Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 273065400 - Original comment: ** |
Wikispaces>hstraub **Imported revision 273066306 - 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 07:39:34 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>273066306</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: | |||
<span style="color: #00000a; font-family: Tahoma;">81/80, 125/124, 124/123, 123/122, 122/121, 121/120, 81/80</span> | |||
Table of pitches from C to F (approximations in cents): | Table of pitches from C to F (approximations in cents): | ||
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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, 256/243 | ||
* On the D string (from Db to D): | * On the D string (from Db to D): | ||
> XXX | > XXX | ||
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© J.J. Weiss | © J.J. Weiss | ||
The idea behind this system is as follows: | The idea behind this system is as follows: | ||
Dividing the apotome (114 cents) into 3 equal parts gives 38 cents, and adding this to the pythagorean limma (90 cents) gives 128 cents, which is an approximation for [[14_13|14/13 ]](two-third tone,a favorite interval of [[http://en.wikipedia.org/wiki/Avicenna|Avicenna/Ibn Sina]]). | Dividing the apotome (114 cents) into 3 equal parts gives 38 cents, and adding this to the pythagorean limma (90 cents) gives 128 cents, which is an approximation for [[14_13|14/13 ]](two-third tone, a favorite interval of [[http://en.wikipedia.org/wiki/Avicenna|Avicenna/Ibn Sina]]). | ||
The division of the apotome derived from this combines the known basic division into apotome, Zarlinian semitone and apotome with an equal division into 3 parts, which yields the following mandal positions (cents): | The division of the apotome derived from this combines the known basic division into apotome, Zarlinian semitone and apotome with an equal division into 3 parts, which yields the following mandal positions (cents): | ||
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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 /> | |||
<span style="color: #00000a; font-family: Tahoma;">81/80, 125/124, 124/123, 123/122, 122/121, 121/120, 81/80</span><br /> | |||
<br /> | <br /> | ||
Table of pitches from C to F (approximations in cents):<br /> | Table of pitches from C to F (approximations in cents):<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, 248/225 (168.49), 82/75 (154.47), 244/225 (140.34), 242/225 (126.09), 16/15, 256/243</li><li>On the D string (from Db to D):<br /> | |||
XXX</li></ul><br /> | 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 /> | ||
The idea behind this system is as follows:<br /> | The idea behind this system is as follows:<br /> | ||
Dividing the apotome (114 cents) into 3 equal parts gives 38 cents, and adding this to the pythagorean limma (90 cents) gives 128 cents, which is an approximation for <a class="wiki_link" href="/14_13">14/13 </a>(two-third tone,a favorite interval of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Avicenna" rel="nofollow">Avicenna/Ibn Sina</a>).<br /> | Dividing the apotome (114 cents) into 3 equal parts gives 38 cents, and adding this to the pythagorean limma (90 cents) gives 128 cents, which is an approximation for <a class="wiki_link" href="/14_13">14/13 </a>(two-third tone, a favorite interval of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Avicenna" rel="nofollow">Avicenna/Ibn Sina</a>).<br /> | ||
<br /> | |||
The division of the apotome derived from this combines the known basic division into apotome, Zarlinian semitone and apotome with an equal division into 3 parts, which yields the following mandal positions (cents):<br /> | The division of the apotome derived from this combines the known basic division into apotome, Zarlinian semitone and apotome with an equal division into 3 parts, which yields the following mandal positions (cents):<br /> | ||
<br /> | <br /> | ||