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 2em;"><a href="#Newer systems-System Jacques Dudon (2006)">System Jacques Dudon (2006)</a></div>
<!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --></div>
<!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Explanation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Explanation</h1>
 The tuning tables on this page are specifically designed for the tuning system of the <a class="wiki_link" href="/qanun">qanun</a> (see the link for details on the system of tuning and playing a qanun with &quot;mandals/orabs&quot;).<br />
<br />
The whole table covers roughly the range of a fourth (the range where the ajnas - maqam tetrachords - reside). Each row corresponds to one string of the qanun. In the first column stands the basic (relative) tuning of a string while the following columns indicate possible intervals that can be reached via lowering the mandals/orabs.<br />
<br />
The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.<br />
<br />
Any given configuration of mandal/orab positions, resulting in a certain set of pitches that can be played at a given time<br />
(base for a maqam tetrachord) is represented by a choice of one cell in each row.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Older systems"></a><!-- ws:end:WikiTextHeadingRule:2 -->Older systems</h1>
 <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Older systems-First System J.J.Weiss"></a><!-- ws:end:WikiTextHeadingRule:4 -->First System J.J.Weiss</h2>
 Inequal subdivision of the <a class="wiki_link" href="/2187_2048">apotome (2187/2048, 113.7 cents)</a> into 7 parts (8 mandals/orabs), in the following manner:<br />
<ul><li>Subdivision into one <a class="wiki_link" href="/81_80">syntonic comma (81/80, 21.5 cents)</a>, one <a class="wiki_link" href="/25_24">Zarlinian semitone (25/24, 70.7 cents)</a> and another syntonic comma.</li><li>Further subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).</li><li>65/64 and 55/54 are each split into two.</li></ul><br />
This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.<br />
Luthier: Ejder Gulec<br />
<br />
Interval Table (cents):<br />


<table class="wiki_table">
    <tr>
        <td>0<br />
</td>
        <td>22<br />
</td>
        <td>35<br />
</td>
        <td>48<br />
</td>
        <td>60<br />
</td>
        <td>76<br />
</td>
        <td>92<br />
</td>
        <td>114<br />
</td>
    </tr>
    <tr>
        <td>90<br />
</td>
        <td>112<br />
</td>
        <td>125<br />
</td>
        <td>138<br />
</td>
        <td>150<br />
</td>
        <td>166<br />
</td>
        <td>182<br />
</td>
        <td>204<br />
</td>
    </tr>
    <tr>
        <td>294<br />
</td>
        <td>316<br />
</td>
        <td>330<br />
</td>
        <td>342<br />
</td>
        <td>354<br />
</td>
        <td>370<br />
</td>
        <td>386<br />
</td>
        <td>408<br />
</td>
    </tr>
    <tr>
        <td>384<br />
</td>
        <td>406<br />
</td>
        <td>420<br />
</td>
        <td>432<br />
</td>
        <td>444<br />
</td>
        <td>460<br />
</td>
        <td>476<br />
</td>
        <td>498<br />
</td>
    </tr>
    <tr>
        <td>498<br />
</td>
        <td>520<br />
</td>
        <td>533<br />
</td>
        <td>546<br />
</td>
        <td>558<br />
</td>
        <td>574<br />
</td>
        <td>590<br />
</td>
        <td>612<br />
</td>
    </tr>
</table>

<br />
Interval table of just intervals (ascending, descending):<br />


<table class="wiki_table">
    <tr>
        <td>1/1<br />
</td>
        <td>81/80<br />
</td>
        <td>49/48<br />
</td>
        <td>1053/1024<br />
</td>
        <td>729/704<br />
</td>
        <td>2673/2560<br />
</td>
        <td>135/128<br />
</td>
        <td>2187/2048<br />
</td>
    </tr>
    <tr>
        <td>256/243<br />
</td>
        <td>16/15<br />
</td>
        <td>784/729, 128/119, 43/40 (asc.)<br />
320/297 (desc.)<br />
</td>
        <td>13/12 (asc.)<br />
88/81 (desc.)<br />
</td>
        <td>12/11 (asc.)<br />
128/117 (desc.)<br />
</td>
        <td>11/10, 208/189 (asc.)<br />
54/49 (desc.)<br />
</td>
        <td>10/9<br />
</td>
        <td>9/8<br />
</td>
    </tr>
    <tr>
        <td>32/27<br />
</td>
        <td>6/5<br />
</td>
        <td>98/81 (asc.)<br />
40/33 (desc.)<br />
</td>
        <td>39/32 (asc.)<br />
XXX<br />
</td>
        <td>27/22 (asc.)<br />
XXX<br />
</td>
        <td>99/80, 26/21 (asc.)<br />
XXX<br />
</td>
        <td>5/4<br />
</td>
        <td>81/64<br />
</td>
    </tr>
    <tr>
        <td>8192/6581<br />
</td>
        <td>XXX<br />
</td>
        <td>25088/19683<br />
</td>
        <td>104/81<br />
</td>
        <td>XXX<br />
</td>
        <td>176/135<br />
</td>
        <td>320/243<br />
</td>
        <td>4/3<br />
</td>
    </tr>
    <tr>
        <td>XXX<br />
</td>
        <td>27/20<br />
</td>
        <td>351/258<br />
</td>
        <td>XXX<br />
</td>
        <td>243/176<br />
</td>
        <td>891/640<br />
</td>
        <td>45/32<br />
</td>
        <td>729/512<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Older systems-Older system, variant"></a><!-- ws:end:WikiTextHeadingRule:6 -->Older system, variant</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Newer systems"></a><!-- ws:end:WikiTextHeadingRule:8 -->Newer systems</h1>
 <!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Newer systems-System 2 J.J. Weiss, better suited for ottoman maqams"></a><!-- ws:end:WikiTextHeadingRule:10 -->System 2 J.J. Weiss, better suited for ottoman maqams</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Newer systems-Symmetrical model J.J. Weiss"></a><!-- ws:end:WikiTextHeadingRule:12 -->Symmetrical model J.J. Weiss</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><h2 id="toc7"><a name="Newer systems-Super-symmetrical model J.J. Weiss"></a><!-- ws:end:WikiTextHeadingRule:14 -->Super-symmetrical model J.J. Weiss</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Newer systems-Super-symmetrical model J.J. Weiss, variant"></a><!-- ws:end:WikiTextHeadingRule:16 -->Super-symmetrical model J.J. Weiss, variant</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Newer systems-Equal division of the Zarlinian semitone, J.J. Weiss"></a><!-- ws:end:WikiTextHeadingRule:18 -->Equal division of the Zarlinian semitone, J.J. Weiss</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Newer systems-Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss"></a><!-- ws:end:WikiTextHeadingRule:20 -->Super-symmetrical system, ascending/descending with 54/49, J.J. Weiss</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:&lt;h2&gt; --><h2 id="toc11"><a name="Newer systems-Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss"></a><!-- ws:end:WikiTextHeadingRule:22 -->Super-symmetrical system, ascending/descending with 14/13, J.J. Weiss</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:&lt;h2&gt; --><h2 id="toc12"><a name="Newer systems-9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss"></a><!-- ws:end:WikiTextHeadingRule:24 -->9) Super-symmetrical system, ascening/descending with 11/10, J.J. Weiss</h2>
 XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:&lt;h2&gt; --><h2 id="toc13"><a name="Newer systems-System Jacques Dudon (2006)"></a><!-- ws:end:WikiTextHeadingRule:26 -->System Jacques Dudon (2006)</h2>
 XXX</body></html>
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