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 | : 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> | : 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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> 81/64 (408), 5/4 (386), **243/196 (372)**, **16/13 (360)**, **11/9 (348)**, **40/33 (333)**, 6/5 (316), 32/27 (294) | > 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 | Mandal positions in ratios: | ||
81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80 | |||
Intervals ratios XXX | In cents (approximations: | ||
<span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span> | |||
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) | ||
in cents (approximations): | |||
<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> | |||
Intervals ratios XXX | Intervals ratios XXX | ||
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22, 13, 13, 12, 16, 16, 22<br /> | 22, 13, 13, 12, 16, 16, 22<br /> | ||
<br /> | <br /> | ||
Rational intervals each string can be detuned:<br /> | Rational intervals each string can be detuned (cents in parentheses):<br /> | ||
81/80, 49/48, 1053/1024, 729/704, 2673/2560, 135/128, 2187/2048<br /> | 81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114)<br /> | ||
<br /> | <br /> | ||
Intervals ratios, ascending from C (cent values in parentheses):<br /> | Intervals ratios, ascending from C (cent values in parentheses):<br /> | ||
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9/8 (204), 10/9 (182), <strong>54/49 (169)</strong>, <strong>128/117 (156)</strong>, <strong>88/81 (144)</strong>, <strong>320/297 (129)</strong>, 16/15 (112), 256/243 (90)</li><li>On the D string (from Db to D):<br /> | 9/8 (204), 10/9 (182), <strong>54/49 (169)</strong>, <strong>128/117 (156)</strong>, <strong>88/81 (144)</strong>, <strong>320/297 (129)</strong>, 16/15 (112), 256/243 (90)</li><li>On the D string (from Db to D):<br /> | ||
81/64 (408), 5/4 (386), <strong>243/196 (372)</strong>, <strong>16/13 (360)</strong>, <strong>11/9 (348)</strong>, <strong>40/33 (333)</strong>, 6/5 (316), 32/27 (294)</li></ul><br /> | 81/64 (408), 5/4 (386), <strong>243/196 (372)</strong>, <strong>16/13 (360)</strong>, <strong>11/9 (348)</strong>, <strong>40/33 (333)</strong>, 6/5 (316), 32/27 (294)</li></ul><br /> | ||
A complete list of all intervals available within one octave can be found in the above-mentioned document (first page).<br /> | A complete list of all intervals available within one octave can be found in the above-mentioned <a href="http://xenharmonic.wikispaces.com/file/view/Tableaux+JJW+VIII-2011.pdf">document</a> (on the first page).<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Older systems-System 1 J.J.Weiss-Variant with 128/119"></a><!-- ws:end:WikiTextHeadingRule:6 -->Variant with 128/119</h3> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Older systems-System 1 J.J.Weiss-Variant with 128/119"></a><!-- ws:end:WikiTextHeadingRule:6 -->Variant with 128/119</h3> | ||
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J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.<br /> | J.J. Weiss, Qanun no. 9. Luthier: Kenan Ozten.<br /> | ||
<br /> | <br /> | ||
Mandal positions ( | Mandal positions in ratios:<br /> | ||
81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80<br /> | |||
<br /> | |||
In cents (approximations: <br /> | |||
<span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span><br /> | |||
<br /> | |||
Rational intervals each string can be detuned (cents in parentheses):<br /> | |||
81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114)<br /> | |||
<br /> | |||
Intervals ratios, ascending from C:<br /> | |||
XXX<br /> | |||
<br /> | |||
Interval ratios descending from F:<br /> | |||
XXX<br /> | |||
<br /> | <br /> | ||
A complete list of all intervals available within one octave can be found in the above-mentioned <a href="http://xenharmonic.wikispaces.com/file/view/Tableaux+JJW+VIII-2011.pdf">document</a> (on the second page).<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Newer systems-Symmetrical model"></a><!-- ws:end:WikiTextHeadingRule:16 -->Symmetrical model</h2> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h2&gt; --><h2 id="toc8"><a name="Newer systems-Symmetrical model"></a><!-- ws:end:WikiTextHeadingRule:16 -->Symmetrical model</h2> | ||
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Aliquot division of 65/54 (320.98 cents)<br /> | Aliquot division of 65/54 (320.98 cents)<br /> | ||
<br /> | <br /> | ||
in cents (approximations):<br /> | |||
<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 /> | <br /> | ||
Intervals ratios XXX<br /> | Intervals ratios XXX<br /> | ||