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>2011-11-08 06: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-11-08 06:50:03 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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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]] . | 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/ | ==Super-symmetric model with non-aliquot division of 65/64== | ||
© J.J. Weiss | © J.J. Weiss | ||
Similar to [[tuning systems for qanun#System%201|system 1]], but with 65/64 (26.84 cents) divided into two non-equal parts (14 and 12 cents instead of 13 and 13). | |||
Mandal positions in ratios: | Mandal positions in ratios: | ||
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||~ String ||~ b ||~ ||~ ||~ ||~ ||~ ||~ ||~ Base note ||~ ||~ ||~ ||~ ||~ ||~ ||~ # || | ||~ String ||~ b ||~ ||~ ||~ ||~ ||~ ||~ ||~ Base note ||~ ||~ ||~ ||~ ||~ ||~ ||~ # || | ||
||~ C || || || || || || || ||= 0 || 22 || || || || || 92 || 114 || | ||~ C || || || || || || || ||= 0 || 22 || || || || || 92 || 114 || | ||
||~ D || 90 || 112 || | ||~ D || 90 || 112 || 126 || 138 || 156 || 168 || 182 ||= 204 || 226 || || || || || 196 || 318 || | ||
||~ E || 294 || 316 || || || || || 386 ||= 408 || 430 || || || || || 500 || 522 || | ||~ E || 294 || 316 || || || || || 386 ||= 408 || 430 || || || || || 500 || 522 || | ||
||~ F || 384 || 406 || || || || || 476 ||= 498 || 520 || || || || || 590 || 612 || | ||~ F || 384 || 406 || || || || || 476 ||= 498 || 520 || || || || || 590 || 612 || | ||
Interval ratios, ascending from C: | Interval ratios, ascending from C: | ||
* On the D string (from Db to D): | |||
XXX | > 245/243 (90), 16/15 (112), **128/119 (126), 13/12 (138), 128/117 (156), 119/108 (168),** 10/9 (182), 9/8 (204) | ||
> On the E string (from Eb to E): | |||
> XXX | |||
Interval ratios descending from F: | Interval ratios descending from F: | ||
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<!-- 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: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:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 1em;"><a href="#Other models">Other models</a></div> | <!-- ws:end:WikiTextTocRule:17 --><!-- ws:start:WikiTextTocRule:18: --><div style="margin-left: 1em;"><a href="#Other models">Other models</a></div> | ||
<!-- 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/ | <!-- 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 65/64">Super-symmetric model with non-aliquot division of 65/64</a></div> | ||
<!-- 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: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: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: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> | ||
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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:594:&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:594 --><br /> | ||
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(used with permission J. J. Weiss/S. Pohlit)<br /> | (used with permission J. J. Weiss/S. Pohlit)<br /> | ||
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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 /> | 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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Other models-Super-symmetric model with non-aliquot division of 65/ | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><h2 id="toc4"><a name="Other models-Super-symmetric model with non-aliquot division of 65/64"></a><!-- ws:end:WikiTextHeadingRule:8 -->Super-symmetric model with non-aliquot division of 65/64</h2> | ||
© J.J. Weiss<br /> | © J.J. Weiss<br /> | ||
Similar to <a class="wiki_link" href="/tuning%20systems%20for%20qanun#System%201">system 1</a>, but with 65/64 (26.84 cents) divided into two non-equal parts (14 and 12 cents instead of 13 and 13).<br /> | |||
<br /> | <br /> | ||
Mandal positions in ratios:<br /> | Mandal positions in ratios:<br /> | ||
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<td>112<br /> | <td>112<br /> | ||
</td> | </td> | ||
<td><br /> | <td>126<br /> | ||
</td> | </td> | ||
<td><br /> | <td>138<br /> | ||
</td> | </td> | ||
<td><br /> | <td>156<br /> | ||
</td> | </td> | ||
<td><br /> | <td>168<br /> | ||
</td> | </td> | ||
<td>182<br /> | <td>182<br /> | ||
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</table> | </table> | ||
<br /> | <br /> | ||
Interval ratios, ascending from C:<br /> | Interval ratios, ascending from C:<br /> | ||
<br /> | <ul><li>On the D string (from Db to D):<br /> | ||
245/243 (90), 16/15 (112), <strong>128/119 (126), 13/12 (138), 128/117 (156), 119/108 (168),</strong> 10/9 (182), 9/8 (204)<br /> | |||
<br /> | On the E string (from Eb to E):<br /> | ||
XXX</li></ul><br /> | |||
Interval ratios descending from F:<br /> | Interval ratios descending from F:<br /> | ||
<br /> | <br /> | ||