Tuning systems for qanun: Difference between revisions
Wikispaces>guest **Imported revision 259756812 - Original comment: ** |
Wikispaces>hstraub **Imported revision 259901946 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-30 02:54:14 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>259901946</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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Each apotome is divided into 7 parts, which requires 14 mandals per string. 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. | Each apotome is divided into 7 parts, which requires 14 mandals per string. 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. | ||
The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO). | The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning, mainly in the range of a fourth (the range where the ajnas - maqam tetrachords - reside), (XXX STILL TO DO). | ||
An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one [[32805_32768|schisma (2 cents)]]. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here. | An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one [[32805_32768|schisma (2 cents)]]. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here. | ||
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65/64 and 55/54 are each split into two. | 65/64 and 55/54 are each split into two. | ||
This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents. | This gives the following interval positions of the mandals (approximations): 22, 13, 13, 12, 16, 16, 22 cents. | ||
Intervals ratios, ascending from C: | |||
XXX | |||
Interval ratios, descending from F: | |||
XXX | XXX | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span> | ||
XXX | Intervals ratios XXX | ||
==Symmetrical model== | ==Symmetrical model== | ||
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Mandal positions (cents): <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> | Mandal positions (cents): <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> | ||
XXX | Intervals ratios XXX | ||
==Super-symmetrical models== | ==Super-symmetrical models== | ||
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Mandal positions (cents): <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</span><span style="color: #00000a; font-family: Tahoma;">|</span><span style="font-family: Tahoma;">22</span> | Mandal positions (cents): <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</span><span style="color: #00000a; font-family: Tahoma;">|</span><span style="font-family: Tahoma;">22</span> | ||
XXX | Intervals ratios XXX | ||
===Non-aliquot division of 65/54=== | ===Non-aliquot division of 65/54=== | ||
J.J. Weiss | J.J. Weiss | ||
XXX | Intervals ratios XXX | ||
===Equal division of the Zarlinian semitone=== | ===Equal division of the Zarlinian semitone=== | ||
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<span style="color: #00000a; font-family: Tahoma;">XXX</span> There seem to be typos here... | <span style="color: #00000a; font-family: Tahoma;">XXX</span> There seem to be typos here... | ||
XXX | Intervals ratios XXX | ||
===Ascending/descending with 14/13=== | ===Ascending/descending with 14/13=== | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22, 16, 13, 12, 13, 16, 22</span> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22, 16, 13, 12, 13, 16, 22</span> | ||
XXX | Intervals ratios XXX | ||
===Ascending/descending with 11/10=== | ===Ascending/descending with 11/10=== | ||
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35/32: 155.14 cents | 35/32: 155.14 cents | ||
XXX | Intervals ratios XXX | ||
==Systems by Jacques Dudon== | ==Systems by Jacques Dudon== | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span> | ||
XXX | Intervals ratios XXX | ||
===Arithmetic system=== | ===Arithmetic system=== | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span> | ||
XXX</pre></div> | Intervals ratios XXX</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>tuning systems for qanun</title></head><body><span style="font-size: 150%;"><strong>Tuning systems for the qanun</strong></span><br /> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>tuning systems for qanun</title></head><body><span style="font-size: 150%;"><strong>Tuning systems for the qanun</strong></span><br /> | ||
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Each apotome is divided into 7 parts, which requires 14 mandals per string. The first rough subdivision of the apotome is always into one <a class="wiki_link" href="/81_80">syntonic comma (81/80, 21.5 cents)</a>, one <a class="wiki_link" href="/25_24">Zarlinian semitone (25/24, 70.7 cents)</a> 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.<br /> | Each apotome is divided into 7 parts, which requires 14 mandals per string. The first rough subdivision of the apotome is always into one <a class="wiki_link" href="/81_80">syntonic comma (81/80, 21.5 cents)</a>, one <a class="wiki_link" href="/25_24">Zarlinian semitone (25/24, 70.7 cents)</a> 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.<br /> | ||
<br /> | <br /> | ||
The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).<br /> | The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning, mainly in the range of a fourth (the range where the ajnas - maqam tetrachords - reside), (XXX STILL TO DO).<br /> | ||
<br /> | <br /> | ||
An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one <a class="wiki_link" href="/32805_32768">schisma (2 cents)</a>. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.<br /> | An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one <a class="wiki_link" href="/32805_32768">schisma (2 cents)</a>. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.<br /> | ||
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65/64 and 55/54 are each split into two.<br /> | 65/64 and 55/54 are each split into two.<br /> | ||
<br /> | <br /> | ||
This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.<br /> | This gives the following interval positions of the mandals (approximations): 22, 13, 13, 12, 16, 16, 22 cents.<br /> | ||
<br /> | |||
Intervals ratios, ascending from C:<br /> | |||
XXX<br /> | |||
<br /> | <br /> | ||
Interval ratios, descending from F:<br /> | |||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span><br /> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span><br /> | ||
<br /> | <br /> | ||
XXX<br /> | Intervals ratios XXX<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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Mandal positions (cents): <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 /> | Mandal positions (cents): <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 /> | ||
XXX<br /> | Intervals ratios XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Newer systems-Super-symmetrical models"></a><!-- ws:end:WikiTextHeadingRule:18 -->Super-symmetrical models</h2> | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Newer systems-Super-symmetrical models"></a><!-- ws:end:WikiTextHeadingRule:18 -->Super-symmetrical models</h2> | ||
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Mandal positions (cents): <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</span><span style="color: #00000a; font-family: Tahoma;">|</span><span style="font-family: Tahoma;">22</span><br /> | Mandal positions (cents): <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</span><span style="color: #00000a; font-family: Tahoma;">|</span><span style="font-family: Tahoma;">22</span><br /> | ||
<br /> | <br /> | ||
XXX<br /> | Intervals ratios XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Newer systems-Super-symmetrical models-Non-aliquot division of 65/54"></a><!-- ws:end:WikiTextHeadingRule:22 -->Non-aliquot division of 65/54</h3> | <!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Newer systems-Super-symmetrical models-Non-aliquot division of 65/54"></a><!-- ws:end:WikiTextHeadingRule:22 -->Non-aliquot division of 65/54</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
<br /> | <br /> | ||
XXX<br /> | Intervals ratios XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Newer systems-Super-symmetrical models-Equal division of the Zarlinian semitone"></a><!-- ws:end:WikiTextHeadingRule:24 -->Equal division of the Zarlinian semitone</h3> | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Newer systems-Super-symmetrical models-Equal division of the Zarlinian semitone"></a><!-- ws:end:WikiTextHeadingRule:24 -->Equal division of the Zarlinian semitone</h3> | ||
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<span style="color: #00000a; font-family: Tahoma;">XXX</span> There seem to be typos here...<br /> | <span style="color: #00000a; font-family: Tahoma;">XXX</span> There seem to be typos here...<br /> | ||
<br /> | <br /> | ||
XXX<br /> | Intervals ratios XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 14/13"></a><!-- ws:end:WikiTextHeadingRule:28 -->Ascending/descending with 14/13</h3> | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 14/13"></a><!-- ws:end:WikiTextHeadingRule:28 -->Ascending/descending with 14/13</h3> | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22, 16, 13, 12, 13, 16, 22</span><br /> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">22, 16, 13, 12, 13, 16, 22</span><br /> | ||
<br /> | <br /> | ||
XXX<br /> | Intervals ratios XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 11/10"></a><!-- ws:end:WikiTextHeadingRule:30 -->Ascending/descending with 11/10</h3> | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 11/10"></a><!-- ws:end:WikiTextHeadingRule:30 -->Ascending/descending with 11/10</h3> | ||
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35/32: 155.14 cents<br /> | 35/32: 155.14 cents<br /> | ||
<br /> | <br /> | ||
XXX<br /> | Intervals ratios XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Newer systems-Systems by Jacques Dudon"></a><!-- ws:end:WikiTextHeadingRule:34 -->Systems by Jacques Dudon</h2> | <!-- ws:start:WikiTextHeadingRule:34:&lt;h2&gt; --><h2 id="toc17"><a name="Newer systems-Systems by Jacques Dudon"></a><!-- ws:end:WikiTextHeadingRule:34 -->Systems by Jacques Dudon</h2> | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span><br /> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 14,5 | 14,5 | 14,5 | 15 | 12 | 21,5</span><br /> | ||
<br /> | <br /> | ||
XXX<br /> | Intervals ratios XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:38:&lt;h3&gt; --><h3 id="toc19"><a name="Newer systems-Systems by Jacques Dudon-Arithmetic system"></a><!-- ws:end:WikiTextHeadingRule:38 -->Arithmetic system</h3> | <!-- ws:start:WikiTextHeadingRule:38:&lt;h3&gt; --><h3 id="toc19"><a name="Newer systems-Systems by Jacques Dudon-Arithmetic system"></a><!-- ws:end:WikiTextHeadingRule:38 -->Arithmetic system</h3> | ||
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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span><br /> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;">21,5 | 12 | 15 | 14,5 | 14,5 | 14,5 | 21,5 </span><br /> | ||
<br /> | <br /> | ||
XXX</body></html></pre></div> | Intervals ratios XXX</body></html></pre></div> | ||