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:<img id="wikitext@@toc@@normal" class="WikiMedia WikiMediaToc" title="Table of Contents" src="/site/embedthumbnail/toc/normal?w=225&h=100"/> --><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:<h1> --><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 "mandals/orabs").<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:<h1> --><h1 id="toc1"><a name="Older systems"></a><!-- ws:end:WikiTextHeadingRule:2 -->Older systems</h1>
<!-- ws:start:WikiTextHeadingRule:4:<h2> --><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:<h2> --><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:<h1> --><h1 id="toc4"><a name="Newer systems"></a><!-- ws:end:WikiTextHeadingRule:8 -->Newer systems</h1>
<!-- ws:start:WikiTextHeadingRule:10:<h2> --><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:<h2> --><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:<h2> --><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:<h2> --><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:<h2> --><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:<h2> --><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:<h2> --><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:<h2> --><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:<h2> --><h2 id="toc13"><a name="Newer systems-System Jacques Dudon (2006)"></a><!-- ws:end:WikiTextHeadingRule:26 -->System Jacques Dudon (2006)</h2>
XXX</body></html>