Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 270541834 - Original comment: ** |
Wikispaces>hstraub **Imported revision 273045912 - 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>2011-11- | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-11-08 05:47:51 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>273045912</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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==Super-symmetric model with non-aliquot division of 65/54== | ==Super-symmetric model with non-aliquot division of 65/54== | ||
© J.J. Weiss | © J.J. Weiss | ||
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==Equal division of the Zarlinian semitone== | ==Equal division of the Zarlinian semitone== | ||
© J.J. Weiss | © J.J. Weiss | ||
[[#htmldiff76]] | [[#htmldiff76]] | ||
This is the simplest variant for luthiers... | This is the simplest variant for luthiers... | ||
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Table of pitches from C to F (approximations in cents): | Table of pitches from C to F (approximations in cents): | ||
||~ String ||~ b ||~ ||~ ||~ ||~ ||~ ||~ ||~ Base note ||~ ||~ ||~ ||~ ||~ ||~ ||~ # || | |||
||~ C || || || || || || || ||= 0 || 22 || 36 || 50 || 64 || 78 || 92 || 114 || | |||
||~ D || 90 || 112 || 126 || 140 || 154 || 168 || 182 ||= 204 || 226 || 240 || 254 || 268 || 282 || 296 || 318 || | |||
||~ E || 294 || 316 || 330 || 344 || 358 || 372 || 386 ||= 408 || 430 || 444 || 458 || 472 || 486 || 500 || 522 || | |||
||~ F || 384 || 406 || 420 || 434 || 448 || 462 || 476 ||= 498 || 520 || 534 || 548 || 562 || 576 || 590 || 612 || | |||
Interval ratios, ascending from C: | Interval ratios, ascending from C: | ||
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||~ 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 || | ||
||~ D || 90 || 112 || 128 || 141 || 153 || 166 || 182 ||= 204 || 226 || 242 || 255 || 267 || 280 || | ||~ D || 90 || 112 || 128 || 141 || 153 || 166 || 182 ||= 204 || 226 || 242 || 255 || 267 || 280 || 296 || 318 || | ||
||~ E || 294 || 316 || 329 || 341 || 354 || 370 || 386 ||= 408 || 430 || 446 || 459 || 471 || 484 || 500 || 522 || | ||~ E || 294 || 316 || 329 || 341 || 354 || 370 || 386 ||= 408 || 430 || 446 || 459 || 471 || 484 || 500 || 522 || | ||
||~ F || 384 || 406 || 422 || 435 || 447 || 460 || 476 ||= 498 || 520 || 536 || 549 || 561 || 574 || 590 || 612 || | ||~ F || 384 || 406 || 422 || 435 || 447 || 460 || 476 ||= 498 || 520 || 536 || 549 || 561 || 574 || 590 || 612 || | ||
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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:408:&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:408 --><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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<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> | <!-- 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> | ||
<br /> | |||
© J.J. Weiss<br /> | © J.J. Weiss<br /> | ||
<br /> | <br /> | ||
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<!-- 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> | <!-- 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 /> | © 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 -- | <!-- 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 --><br /> | ||
This is the simplest variant for luthiers...<br /> | This is the simplest variant for luthiers...<br /> | ||
<br /> | <br /> | ||
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<br /> | <br /> | ||
Table of pitches from C to F (approximations in cents):<br /> | Table of pitches from C to F (approximations in cents):<br /> | ||
<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>36<br /> | |||
</td> | |||
<td>50<br /> | |||
</td> | |||
<td>64<br /> | |||
</td> | |||
<td>78<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>126<br /> | |||
</td> | |||
<td>140<br /> | |||
</td> | |||
<td>154<br /> | |||
</td> | |||
<td>168<br /> | |||
</td> | |||
<td>182<br /> | |||
</td> | |||
<td style="text-align: center;">204<br /> | |||
</td> | |||
<td>226<br /> | |||
</td> | |||
<td>240<br /> | |||
</td> | |||
<td>254<br /> | |||
</td> | |||
<td>268<br /> | |||
</td> | |||
<td>282<br /> | |||
</td> | |||
<td>296<br /> | |||
</td> | |||
<td>318<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<th>E<br /> | |||
</th> | |||
<td>294<br /> | |||
</td> | |||
<td>316<br /> | |||
</td> | |||
<td>330<br /> | |||
</td> | |||
<td>344<br /> | |||
</td> | |||
<td>358<br /> | |||
</td> | |||
<td>372<br /> | |||
</td> | |||
<td>386<br /> | |||
</td> | |||
<td style="text-align: center;">408<br /> | |||
</td> | |||
<td>430<br /> | |||
</td> | |||
<td>444<br /> | |||
</td> | |||
<td>458<br /> | |||
</td> | |||
<td>472<br /> | |||
</td> | |||
<td>486<br /> | |||
</td> | |||
<td>500<br /> | |||
</td> | |||
<td>522<br /> | |||
</td> | |||
</tr> | |||
<tr> | |||
<th>F<br /> | |||
</th> | |||
<td>384<br /> | |||
</td> | |||
<td>406<br /> | |||
</td> | |||
<td>420<br /> | |||
</td> | |||
<td>434<br /> | |||
</td> | |||
<td>448<br /> | |||
</td> | |||
<td>462<br /> | |||
</td> | |||
<td>476<br /> | |||
</td> | |||
<td style="text-align: center;">498<br /> | |||
</td> | |||
<td>520<br /> | |||
</td> | |||
<td>534<br /> | |||
</td> | |||
<td>548<br /> | |||
</td> | |||
<td>562<br /> | |||
</td> | |||
<td>576<br /> | |||
</td> | |||
<td>590<br /> | |||
</td> | |||
<td>612<br /> | |||
</td> | |||
</tr> | |||
</table> | |||
<br /> | <br /> | ||
Interval ratios, ascending from C:<br /> | Interval ratios, ascending from C:<br /> | ||
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<td>280<br /> | <td>280<br /> | ||
</td> | </td> | ||
<td> | <td>296<br /> | ||
</td> | </td> | ||
<td>318<br /> | <td>318<br /> | ||