Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 259921722 - Original comment: ** |
Wikispaces>hstraub **Imported revision 259923008 - 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>2011-09-30 | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-30 06:04:18 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>259923008</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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81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80 | 81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80 | ||
In cents (approximations): | In cents (approximations): | ||
22, 13, 13, 12, 16, 16, 22 | 22, 13, 13, 12, 16, 16, 22 | ||
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Intervals ratios, ascending from C (cent values in parentheses): | Intervals ratios, ascending from C (cent values in parentheses): | ||
* On the D string (from Db to D): | * On the D string (from Db to D): | ||
> 256/243 (90), 16/15 (112), 784/729 (126), 13/12 (138), 12/11 (150), 11/10 (166), 10/9 (182), 9/8 (204) | > 256/243 (90), 16/15 (112), **784/729 (126)**, **13/12 (138)**, **12/11 (150)**, **11/10 (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), 98/81 (330), 39/32 (342), 27/22 (354), | > 32/27 (294), 6/5 (316), **98/81 (330)**, **39/32 (342)**, **27/22 (354)**, **89/80 (370)**, 5/4 (386), 81/64 (408) | ||
Interval ratios, descending from F: | Interval ratios, descending from F: | ||
* On the E string (from Eb to E): | |||
> 9/8 (204), 10/9 (182), **54/49 (169)**, **128/117 (156)**, **88/81 (144)**, **320/297 (129)**, 16/15 (112), 256/243 (90) | |||
* On the D string (from Db to D): | |||
> 81/64 (408), 5/4 (386), **243/196 (372)**, **16/13 (360)**, **11/9 (348)**, **40/33 (333)**, 6/5 (316), 32/27 (294) | |||
===Variant with 128/119=== | ===Variant with 128/119=== | ||
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<br /> | <br /> | ||
This gives 15 potential different pitches per base note, in accordance with the real playing capabilities of the qanun. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si) lead to a notation system of 7*15=105 pitches. 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, in accordance with the real playing capabilities of the qanun. Seven base notes (C, D, E, F, G, A, B or Do, Re, Mi, Fa, Sol, La, Si) lead to a notation system of 7*15=105 pitches. 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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<br /> | <br /> | ||
(used with permission J. J. Weiss/S. Pohlit)<br /> | (used with permission J. J. Weiss/S. Pohlit)<br /> | ||
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81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80<br /> | 81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80<br /> | ||
<br /> | <br /> | ||
In cents (approximations): <br /> | In cents (approximations):<br /> | ||
22, 13, 13, 12, 16, 16, 22<br /> | 22, 13, 13, 12, 16, 16, 22<br /> | ||
<br /> | <br /> | ||
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Intervals ratios, ascending from C (cent values in parentheses):<br /> | Intervals ratios, ascending from C (cent values in parentheses):<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), 784/729 (126), 13/12 (138), 12/11 (150), 11/10 (166), 10/9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):<br /> | 256/243 (90), 16/15 (112), <strong>784/729 (126)</strong>, <strong>13/12 (138)</strong>, <strong>12/11 (150)</strong>, <strong>11/10 (166)</strong>, 10/9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):<br /> | ||
32/27 (294), 6/5 (316), 98/81 (330), 39/32 (342), 27/22 (354), | 32/27 (294), 6/5 (316), <strong>98/81 (330)</strong>, <strong>39/32 (342)</strong>, <strong>27/22 (354)</strong>, <strong>89/80 (370)</strong>, 5/4 (386), 81/64 (408)</li></ul><br /> | ||
Interval ratios, descending from F:<br /> | Interval ratios, descending from F:<br /> | ||
<ul><li>On the E string (from Eb to E):<br /> | |||
<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 /> | |||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Older systems-System 1 J.J.Weiss-Variant with 128/119"></a><!-- ws:end:WikiTextHeadingRule:6 -->Variant with 128/119</h3> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h3&gt; --><h3 id="toc3"><a name="Older systems-System 1 J.J.Weiss-Variant with 128/119"></a><!-- ws:end:WikiTextHeadingRule:6 -->Variant with 128/119</h3> | ||
128/119: 126.2 cents<br /> | 128/119: 126.2 cents<br /> | ||