Tuning systems for qanun: Difference between revisions

Wikispaces>hstraub
**Imported revision 259921722 - Original comment: **
Wikispaces>hstraub
**Imported revision 259923008 - 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 05:53:56 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-30 06:04:18 UTC</tt>.<br>
: The original revision id was <tt>259921722</tt>.<br>
: The original revision id was <tt>259923008</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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81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80
81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80


In cents (approximations):  
In cents (approximations):
22, 13, 13, 12, 16, 16, 22
22, 13, 13, 12, 16, 16, 22


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Intervals ratios, ascending from C (cent values in parentheses):
Intervals ratios, ascending from C (cent values in parentheses):
* On the D string (from Db to D):
* On the D string (from Db to D):
&gt; 256/243 (90), 16/15 (112), 784/729 (126), 13/12 (138), 12/11 (150), 11/10 (166), 10/9 (182), 9/8 (204)
&gt; 256/243 (90), 16/15 (112), **784/729 (126)**, **13/12 (138)**, **12/11 (150)**, **11/10 (166)**, 10/9 (182), 9/8 (204)
* On the E string (from Eb to E):
* On the E string (from Eb to E):
&gt; 32/27 (294), 6/5 (316), 98/81 (330), 39/32 (342), 27/22 (354),8 9/80 (370), 5/4 (386), 81/64 (408)
&gt; 32/27 (294), 6/5 (316), **98/81 (330)**, **39/32 (342)**, **27/22 (354)**, **89/80 (370)**, 5/4 (386), 81/64 (408)


Interval ratios, descending from F:
Interval ratios, descending from F:
XXX
* On the E string (from Eb to E):
&gt; 9/8 (204), 10/9 (182), **54/49 (169)**, **128/117 (156)**, **88/81 (144)**, **320/297 (129)**, 16/15 (112), 256/243 (90)
* On the D string (from Db to D):
&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)


===Variant with 128/119===  
===Variant with 128/119===  
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&lt;br /&gt;
&lt;br /&gt;
This gives 15 potential different pitches per base note, in accordance with the real playing capabilities of the qanun. 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, which also gives all the pitches in one octave (in ratios and cents) that can be played by system 1 and 2.&lt;br /&gt;
This gives 15 potential different pitches per base note, in accordance with the real playing capabilities of the qanun. 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, which also gives all the pitches in one octave (in ratios and cents) that can be played by system 1 and 2.&lt;br /&gt;
&lt;!-- ws:start:WikiTextFileRule:70:&amp;lt;img src=&amp;quot;http://www.wikispaces.com/site/embedthumbnail/file/Tableaux%20JJW%20VIII-2011.pdf?h=52&amp;amp;w=320&amp;quot; class=&amp;quot;WikiFile&amp;quot; id=&amp;quot;wikitext@@file@@Tableaux JJW VIII-2011.pdf&amp;quot; title=&amp;quot;File: Tableaux JJW VIII-2011.pdf&amp;quot; width=&amp;quot;320&amp;quot; height=&amp;quot;52&amp;quot; /&amp;gt; --&gt;&lt;div class="objectEmbed"&gt;&lt;a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');"&gt;&lt;img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="Tableaux JJW VIII-2011.pdf" /&gt;&lt;/a&gt;&lt;div&gt;&lt;a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');" class="filename" title="Tableaux JJW VIII-2011.pdf"&gt;Tableaux JJW VIII-2011.pdf&lt;/a&gt;&lt;br /&gt;&lt;ul&gt;&lt;li&gt;&lt;a href="/file/detail/Tableaux%20JJW%20VIII-2011.pdf"&gt;Details&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf"&gt;Download&lt;/a&gt;&lt;/li&gt;&lt;li style="color: #666"&gt;130 KB&lt;/li&gt;&lt;/ul&gt;&lt;/div&gt;&lt;/div&gt;&lt;!-- ws:end:WikiTextFileRule:70 --&gt;&lt;br /&gt;
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&lt;br /&gt;
&lt;br /&gt;
(used with permission J. J. Weiss/S. Pohlit)&lt;br /&gt;
(used with permission J. J. Weiss/S. Pohlit)&lt;br /&gt;
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81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80&lt;br /&gt;
81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In cents (approximations): &lt;br /&gt;
In cents (approximations):&lt;br /&gt;
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;
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Intervals ratios, ascending from C (cent values in parentheses):&lt;br /&gt;
Intervals ratios, ascending from C (cent values in parentheses):&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;On the D string (from Db to D):&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;On the D string (from Db to D):&lt;br /&gt;
256/243 (90), 16/15 (112), 784/729 (126), 13/12 (138), 12/11 (150), 11/10 (166), 10/9 (182), 9/8 (204)&lt;/li&gt;&lt;li&gt;On the E string (from Eb to E):&lt;br /&gt;
256/243 (90), 16/15 (112), &lt;strong&gt;784/729 (126)&lt;/strong&gt;, &lt;strong&gt;13/12 (138)&lt;/strong&gt;, &lt;strong&gt;12/11 (150)&lt;/strong&gt;, &lt;strong&gt;11/10 (166)&lt;/strong&gt;, 10/9 (182), 9/8 (204)&lt;/li&gt;&lt;li&gt;On the E string (from Eb to E):&lt;br /&gt;
32/27 (294), 6/5 (316), 98/81 (330), 39/32 (342), 27/22 (354),8 9/80 (370), 5/4 (386), 81/64 (408)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
32/27 (294), 6/5 (316), &lt;strong&gt;98/81 (330)&lt;/strong&gt;, &lt;strong&gt;39/32 (342)&lt;/strong&gt;, &lt;strong&gt;27/22 (354)&lt;/strong&gt;, &lt;strong&gt;89/80 (370)&lt;/strong&gt;, 5/4 (386), 81/64 (408)&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
Interval ratios, descending from F:&lt;br /&gt;
Interval ratios, descending from F:&lt;br /&gt;
XXX&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;On the E string (from Eb to E):&lt;br /&gt;
&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;
&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;
  128/119: 126.2 cents&lt;br /&gt;
  128/119: 126.2 cents&lt;br /&gt;