Tuning systems for qanun
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<span style="font-size: 150%;">**Tuning systems for the qanun**</span> [[toc]] Julien Jalaleddine Weiss, used with permission. 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. Online version of Stefan Pohlit's dissertation: see [[http://stefanpohlit.com/dissertation.engl..htm]] 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 possible pitches of a string obtained via raising/lowering the mandals lie within one [[2187_2048|apotome (2187/2048, 113.7 cents)]], in both directions. All systems divde the apotome into 7 parts, which requires 14 mandals per string (one apotome up and down). The first rough subdivision of the apotome is always 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. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part. =Notation= Raising a pitch by an apotome is notated with "#", lowering a pitch by the same amount is notated with "b". For the steps in between, additional symbols are used - altogether 7 symbols for raising pitches and 7 for lowering pitches. This gives 15 potential different pitches per base note. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si) lead to a notation system of 7*15=105 pitches. See the following document. [[file:Tableaux JJW VIII-2011.pdf]] (used with permission J. J. Weiss/S. Pohlit) The base notes without accidentals form a pythagorean diatonic scale, with a major third of [[81_80|81/80]], a major sixth of [[27_16|27/16]] and a major seventh of [[243_128|243/128]]. A first characteristic of this system is that sharps are higher than flats: C# is one apotome (114 cents) above C, while Db is 9/8 (214 cents) minus one apotome = 90 cents. Sharps being higher than flats is a property of pythagorean systems (unlike [[meantone]] systems). A second characteristic is that one mandal position below C# (i.e. one syntonic comma down) gives 114 - 22 = 92 cents, differing from Db by one [[32805_32768|schisma (2 cents)]]. The interval of the schisma is present and can be played on a qanun in any of the tuning systems described here. =Older systems= ==First System J.J.Weiss== Luthier: Ejder Gulec. 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. XXX ===Variant with 128/119=== 128/119: 126.2 cents XXX ===Variant with 128/119 ascending/descending=== XXX ===Variant with 43/40 ascending/descending=== 43/40: 125.2 cents XXX =Newer systems= ==System 2, better suited for ottoman maqams== J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten. Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span> XXX ==Symmetrical model== J.J. Weiss Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast. Aliquot division of 65/54 (320.98 cents) Mandal positions (cents): <span style="font-family: Tahoma;">22|13|13|1</span><span style="color: #00000a; font-family: Tahoma;">8</span><span style="font-family: Tahoma;">|13|13|22</span> XXX ==Super-symmetrical models== Characteristics of super-symmetric systems: no difference between ascending and descending ratios. ===Aliquot division of 65/54 and its inverse=== J.J. Weiss (XXX Is that formulation correct?) Ascending/descending with 43/40 (125.2 cents). Mandal positions (cents): <span style="font-family: Tahoma;">22|13|13|1</span><span style="color: #00000a; font-family: Tahoma;">8</span><span style="font-family: Tahoma;">|13|13</span><span style="color: #00000a; font-family: Tahoma;">|</span><span style="font-family: Tahoma;">22</span> XXX ===Non-aliquot division of 65/54=== J.J. Weiss XXX ===Equal division of the Zarlinian semitone=== J.J. Weiss This is the simplest variant for luthiers... Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|14|14|14|14|14|22</span> ===Ascending/descending with 54/49=== J.J. Weiss [[54_49|54/49]]: 168.2 cents, Zalzal's mujannab (Al Farabi) Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|14|17|13|13|13|22</span> <span style="color: #00000a; font-family: Tahoma;">XXX</span> There seem to be typos here... XXX ===Ascending/descending with 14/13=== J.J. Weiss <span style="color: #00000a; font-family: Tahoma;">14/13: 128.3 cents</span> <span style="color: #00000a; font-family: Tahoma;">XXX</span> Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22, 16, 13, 12, 13, 16, 22</span> XXX ===Ascending/descending with 11/10=== J.J. Weiss 11/10: 165 cents Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|13|13|13|22</span> XXX ===Ascending/descending with 35/32=== J.J. Weiss 35/32: 155.14 cents XXX ==Systems by Jacques Dudon== ===Aliquot system (2006)=== Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span> XXX ===Arithmetic system=== Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span> 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 />
<!-- ws:start:WikiTextTocRule:40:<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:40 --><!-- ws:start:WikiTextTocRule:41: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div>
<!-- ws:end:WikiTextTocRule:41 --><!-- ws:start:WikiTextTocRule:42: --><div style="margin-left: 1em;"><a href="#Older systems">Older systems</a></div>
<!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 2em;"><a href="#Older systems-First System J.J.Weiss">First System J.J.Weiss</a></div>
<!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 3em;"><a href="#Older systems-First System J.J.Weiss-Variant with 128/119">Variant with 128/119</a></div>
<!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 3em;"><a href="#Older systems-First System J.J.Weiss-Variant with 128/119 ascending/descending">Variant with 128/119 ascending/descending</a></div>
<!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 3em;"><a href="#Older systems-First System J.J.Weiss-Variant with 43/40 ascending/descending">Variant with 43/40 ascending/descending</a></div>
<!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 1em;"><a href="#Newer systems">Newer systems</a></div>
<!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 2em;"><a href="#Newer systems-System 2, better suited for ottoman maqams">System 2, better suited for ottoman maqams</a></div>
<!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 2em;"><a href="#Newer systems-Symmetrical model">Symmetrical model</a></div>
<!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Newer systems-Super-symmetrical models">Super-symmetrical models</a></div>
<!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Aliquot division of 65/54 and its inverse">Aliquot division of 65/54 and its inverse</a></div>
<!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Non-aliquot division of 65/54">Non-aliquot division of 65/54</a></div>
<!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Equal division of the Zarlinian semitone">Equal division of the Zarlinian semitone</a></div>
<!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 54/49">Ascending/descending with 54/49</a></div>
<!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 14/13">Ascending/descending with 14/13</a></div>
<!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 11/10">Ascending/descending with 11/10</a></div>
<!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 35/32">Ascending/descending with 35/32</a></div>
<!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 2em;"><a href="#Newer systems-Systems by Jacques Dudon">Systems by Jacques Dudon</a></div>
<!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 3em;"><a href="#Newer systems-Systems by Jacques Dudon-Aliquot system (2006)">Aliquot system (2006)</a></div>
<!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 3em;"><a href="#Newer systems-Systems by Jacques Dudon-Arithmetic system">Arithmetic system</a></div>
<!-- ws:end:WikiTextTocRule:60 --><!-- ws:start:WikiTextTocRule:61: --></div>
<!-- ws:end:WikiTextTocRule:61 -->Julien Jalaleddine Weiss, used with permission.<br />
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.<br />
<br />
Online version of Stefan Pohlit's dissertation: see <a class="wiki_link_ext" href="http://stefanpohlit.com/dissertation.engl..htm" rel="nofollow">http://stefanpohlit.com/dissertation.engl..htm</a><br />
<br />
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 possible pitches of a string obtained via raising/lowering the mandals lie within one <a class="wiki_link" href="/2187_2048">apotome (2187/2048, 113.7 cents)</a>, in both directions. All systems divde the apotome into 7 parts, which requires 14 mandals per string (one apotome up and down).<br />
<br />
The first rough subdivision of the apotome is always 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. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Notation"></a><!-- ws:end:WikiTextHeadingRule:0 -->Notation</h1>
Raising a pitch by an apotome is notated with "#", lowering a pitch by the same amount is notated with "b".<br />
For the steps in between, additional symbols are used - altogether 7 symbols for raising pitches and 7 for lowering pitches.<br />
This gives 15 potential different pitches per base note. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si) lead to a notation system of 7*15=105 pitches. See the following document.<br />
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<br />
(used with permission J. J. Weiss/S. Pohlit)<br />
<br />
The base notes without accidentals form a pythagorean diatonic scale, with a major third of <a class="wiki_link" href="/81_80">81/80</a>, a major sixth of <a class="wiki_link" href="/27_16">27/16</a> and a major seventh of <a class="wiki_link" href="/243_128">243/128</a>.<br />
<br />
A first characteristic of this system is that sharps are higher than flats: C# is one apotome (114 cents) above C, while Db is 9/8 (214 cents) minus one apotome = 90 cents. Sharps being higher than flats is a property of pythagorean systems (unlike <a class="wiki_link" href="/meantone">meantone</a> systems).<br />
<br />
A second characteristic is that one mandal position below C# (i.e. one syntonic comma down) gives 114 - 22 = 92 cents, differing from Db by one <a class="wiki_link" href="/32805_32768">schisma (2 cents)</a>.<br />
The interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.<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>
Luthier: Ejder Gulec.<br />
Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).<br />
65/64 and 55/54 are each split into two.<br />
<br />
This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.<br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:6:<h3> --><h3 id="toc3"><a name="Older systems-First System J.J.Weiss-Variant with 128/119"></a><!-- ws:end:WikiTextHeadingRule:6 -->Variant with 128/119</h3>
128/119: 126.2 cents<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:8:<h3> --><h3 id="toc4"><a name="Older systems-First System J.J.Weiss-Variant with 128/119 ascending/descending"></a><!-- ws:end:WikiTextHeadingRule:8 -->Variant with 128/119 ascending/descending</h3>
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:10:<h3> --><h3 id="toc5"><a name="Older systems-First System J.J.Weiss-Variant with 43/40 ascending/descending"></a><!-- ws:end:WikiTextHeadingRule:10 -->Variant with 43/40 ascending/descending</h3>
43/40: 125.2 cents<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Newer systems"></a><!-- ws:end:WikiTextHeadingRule:12 -->Newer systems</h1>
<!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><a name="Newer systems-System 2, better suited for ottoman maqams"></a><!-- ws:end:WikiTextHeadingRule:14 -->System 2, better suited for ottoman maqams</h2>
J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.<br />
<br />
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span><br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Newer systems-Symmetrical model"></a><!-- ws:end:WikiTextHeadingRule:16 -->Symmetrical model</h2>
J.J. Weiss<br />
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.<br />
Aliquot division of 65/54 (320.98 cents)<br />
<br />
Mandal positions (cents): <span style="font-family: Tahoma;">22|13|13|1</span><span style="color: #00000a; font-family: Tahoma;">8</span><span style="font-family: Tahoma;">|13|13|22</span><br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:18:<h2> --><h2 id="toc9"><a name="Newer systems-Super-symmetrical models"></a><!-- ws:end:WikiTextHeadingRule:18 -->Super-symmetrical models</h2>
Characteristics of super-symmetric systems: no difference between ascending and descending ratios.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:20:<h3> --><h3 id="toc10"><a name="Newer systems-Super-symmetrical models-Aliquot division of 65/54 and its inverse"></a><!-- ws:end:WikiTextHeadingRule:20 -->Aliquot division of 65/54 and its inverse</h3>
J.J. Weiss<br />
(XXX Is that formulation correct?)<br />
Ascending/descending with 43/40 (125.2 cents).<br />
<br />
Mandal positions (cents): <span style="font-family: Tahoma;">22|13|13|1</span><span style="color: #00000a; font-family: Tahoma;">8</span><span style="font-family: Tahoma;">|13|13</span><span style="color: #00000a; font-family: Tahoma;">|</span><span style="font-family: Tahoma;">22</span><br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:22:<h3> --><h3 id="toc11"><a name="Newer systems-Super-symmetrical models-Non-aliquot division of 65/54"></a><!-- ws:end:WikiTextHeadingRule:22 -->Non-aliquot division of 65/54</h3>
J.J. Weiss<br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:24:<h3> --><h3 id="toc12"><a name="Newer systems-Super-symmetrical models-Equal division of the Zarlinian semitone"></a><!-- ws:end:WikiTextHeadingRule:24 -->Equal division of the Zarlinian semitone</h3>
J.J. Weiss<br />
This is the simplest variant for luthiers...<br />
<br />
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|14|14|14|14|14|22</span><br />
<br />
<!-- ws:start:WikiTextHeadingRule:26:<h3> --><h3 id="toc13"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 54/49"></a><!-- ws:end:WikiTextHeadingRule:26 -->Ascending/descending with 54/49</h3>
J.J. Weiss<br />
<a class="wiki_link" href="/54_49">54/49</a>: 168.2 cents, Zalzal's mujannab (Al Farabi)<br />
<br />
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|14|17|13|13|13|22</span><br />
<span style="color: #00000a; font-family: Tahoma;">XXX</span> There seem to be typos here...<br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:28:<h3> --><h3 id="toc14"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 14/13"></a><!-- ws:end:WikiTextHeadingRule:28 -->Ascending/descending with 14/13</h3>
J.J. Weiss<br />
<span style="color: #00000a; font-family: Tahoma;">14/13: 128.3 cents</span><br />
<span style="color: #00000a; font-family: Tahoma;">XXX</span><br />
<br />
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22, 16, 13, 12, 13, 16, 22</span><br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:30:<h3> --><h3 id="toc15"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 11/10"></a><!-- ws:end:WikiTextHeadingRule:30 -->Ascending/descending with 11/10</h3>
J.J. Weiss<br />
11/10: 165 cents<br />
<br />
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|13|13|13|22</span><br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:32:<h3> --><h3 id="toc16"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 35/32"></a><!-- ws:end:WikiTextHeadingRule:32 -->Ascending/descending with 35/32</h3>
J.J. Weiss<br />
35/32: 155.14 cents<br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:34:<h2> --><h2 id="toc17"><a name="Newer systems-Systems by Jacques Dudon"></a><!-- ws:end:WikiTextHeadingRule:34 -->Systems by Jacques Dudon</h2>
<!-- ws:start:WikiTextHeadingRule:36:<h3> --><h3 id="toc18"><a name="Newer systems-Systems by Jacques Dudon-Aliquot system (2006)"></a><!-- ws:end:WikiTextHeadingRule:36 -->Aliquot system (2006)</h3>
<br />
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span><br />
<br />
XXX<br />
<br />
<!-- ws:start:WikiTextHeadingRule:38:<h3> --><h3 id="toc19"><a name="Newer systems-Systems by Jacques Dudon-Arithmetic system"></a><!-- ws:end:WikiTextHeadingRule:38 -->Arithmetic system</h3>
<br />
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span><br />
<br />
XXX</body></html>