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Tuning systems for qanun: Difference between revisions

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**Imported revision 247616689 - Original comment: **
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**Imported revision 247617429 - 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>2011-08-22 06:24:25 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-22 06:28:52 UTC</tt>.<br>
: The original revision id was <tt>247616689</tt>.<br>
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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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The possible pitches of a string obtained via raising/lowering the mandals/orabs lie within one [[2187_2048|apotome (2187/2048, 113.7 cents)]]. All systems use 8 mandals, allowing a subdivision of the apotome into 7 parts.
The possible pitches of a string obtained via raising/lowering the mandals/orabs lie within one [[2187_2048|apotome (2187/2048, 113.7 cents)]]. All systems use 8 mandals, allowing a subdivision of the apotome into 7 parts.


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 (Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.
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.


=Explanation of the tuning tables=  
=Explanation of the tuning tables=  
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 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.


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==Symmetrical and super-symmetrical models==  
==Symmetrical and super-symmetrical models==  
Characteristics: XXX
XXX
Characteristics of super-symmetric systems: no difference between ascending and descending ratios.


===Symmetrical model===  
===Symmetrical model===  
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The possible pitches of a string obtained via raising/lowering the mandals/orabs lie within one &lt;a class="wiki_link" href="/2187_2048"&gt;apotome (2187/2048, 113.7 cents)&lt;/a&gt;. All systems use 8 mandals, allowing a subdivision of the apotome into 7 parts.&lt;br /&gt;
The possible pitches of a string obtained via raising/lowering the mandals/orabs lie within one &lt;a class="wiki_link" href="/2187_2048"&gt;apotome (2187/2048, 113.7 cents)&lt;/a&gt;. All systems use 8 mandals, allowing a subdivision of the apotome into 7 parts.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The first rough subdivision of the apotome is always into one &lt;a class="wiki_link" href="/81_80"&gt;syntonic comma (81/80, 21.5 cents)&lt;/a&gt;, one &lt;a class="wiki_link" href="/25_24"&gt;Zarlinian semitone (25/24, 70.7 cents)&lt;/a&gt; and another syntonic comma. The middle part (Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.&lt;br /&gt;
The first rough subdivision of the apotome is always into one &lt;a class="wiki_link" href="/81_80"&gt;syntonic comma (81/80, 21.5 cents)&lt;/a&gt;, one &lt;a class="wiki_link" href="/25_24"&gt;Zarlinian semitone (25/24, 70.7 cents)&lt;/a&gt; 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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Explanation of the tuning tables"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Explanation of the tuning tables&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc0"&gt;&lt;a name="Explanation of the tuning tables"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;Explanation of the tuning tables&lt;/h1&gt;
  &lt;br /&gt;
  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.&lt;br /&gt;
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.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.&lt;br /&gt;
The first table contains the cent values and the second the just intervals, sometimes differing between ascending and descending ratios.&lt;br /&gt;
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&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 and super-symmetrical models"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Symmetrical and super-symmetrical models&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;
  XXX&lt;br /&gt;
Characteristics of super-symmetric systems: no difference between ascending and descending ratios.&lt;br /&gt;
&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;
&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;
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