Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 273067010 - Original comment: ** |
Wikispaces>hstraub **Imported revision 273067222 - 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>2011-11-08 07: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-11-08 07:43:49 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>273067222</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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Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;"> 22|14|14|14|14|14|22 </span> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;"> 22|14|14|14|14|14|22 </span> | ||
Mandal positions in ratios: | Mandal positions in ratios: | ||
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Interval ratios descending from F: | Interval ratios descending from F: | ||
* On the E string (from Eb to E): | * On the E string (from Eb to E): | ||
> 9/8, 10/9, **248/225 (168.49), 82/75 (154.47), 244/225 (140.34), 242/225 (126.09**), 16/15, 256/243or approximating ratios: | > 9/8, 10/9, **248/225 (168.49), 82/75 (154.47), 244/225 (140.34), 242/225 (126.09**), 16/15, 256/243or approximating ratios: XXX | ||
* On the D string (from Db to D): | * On the D string (from Db to D): | ||
> 81/64, 5/4, **31/25 (372.40), 49/40 (351.33), 61/50 (344.25), 121/100 (330)**, 6/5, 32/27Or approximatiing ratios: | > 81/64, 5/4, **31/25 (372.40), 49/40 (351.33), 61/50 (344.25), 121/100 (330)**, 6/5, 32/27Or approximatiing ratios: XXX | ||
==Super-symmetrical model with 14/13== | ==Super-symmetrical model with 14/13== | ||
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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 /> | ||
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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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<br /> | <br /> | ||
Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;"> 22|14|14|14|14|14|22 </span><br /> | Mandal positions (cents): <span style="color: #00000a; font-family: Tahoma;"> 22|14|14|14|14|14|22 </span><br /> | ||
<br /> | <br /> | ||
Mandal positions in ratios:<br /> | Mandal positions in ratios:<br /> | ||
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Interval ratios descending from F:<br /> | Interval ratios descending from F:<br /> | ||
<ul><li>On the E string (from Eb to E):<br /> | <ul><li>On the E string (from Eb to E):<br /> | ||
9/8, 10/9, <strong>248/225 (168.49), 82/75 (154.47), 244/225 (140.34), 242/225 (126.09</strong>), 16/15, 256/243or approximating ratios: | 9/8, 10/9, <strong>248/225 (168.49), 82/75 (154.47), 244/225 (140.34), 242/225 (126.09</strong>), 16/15, 256/243or approximating ratios: XXX</li><li>On the D string (from Db to D):<br /> | ||
XXX</li><li>On the D string (from Db to D):<br /> | 81/64, 5/4, <strong>31/25 (372.40), 49/40 (351.33), 61/50 (344.25), 121/100 (330)</strong>, 6/5, 32/27Or approximatiing ratios: XXX</li></ul><br /> | ||
81/64, 5/4, <strong>31/25 (372.40), 49/40 (351.33), 61/50 (344.25), 121/100 (330)</strong>, 6/5, 32/27Or approximatiing ratios: | |||
XXX</li></ul><br /> | |||
<!-- 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> | <!-- 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 /> | ||