Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 262990758 - Original comment: ** |
Wikispaces>hstraub **Imported revision 270541834 - 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- | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-11-01 04:32:16 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>270541834</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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Julien 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 show slight differences in the previous two systems, marked in **bold** above) are the same. | Julien 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 show slight differences in the previous two systems, marked in **bold** above) are the same. | ||
3 examples are described below. For more and detailed descriptions see chapter 3.4 and appendix I in [[http://stefanpohlit.com/dissertation.engl..htm|Stefan Pohlit's dissertation]] . | |||
== | ==Super-symmetric model with non-aliquot division of 65/54== | ||
<span style="background-color: #aaffaa; color: #008800; text-decoration: inherit;"> </span> | |||
© J.J. Weiss | |||
Mandal positions in ratios: | |||
81/80 (22), 120/119 (14), 1547/1536 (12), <span style="color: #00000a; font-family: 'Tahoma','sans-serif';">512/507 (17), </span>1547/1536 (12), 120/119 (14)<span style="color: #00000a; font-family: 'Tahoma','sans-serif';">, 81/80 (22)</span> | |||
Table of pitches from C to F (approximations in cents): | |||
XXX | |||
Interval ratios, ascending from C: | |||
XXX | |||
Interval ratios descending from F: | |||
XXX | |||
==Equal division of the Zarlinian semitone== | |||
© J.J. Weiss | |||
[[#htmldiff76]]<span style="background-color: #aaffaa; color: #008800; text-decoration: inherit;"> </span> | |||
This is the simplest variant for luthiers... | |||
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;"> 22|14|14|14|14|14|22 </span> | |||
Table of pitches from C to F (approximations in cents): | |||
XXX | |||
Interval ratios, ascending from C: | |||
XXX | |||
Interval ratios descending from F: | |||
XXX | |||
==Super-symmetrical model with 14/13== | |||
© J.J. Weiss | © J.J. Weiss | ||
The idea behind this system is as follows: | The idea behind this system is as follows: | ||
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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. | 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) | Table of pitches from C to F (approximations in cents): | ||
||~ String ||~ b ||~ ||~ ||~ ||~ ||~ ||~ ||~ Base note ||~ ||~ ||~ ||~ ||~ ||~ ||~ # || | ||~ String ||~ b ||~ ||~ ||~ ||~ ||~ ||~ ||~ Base note ||~ ||~ ||~ ||~ ||~ ||~ ||~ # || | ||
||~ C || || || || || || || ||= 0 || 22 || 38 || 51 || 63 || 76 || 92 || 114 || | ||~ C || || || || || || || ||= 0 || 22 || 38 || 51 || 63 || 76 || 92 || 114 || | ||
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<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:14:&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:14 --><!-- ws:start:WikiTextTocRule:15: --><div style="margin-left: 1em;"><a href="#Notation">Notation</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:15 --><!-- ws:start:WikiTextTocRule:16: --><div style="margin-left: 1em;"><a href="#System 1">System 1</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:16 --><!-- ws:start:WikiTextTocRule:17: --><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:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 1em;"><a href="#Other models">Other models</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:18 --><!-- ws:start:WikiTextTocRule:19: --><div style="margin-left: 2em;"><a href="#Other models-Super-symmetric model with non-aliquot division of 65/54">Super-symmetric model with non-aliquot division of 65/54</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:19 --><!-- ws:start:WikiTextTocRule:20: --><div style="margin-left: 2em;"><a href="#Other models-Equal division of the Zarlinian semitone">Equal division of the Zarlinian semitone</a></div> | ||
<!-- ws:end:WikiTextTocRule: | <!-- ws:end:WikiTextTocRule:20 --><!-- ws:start:WikiTextTocRule:21: --><div style="margin-left: 2em;"><a href="#Other models-Super-symmetrical model with 14/13">Super-symmetrical model with 14/13</a></div> | ||
<!-- ws:end:WikiTextTocRule:21 --><!-- ws:start:WikiTextTocRule:22: --></div> | |||
<!-- ws:end:WikiTextTocRule:22 -->Julien Jalaleddine Weiss, used with permission.<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 /> | 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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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:236:&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:236 --><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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Julien 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 show slight differences in the previous two systems, marked in <strong>bold</strong> above) are the same.<br /> | Julien 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 show slight differences in the previous two systems, marked in <strong>bold</strong> above) are the same.<br /> | ||
<br /> | <br /> | ||
3 examples are described below. For more and detailed descriptions 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> .<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Other models-Super-symmetric model with non-aliquot division of 65/54"></a><!-- ws:end:WikiTextHeadingRule:8 -->Super-symmetric model with non-aliquot division of 65/54</h2> | |||
<span style="background-color: #aaffaa; color: #008800; text-decoration: inherit;"> </span><br /> | |||
© J.J. Weiss<br /> | |||
<br /> | |||
Mandal positions in ratios:<br /> | |||
81/80 (22), 120/119 (14), 1547/1536 (12), <span style="color: #00000a; font-family: 'Tahoma','sans-serif';">512/507 (17), </span>1547/1536 (12), 120/119 (14)<span style="color: #00000a; font-family: 'Tahoma','sans-serif';">, 81/80 (22)</span><br /> | |||
<br /> | |||
Table of pitches from C to F (approximations in cents):<br /> | |||
<br /> | |||
<br /> | |||
XXX<br /> | |||
<br /> | |||
Interval ratios, ascending from C:<br /> | |||
<br /> | |||
XXX<br /> | |||
<br /> | |||
Interval ratios descending from F:<br /> | |||
<br /> | |||
XXX<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:10:&lt;h2&gt; --><h2 id="toc5"><a name="Other models-Equal division of the Zarlinian semitone"></a><!-- ws:end:WikiTextHeadingRule:10 -->Equal division of the Zarlinian semitone</h2> | |||
© J.J. Weiss<br /> | |||
<!-- ws:start:WikiTextAnchorRule:23:&lt;img src=&quot;/i/anchor.gif&quot; class=&quot;WikiAnchor&quot; alt=&quot;Anchor&quot; id=&quot;wikitext@@anchor@@htmldiff76&quot; title=&quot;Anchor: htmldiff76&quot;/&gt; --><a name="htmldiff76"></a><!-- ws:end:WikiTextAnchorRule:23 --><span style="background-color: #aaffaa; color: #008800; text-decoration: inherit;"> </span><br /> | |||
This is the simplest variant for luthiers...<br /> | |||
<br /> | |||
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;"> 22|14|14|14|14|14|22 </span><br /> | |||
<br /> | |||
Table of pitches from C to F (approximations in cents):<br /> | |||
<br /> | |||
XXX<br /> | |||
<br /> | |||
Interval ratios, ascending from C:<br /> | |||
<br /> | |||
XXX<br /> | |||
<br /> | |||
Interval ratios descending from F:<br /> | |||
<br /> | |||
XXX<br /> | |||
<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:12:&lt;h2&gt; --><h2 id="toc6"><a name="Other models-Super-symmetrical model with 14/13"></a><!-- ws:end:WikiTextHeadingRule:12 -->Super-symmetrical model with 14/13</h2> | ||
© J.J. Weiss<br /> | © J.J. Weiss<br /> | ||
The idea behind this system is as follows:<br /> | The idea behind this system is as follows:<br /> | ||
| Line 222: | Line 304: | ||
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 /> | 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 /> | <br /> | ||
Table of pitches from C to F (approximations in cents) | Table of pitches from C to F (approximations in cents):<br /> | ||