Tuning systems for qanun: Difference between revisions
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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 10:20:55 UTC</tt>.<br> | ||
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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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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). | 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). | ||
= | =Other models= | ||
J. J. Weiss has developed a number of other systems besides the two described above. A notable class of these are so-called super-symmetrical systems, which have the property that the intervals ascending from C and the intervals descending from F (which sho slight differences in the previous two systems, as shown above) are the same. | |||
See chapter 3.4 and appendix I in [[http://stefanpohlit.com/dissertation.engl..htm|Stefan Pohlit's dissertation]] for detailed descriptions. | |||
== | ==Example: Super-symmetrical model with 14/13== | ||
© J.J. Weiss | © J.J. Weiss | ||
The idea behind this system is as folows: | |||
Dividing the apotome (114 cents) into 3 equal parts gives 38 cents, and adding this to the pythagorean limma (90 cents) gives 128 cents, which is the approximation for 14/13. | |||
The division of the apotome derived from this combines the known basic division into apotome, Zarlinian semitone and apotoms with an equal division into 3 parts, which yields the following mandal positions (cents): | |||
22, 16, 13, 12, 13, 16, 22 | |||
(Observe that 22+16 = 38, as wqell as 13+12+13.) | |||
XXX</pre></div> | Since the pythagorean limma appears prominently in the basic framework anyway (as semitone from E to F and from B to C as well as one apotome minus a syntonic comma several times on each string), 14/13 also appears at various positions. | ||
Table of pitches from C to F (approximations in cents). | |||
||~ String ||~ b ||~ ||~ ||~ ||~ ||~ ||~ ||~ Base note ||~ ||~ ||~ ||~ ||~ ||~ ||~ # || | |||
||~ C || || || || || || || ||= 0 || 22 || 38 || 51 || 63 || 76 || 92 || 114 || | |||
||~ D || 90 || 112 || 128 || 141 || 153 || 166 || 182 ||= 204 || 226 || 242 || 255 || 267 || 280 || 196 || 318 || | |||
||~ E || 294 || || || || || || ||= 408 || || || || || || || 522 || | |||
||~ F || 384 || || || || || || ||= 498 || || || || || || || 612 || | |||
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 /> | ||
<!-- ws:start:WikiTextTocRule: | <!-- ws:start:WikiTextTocRule:10:&lt;img id=&quot;wikitext@@toc@@normal&quot; class=&quot;WikiMedia WikiMediaToc&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/normal?w=225&amp;h=100&quot;/&gt; --><div id="toc"><h1 class="nopad">Table of Contents</h1><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><div style="margin-left: 1em;"><a href="#System 1">System 1</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: --><div style="margin-left: 1em;"><a href="#System 2, better suited for ottoman maqams">System 2, better suited for ottoman maqams</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextTocRule:14: --><div style="margin-left: 1em;"><a href="#Other models">Other models</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 2em;"><a href="#Other models-Example: Super-symmetrical model with 14/13">Example: Super-symmetrical model with 14/13</a></div> | ||
<!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --></div> | |||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:16 -->Julien Jalaleddine Weiss, used with permission.<br /> | ||
<!-- ws:end:WikiTextTocRule: | |||
Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical University.<br /> | Reference: Pohlit, Stefan. 2011. Julien Jalâl Ed-Dine Weiss – A New Qānūn System: Its Application in the Performance Practice of the Ensemble “Al-Kindi” and in Contemporary Western Music. PhD Thesis, MIAM/Istanbul Technical University.<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
This gives 15 potential different pitches per base note, correpsonding to the mandals. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si), corresponding to the strings, lead to a notation system of 7*15=105 pitches, in accordance with the real playing capabilities of the qanun. 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.<br /> | This gives 15 potential different pitches per base note, correpsonding to the mandals. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si), corresponding to the strings, lead to a notation system of 7*15=105 pitches, in accordance with the real playing capabilities of the qanun. 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.<br /> | ||
<!-- ws:start:WikiTextFileRule: | <!-- ws:start:WikiTextFileRule:213:&lt;img src=&quot;http://www.wikispaces.com/site/embedthumbnail/file/Tableaux%20JJW%20VIII-2011.pdf?h=52&amp;w=320&quot; class=&quot;WikiFile&quot; id=&quot;wikitext@@file@@Tableaux JJW VIII-2011.pdf&quot; title=&quot;File: Tableaux JJW VIII-2011.pdf&quot; width=&quot;320&quot; height=&quot;52&quot; /&gt; --><div class="objectEmbed"><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');"><img src="http://www.wikispaces.com/i/mime/32/application/pdf.png" height="32" width="32" alt="Tableaux JJW VIII-2011.pdf" /></a><div><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">Tableaux JJW VIII-2011.pdf</a><br /><ul><li><a href="/file/detail/Tableaux%20JJW%20VIII-2011.pdf">Details</a></li><li><a href="/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf">Download</a></li><li style="color: #666">130 KB</li></ul></div></div><!-- ws:end:WikiTextFileRule:213 --><br /> | ||
<br /> | <br /> | ||
(used with permission J. J. Weiss/S. Pohlit)<br /> | (used with permission J. J. Weiss/S. Pohlit)<br /> | ||
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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 /> | 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:6:&lt;h1&gt; --><h1 id="toc3"><a name=" | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Other models"></a><!-- ws:end:WikiTextHeadingRule:6 -->Other models</h1> | ||
J. J. Weiss has developed a number of other systems besides the two described above. A notable class of these are so-called super-symmetrical systems, which have the property that the intervals ascending from C and the intervals descending from F (which sho slight differences in the previous two systems, as shown above) are the same.<br /> | |||
<br /> | <br /> | ||
See chapter 3.4 and appendix I in <a class="wiki_link_ext" href="http://stefanpohlit.com/dissertation.engl..htm" rel="nofollow">Stefan Pohlit's dissertation</a> for detailed descriptions.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Other models-Example: Super-symmetrical model with 14/13"></a><!-- ws:end:WikiTextHeadingRule:8 -->Example: Super-symmetrical model with 14/13</h2> | ||
© J.J. Weiss<br /> | © J.J. Weiss<br /> | ||
The idea behind this system is as folows:<br /> | |||
Dividing the apotome (114 cents) into 3 equal parts gives 38 cents, and adding this to the pythagorean limma (90 cents) gives 128 cents, which is the approximation for 14/13.<br /> | |||
The division of the apotome derived from this combines the known basic division into apotome, Zarlinian semitone and apotoms with an equal division into 3 parts, which yields the following mandal positions (cents):<br /> | |||
<br /> | |||
22, 16, 13, 12, 13, 16, 22<br /> | |||
<br /> | |||
(Observe that 22+16 = 38, as wqell as 13+12+13.)<br /> | |||
<br /> | |||
Since the pythagorean limma appears prominently in the basic framework anyway (as semitone from E to F and from B to C as well as one apotome minus a syntonic comma several times on each string), 14/13 also appears at various positions.<br /> | |||
<br /> | |||
Table of pitches from C to F (approximations in cents).<br /> | |||
<table class="wiki_table"> | |||
<tr> | |||
<th>String<br /> | |||
</th> | |||
<th>b<br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th>Base note<br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th><br /> | |||
</th> | |||
<th>#<br /> | |||
</th> | |||
</tr> | |||
<tr> | |||
<th>C<br /> | |||
</th> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: center;">0<br /> | |||
</td> | |||
<td>22<br /> | |||
</td> | |||
<td>38<br /> | |||
</td> | |||
<td>51<br /> | |||
</td> | |||
<td>63<br /> | |||
</td> | |||
<td>76<br /> | |||
</td> | |||
<td>92<br /> | |||
</td> | |||
<td>114<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<th>D<br /> | |||
</th> | |||
<td>90<br /> | |||
</td> | |||
<td>112<br /> | |||
</td> | |||
<td>128<br /> | |||
</td> | |||
<td>141<br /> | |||
</td> | |||
<td>153<br /> | |||
</td> | |||
<td>166<br /> | |||
</td> | |||
<td>182<br /> | |||
</td> | |||
<td style="text-align: center;">204<br /> | |||
</td> | |||
<td>226<br /> | |||
</td> | |||
<td>242<br /> | |||
</td> | |||
<td>255<br /> | |||
</td> | |||
<td>267<br /> | |||
</td> | |||
<td>280<br /> | |||
</td> | |||
<td>196<br /> | |||
</td> | |||
<td>318<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<th>E<br /> | |||
</th> | |||
<td>294<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: center;">408<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>522<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<th>F<br /> | |||
</th> | |||
<td>384<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td style="text-align: center;">498<br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td><br /> | |||
</td> | |||
<td>612<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | <br /> | ||
<br /> | <br /> | ||
XXX</body></html></pre></div> | Ratios XXX</body></html></pre></div> | ||