Tuning systems for qanun: Difference between revisions

Wikispaces>hstraub
**Imported revision 259930568 - Original comment: **
Wikispaces>hstraub
**Imported revision 259941894 - 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 07:04:31 UTC</tt>.<br>
: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-30 08:08:58 UTC</tt>.<br>
: The original revision id was <tt>259930568</tt>.<br>
: The original revision id was <tt>259941894</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 (cents in parentheses):
Rational intervals each string can be detuned (approximations in cents in parentheses):
81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114)
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:
* 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)
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81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80
81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80


In cents (approximations:  
In cents (approximations):
&lt;span style="color: #00000a; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;
&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):
Rational intervals each string can be detuned (approximations in cents in parentheses):
81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114)
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:
Intervals ratios, ascending from C:
XXX
* On the D string (from Db to D):
&gt; 256/243 (90), 16/15 (112), **14/13 (128), 88/81 (144), 128/117 or 35/32 (156), 119/108 (168)**, 10/9 (182), 9/8 (204)
* On the E string (from Eb to E):
&gt; 32/27 (294), 6/5 (316), **63/52 (332), 11/9 (348), 16/13 or 315/256 (360), 119/96 (372)**, 5/4 (386), 81/64 (408)


Interval ratios descending from F:
Interval ratios descending from F:
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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:78:&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:78 --&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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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 (cents in parentheses):&lt;br /&gt;
Rational intervals each string can be detuned (approximations in cents in parentheses):&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;
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:&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), &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;
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;
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81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80&lt;br /&gt;
81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
In cents (approximations: &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;span style="color: #00000a; font-family: Tahoma;"&gt;22|16|15|12|13|14|22&lt;/span&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
Rational intervals each string can be detuned (cents in parentheses):&lt;br /&gt;
Rational intervals each string can be detuned (approximations in 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;
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;
&lt;br /&gt;
Intervals ratios, ascending from C:&lt;br /&gt;
Intervals ratios, ascending from C:&lt;br /&gt;
XXX&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;On the D string (from Db to D):&lt;br /&gt;
&lt;br /&gt;
256/243 (90), 16/15 (112), &lt;strong&gt;14/13 (128), 88/81 (144), 128/117 or 35/32 (156), 119/108 (168)&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), &lt;strong&gt;63/52 (332), 11/9 (348), 16/13 or 315/256 (360), 119/96 (372)&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;
XXX&lt;br /&gt;