Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 259901946 - Original comment: ** |
Wikispaces>hstraub **Imported revision 259921722 - 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 05:53:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>259921722</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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Luthier: Ejder Gulec. | Luthier: Ejder Gulec. | ||
Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents). | Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents). | ||
65/64 and 55/54 are each split into two. | 65/64 and 55/54 are each split into two roughly equal parts. | ||
This gives the following | This gives the following rational intervals between the mandals: | ||
81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80 | |||
Intervals ratios, ascending from C: | In cents (approximations): | ||
22, 13, 13, 12, 16, 16, 22 | |||
Rational intervals each string can be detuned: | |||
81/80, 49/48, 1053/1024, 729/704, 2673/2560, 135/128, 2187/2048 | |||
Intervals ratios, ascending from C (cent values in parentheses): | |||
* 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) | |||
* On the E string (from Eb to E): | |||
> 32/27 (294), 6/5 (316), 98/81 (330), 39/32 (342), 27/22 (354),8 9/80 (370), 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 /> | ||
| Line 198: | Line 208: | ||
Luthier: Ejder Gulec.<br /> | Luthier: Ejder Gulec.<br /> | ||
Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).<br /> | Subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).<br /> | ||
65/64 and 55/54 are each split into two.<br /> | 65/64 and 55/54 are each split into two roughly equal parts.<br /> | ||
<br /> | |||
This gives the following rational intervals between the mandals:<br /> | |||
81/80, 245/243, 3159/3136, 144/143, 121/120, 100/99, 81/80<br /> | |||
<br /> | <br /> | ||
In cents (approximations): <br /> | |||
22, 13, 13, 12, 16, 16, 22<br /> | |||
<br /> | <br /> | ||
Rational intervals each string can be detuned:<br /> | |||
81/80, 49/48, 1053/1024, 729/704, 2673/2560, 135/128, 2187/2048<br /> | |||
<br /> | <br /> | ||
Intervals ratios, ascending from C (cent values in parentheses):<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 /> | |||
32/27 (294), 6/5 (316), 98/81 (330), 39/32 (342), 27/22 (354),8 9/80 (370), 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 /> | ||