Tuning systems for qanun: Difference between revisions

Wikispaces>hstraub
**Imported revision 259929206 - Original comment: **
Wikispaces>hstraub
**Imported revision 259930568 - 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>2011-09-30 06:54:23 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-30 07:04:31 UTC</tt>.<br>
: The original revision id was <tt>259929206</tt>.<br>
: The original revision id was <tt>259930568</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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22, 13, 13, 12, 16, 16, 22
22, 13, 13, 12, 16, 16, 22


Rational intervals each string can be detuned:
Rational intervals each string can be detuned (cents in parentheses):
81/80, 49/48, 1053/1024, 729/704, 2673/2560, 135/128, 2187/2048
81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114)


Intervals ratios, ascending from C (cent values in parentheses):
Intervals ratios, ascending from C (cent values in parentheses):
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&gt; 81/64 (408), 5/4 (386), **243/196 (372)**, **16/13 (360)**, **11/9 (348)**, **40/33 (333)**, 6/5 (316), 32/27 (294)
&gt; 81/64 (408), 5/4 (386), **243/196 (372)**, **16/13 (360)**, **11/9 (348)**, **40/33 (333)**, 6/5 (316), 32/27 (294)


A complete list of all intervals available within one octave can be found in the above-mentioned document (first page).
A complete list of all intervals available within one octave can be found in the above-mentioned [[http://xenharmonic.wikispaces.com/file/view/Tableaux+JJW+VIII-2011.pdf|document]] (on the first page).


===Variant with 128/119===  
===Variant with 128/119===  
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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; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;
Mandal positions in ratios:
81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80


Intervals ratios XXX
In cents (approximations:
&lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;
 
Rational intervals each string can be detuned (cents in parentheses):
81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114)
 
Intervals ratios, ascending from C:
XXX
 
Interval ratios descending from F:
XXX
 
A complete list of all intervals available within one octave can be found in the above-mentioned [[http://xenharmonic.wikispaces.com/file/view/Tableaux+JJW+VIII-2011.pdf|document]] (on the second page).


==Symmetrical model==  
==Symmetrical model==  
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Aliquot division of 65/54 (320.98 cents)
Aliquot 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; font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13|22&lt;/span&gt;
in cents (approximations):
&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;


Intervals ratios XXX
Intervals ratios XXX
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22, 13, 13, 12, 16, 16, 22&lt;br /&gt;
22, 13, 13, 12, 16, 16, 22&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Rational intervals each string can be detuned:&lt;br /&gt;
Rational intervals each string can be detuned (cents in parentheses):&lt;br /&gt;
81/80, 49/48, 1053/1024, 729/704, 2673/2560, 135/128, 2187/2048&lt;br /&gt;
81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intervals ratios, ascending from C (cent values in parentheses):&lt;br /&gt;
Intervals ratios, ascending from C (cent values in parentheses):&lt;br /&gt;
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9/8 (204), 10/9 (182), &lt;strong&gt;54/49 (169)&lt;/strong&gt;, &lt;strong&gt;128/117 (156)&lt;/strong&gt;, &lt;strong&gt;88/81 (144)&lt;/strong&gt;, &lt;strong&gt;320/297 (129)&lt;/strong&gt;, 16/15 (112), 256/243 (90)&lt;/li&gt;&lt;li&gt;On the D string (from Db to D):&lt;br /&gt;
9/8 (204), 10/9 (182), &lt;strong&gt;54/49 (169)&lt;/strong&gt;, &lt;strong&gt;128/117 (156)&lt;/strong&gt;, &lt;strong&gt;88/81 (144)&lt;/strong&gt;, &lt;strong&gt;320/297 (129)&lt;/strong&gt;, 16/15 (112), 256/243 (90)&lt;/li&gt;&lt;li&gt;On the D string (from Db to D):&lt;br /&gt;
81/64 (408), 5/4 (386), &lt;strong&gt;243/196 (372)&lt;/strong&gt;, &lt;strong&gt;16/13 (360)&lt;/strong&gt;, &lt;strong&gt;11/9 (348)&lt;/strong&gt;, &lt;strong&gt;40/33 (333)&lt;/strong&gt;, 6/5 (316), 32/27 (294)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
81/64 (408), 5/4 (386), &lt;strong&gt;243/196 (372)&lt;/strong&gt;, &lt;strong&gt;16/13 (360)&lt;/strong&gt;, &lt;strong&gt;11/9 (348)&lt;/strong&gt;, &lt;strong&gt;40/33 (333)&lt;/strong&gt;, 6/5 (316), 32/27 (294)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
A complete list of all intervals available within one octave can be found in the above-mentioned document (first page).&lt;br /&gt;
A complete list of all intervals available within one octave can be found in the above-mentioned &lt;a href="http://xenharmonic.wikispaces.com/file/view/Tableaux+JJW+VIII-2011.pdf"&gt;document&lt;/a&gt; (on the first page).&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Older systems-System 1 J.J.Weiss-Variant with 128/119"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Variant with 128/119&lt;/h3&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h3&amp;gt; --&gt;&lt;h3 id="toc3"&gt;&lt;a name="Older systems-System 1 J.J.Weiss-Variant with 128/119"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Variant with 128/119&lt;/h3&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; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;&lt;br /&gt;
Mandal positions in ratios:&lt;br /&gt;
81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80&lt;br /&gt;
&lt;br /&gt;
In cents (approximations: &lt;br /&gt;
&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;
Rational intervals each string can be detuned (cents in parentheses):&lt;br /&gt;
81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114)&lt;br /&gt;
&lt;br /&gt;
Intervals ratios, ascending from C:&lt;br /&gt;
XXX&lt;br /&gt;
&lt;br /&gt;
Interval ratios descending from F:&lt;br /&gt;
XXX&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Intervals ratios XXX&lt;br /&gt;
A complete list of all intervals available within one octave can be found in the above-mentioned &lt;a href="http://xenharmonic.wikispaces.com/file/view/Tableaux+JJW+VIII-2011.pdf"&gt;document&lt;/a&gt; (on the second page).&lt;br /&gt;
&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 model"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Symmetrical model&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 model"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;Symmetrical model&lt;/h2&gt;
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Aliquot division of 65/54 (320.98 cents)&lt;br /&gt;
Aliquot 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; font-family: Tahoma;"&gt;8&lt;/span&gt;&lt;span style="font-family: Tahoma;"&gt;|13|13|22&lt;/span&gt;&lt;br /&gt;
in cents (approximations):&lt;br /&gt;
&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;
Intervals ratios XXX&lt;br /&gt;
Intervals ratios XXX&lt;br /&gt;