Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 318985762 - Original comment: ** |
Wikispaces>JosephRuhf **Imported revision 341822682 - 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:JosephRuhf|JosephRuhf]] and made on <tt>2012-06-01 13:55:47 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>341822682</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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> 81/64 (408), 5/4 (386), **243/196 (372)**, **16/13 (360)**, **11/9 (348)**, **40/33 (333)**, 6/5 (316), 32/27 (294) | > 81/64 (408), 5/4 (386), **243/196 (372)**, **16/13 (360)**, **11/9 (348)**, **40/33 (333)**, 6/5 (316), 32/27 (294) | ||
A complete list of all intervals available within one octave can be found in the above-mentioned [[ | A complete list of all intervals available within one octave can be found in the above-mentioned [[file:xenharmonic/Tableaux JJW VIII-2011.pdf|document]] (on the first page). | ||
=System 2, better suited for ottoman maqams= | =System 2, better suited for ottoman maqams= | ||
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> 81/64 (408), 5/4 (386), **26/21 (370), 27/22 (354), 39/32 (342), 144/119 (330)**, 6/5 (316), 32/27 (294) | > 81/64 (408), 5/4 (386), **26/21 (370), 27/22 (354), 39/32 (342), 144/119 (330)**, 6/5 (316), 32/27 (294) | ||
A complete list of all intervals available within one octave can be found in the above-mentioned [[ | A complete list of all intervals available within one octave can be found in the above-mentioned [[file:xenharmonic/Tableaux JJW VIII-2011.pdf|document]] (on the second page). | ||
=Other models= | =Other models= | ||
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||~ E || 294 || 316 || 330 || 342 || 360 || 372 || 386 ||= 408 || 430 || 444 || 456 || 374 || 386 || 400 || 422 || | ||~ E || 294 || 316 || 330 || 342 || 360 || 372 || 386 ||= 408 || 430 || 444 || 456 || 374 || 386 || 400 || 422 || | ||
||~ F || 384 || 406 || 420 || 433 || 450 || 462 || 476 ||= 498 || 520 || 534 || 546 || 464 || 476 || 590 || 612 || | ||~ F || 384 || 406 || 420 || 433 || 450 || 462 || 476 ||= 498 || 520 || 534 || 546 || 464 || 476 || 590 || 612 || | ||
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Interval ratios, ascending from C: | Interval ratios, ascending from C: | ||
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Interval ratios, ascending from C: | Interval ratios, ascending from C: | ||
* On the D string (from Db to D): | * On the D string (from Db to D): | ||
> 256/243 (90), 16/15/112), 14/13 (128), 64/59 (141), 59/54 /153), 209/189 (166), 10(9 (182), 9/8 (204) | > 256/243 (90), [[tel:16/15/112|16/15/112]]), 14/13 (128), 64/59 (141), [[tel:59/54 /153|59/54 /153]]), 209/189 (166), 10(9 (182), 9/8 (204) | ||
* On the E string (from Eb to E): | * On the E string (from Eb to E): | ||
> 32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</pre></div> | > 32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</pre></div> | ||
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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:644:&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:644 --><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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9/8 (204), 10/9 (182), <strong>54/49 (169)</strong>, <strong>128/117 (156)</strong>, <strong>88/81 (144)</strong>, <strong>320/297 (129)</strong>, 16/15 (112), 256/243 (90)</li><li>On the D string (from Db to D):<br /> | 9/8 (204), 10/9 (182), <strong>54/49 (169)</strong>, <strong>128/117 (156)</strong>, <strong>88/81 (144)</strong>, <strong>320/297 (129)</strong>, 16/15 (112), 256/243 (90)</li><li>On the D string (from Db to D):<br /> | ||
81/64 (408), 5/4 (386), <strong>243/196 (372)</strong>, <strong>16/13 (360)</strong>, <strong>11/9 (348)</strong>, <strong>40/33 (333)</strong>, 6/5 (316), 32/27 (294)</li></ul><br /> | 81/64 (408), 5/4 (386), <strong>243/196 (372)</strong>, <strong>16/13 (360)</strong>, <strong>11/9 (348)</strong>, <strong>40/33 (333)</strong>, 6/5 (316), 32/27 (294)</li></ul><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 | 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%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');">document</a> (on the first page).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="System 2, better suited for ottoman maqams"></a><!-- ws:end:WikiTextHeadingRule:4 -->System 2, better suited for ottoman maqams</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="System 2, better suited for ottoman maqams"></a><!-- ws:end:WikiTextHeadingRule:4 -->System 2, better suited for ottoman maqams</h1> | ||
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9/8 (204), 10/9 (182), <strong>208/189 (166), 12/11 (150), 13/12 (138), 128/119 (126)</strong>, 16/15 (112), 256/243 (90)</li><li>On the D string (from Db to D):<br /> | 9/8 (204), 10/9 (182), <strong>208/189 (166), 12/11 (150), 13/12 (138), 128/119 (126)</strong>, 16/15 (112), 256/243 (90)</li><li>On the D string (from Db to D):<br /> | ||
81/64 (408), 5/4 (386), <strong>26/21 (370), 27/22 (354), 39/32 (342), 144/119 (330)</strong>, 6/5 (316), 32/27 (294)</li></ul><br /> | 81/64 (408), 5/4 (386), <strong>26/21 (370), 27/22 (354), 39/32 (342), 144/119 (330)</strong>, 6/5 (316), 32/27 (294)</li></ul><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 | 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%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf" onclick="ws.common.trackFileLink('http://xenharmonic.wikispaces.com/file/view/Tableaux%20JJW%20VIII-2011.pdf/253043932/Tableaux%20JJW%20VIII-2011.pdf');">document</a> (on the second page).<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Other models"></a><!-- ws:end:WikiTextHeadingRule:6 -->Other models</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Other models"></a><!-- ws:end:WikiTextHeadingRule:6 -->Other models</h1> | ||
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Interval ratios, ascending from C:<br /> | Interval ratios, ascending from C:<br /> | ||
<ul><li>On the D string (from Db to D):<br /> | <ul><li>On the D string (from Db to D):<br /> | ||
256/243 (90), 16/15/112), 14/13 (128), 64/59 (141), 59/54 /153), 209/189 (166), 10(9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):<br /> | 256/243 (90), [[tel:16/15/112|16/15/112]]), 14/13 (128), 64/59 (141), [[tel:59/54 /153|59/54 /153]]), 209/189 (166), 10(9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):<br /> | ||
32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul></body></html></pre></div> | 32/27 (294), 6/5 (316), 63/52 (332), 72/59 (345), 59/48 (357), 26/21 (370), 5/4 (386), 81/64 (408)</li></ul></body></html></pre></div> | ||