Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 259930568 - Original comment: ** |
Wikispaces>hstraub **Imported revision 259941894 - 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 08:08:58 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>259941894</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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22, 13, 13, 12, 16, 16, 22 | 22, 13, 13, 12, 16, 16, 22 | ||
Rational intervals each string can be detuned (cents in parentheses): | Rational intervals each string can be detuned (approximations in cents in parentheses): | ||
81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114) | 81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114) | ||
Intervals ratios, ascending from C | Intervals 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), **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) | ||
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81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80 | 81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80 | ||
In cents (approximations: | In cents (approximations): | ||
<span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span> | <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span> | ||
Rational intervals each string can be detuned (cents in parentheses): | Rational intervals each string can be detuned (approximations in cents in parentheses): | ||
81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114) | 81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114) | ||
Intervals ratios, ascending from C: | Intervals ratios, ascending from C: | ||
* On the D string (from Db to D): | |||
> 256/243 (90), 16/15 (112), **14/13 (128), 88/81 (144), 128/117 or 35/32 (156), 119/108 (168)**, 10/9 (182), 9/8 (204) | |||
* On the E string (from Eb to E): | |||
> 32/27 (294), 6/5 (316), **63/52 (332), 11/9 (348), 16/13 or 315/256 (360), 119/96 (372)**, 5/4 (386), 81/64 (408) | |||
Interval ratios descending from F: | Interval ratios descending from F: | ||
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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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22, 13, 13, 12, 16, 16, 22<br /> | 22, 13, 13, 12, 16, 16, 22<br /> | ||
<br /> | <br /> | ||
Rational intervals each string can be detuned (cents in parentheses):<br /> | Rational intervals each string can be detuned (approximations in cents in parentheses):<br /> | ||
81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114)<br /> | 81/80 (22), 49/48 (35), 1053/1024 (48), 729/704 (60), 2673/2560 (76), 135/128 (92), 2187/2048 (114)<br /> | ||
<br /> | <br /> | ||
Intervals ratios, ascending from C | Intervals 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), <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 /> | 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 /> | ||
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81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80<br /> | 81/80, 105/104, 572/567, 144/143, 1547/1536, 120/119, 81/80<br /> | ||
<br /> | <br /> | ||
In cents (approximations: <br /> | In cents (approximations):<br /> | ||
<span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span><br /> | <span style="color: #00000a; font-family: Tahoma;">22|16|15|12|13|14|22</span><br /> | ||
<br /> | <br /> | ||
Rational intervals each string can be detuned (cents in parentheses):<br /> | Rational intervals each string can be detuned (approximations in cents in parentheses):<br /> | ||
81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114)<br /> | 81/80 (22), 1701/1664 (38), 33/32 (54), 27/26 (66), 243/232 (78), 135/128 (92), 2187/2048 (114)<br /> | ||
<br /> | <br /> | ||
Intervals ratios, ascending from C:<br /> | Intervals ratios, ascending from C:<br /> | ||
<ul><li>On the D string (from Db to D):<br /> | |||
<br /> | 256/243 (90), 16/15 (112), <strong>14/13 (128), 88/81 (144), 128/117 or 35/32 (156), 119/108 (168)</strong>, 10/9 (182), 9/8 (204)</li><li>On the E string (from Eb to E):<br /> | ||
32/27 (294), 6/5 (316), <strong>63/52 (332), 11/9 (348), 16/13 or 315/256 (360), 119/96 (372)</strong>, 5/4 (386), 81/64 (408)</li></ul><br /> | |||
Interval ratios descending from F:<br /> | Interval ratios descending from F:<br /> | ||
XXX<br /> | XXX<br /> | ||