Tuning systems for qanun: Difference between revisions
Wikispaces>hstraub **Imported revision 254649766 - Original comment: ** |
Wikispaces>hstraub **Imported revision 254655006 - Original comment: ** |
||
| Line 1: | Line 1: | ||
<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>2011-09-16 03: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-16 03:44:48 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>254655006</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> | ||
| Line 65: | Line 65: | ||
|| XXX || 27/20 || **351/258** || **XXX** || **243/176** || **891/640** || 45/32 || 729/512 || | || XXX || 27/20 || **351/258** || **XXX** || **243/176** || **891/640** || 45/32 || 729/512 || | ||
==Variant with 128/119== | ===Variant with 128/119=== | ||
128/119: 126.2 cents | 128/119: 126.2 cents | ||
XXX | XXX | ||
==Variant with 128/119 ascending/descending== | ===Variant with 128/119 ascending/descending=== | ||
XXX | XXX | ||
==Variant with 43/40 ascending/descending== | ===Variant with 43/40 ascending/descending=== | ||
43/40: 125.2 cents | 43/40: 125.2 cents | ||
XXX | XXX | ||
| Line 90: | Line 90: | ||
XXX | XXX | ||
==Symmetrical model== | |||
J.J. Weiss | J.J. Weiss | ||
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast. | Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast. | ||
| Line 109: | Line 105: | ||
XXX | XXX | ||
==Super-symmetrical models== | |||
Characteristics of super-symmetric systems: no difference between ascending and descending ratios. | |||
===Equal division of 65/54 and its inverse=== | |||
J.J. Weiss | J.J. Weiss | ||
(XXX Is that formulation correct?) | |||
Ascending/descending with 43/40 (125.2 cents). | Ascending/descending with 43/40 (125.2 cents). | ||
| Line 227: | Line 226: | ||
<!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 1em;"><a href="#Older systems">Older systems</a></div> | <!-- ws:end:WikiTextTocRule:42 --><!-- ws:start:WikiTextTocRule:43: --><div style="margin-left: 1em;"><a href="#Older systems">Older systems</a></div> | ||
<!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Older systems-First System J.J.Weiss">First System J.J.Weiss</a></div> | <!-- ws:end:WikiTextTocRule:43 --><!-- ws:start:WikiTextTocRule:44: --><div style="margin-left: 2em;"><a href="#Older systems-First System J.J.Weiss">First System J.J.Weiss</a></div> | ||
<!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:44 --><!-- ws:start:WikiTextTocRule:45: --><div style="margin-left: 3em;"><a href="#Older systems-First System J.J.Weiss-Variant with 128/119">Variant with 128/119</a></div> | ||
<!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:45 --><!-- ws:start:WikiTextTocRule:46: --><div style="margin-left: 3em;"><a href="#Older systems-First System J.J.Weiss-Variant with 128/119 ascending/descending">Variant with 128/119 ascending/descending</a></div> | ||
<!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:46 --><!-- ws:start:WikiTextTocRule:47: --><div style="margin-left: 3em;"><a href="#Older systems-First System J.J.Weiss-Variant with 43/40 ascending/descending">Variant with 43/40 ascending/descending</a></div> | ||
<!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 1em;"><a href="#Newer systems">Newer systems</a></div> | <!-- ws:end:WikiTextTocRule:47 --><!-- ws:start:WikiTextTocRule:48: --><div style="margin-left: 1em;"><a href="#Newer systems">Newer systems</a></div> | ||
<!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 2em;"><a href="#Newer systems-System 2, better suited for ottoman maqams">System 2, better suited for ottoman maqams</a></div> | <!-- ws:end:WikiTextTocRule:48 --><!-- ws:start:WikiTextTocRule:49: --><div style="margin-left: 2em;"><a href="#Newer systems-System 2, better suited for ottoman maqams">System 2, better suited for ottoman maqams</a></div> | ||
<!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Newer systems-Symmetrical | <!-- ws:end:WikiTextTocRule:49 --><!-- ws:start:WikiTextTocRule:50: --><div style="margin-left: 2em;"><a href="#Newer systems-Symmetrical model">Symmetrical model</a></div> | ||
<!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: | <!-- ws:end:WikiTextTocRule:50 --><!-- ws:start:WikiTextTocRule:51: --><div style="margin-left: 2em;"><a href="#Newer systems-Super-symmetrical models">Super-symmetrical models</a></div> | ||
<!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 3em;"><a href="#Newer systems- | <!-- ws:end:WikiTextTocRule:51 --><!-- ws:start:WikiTextTocRule:52: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Equal division of 65/54 and its inverse">Equal division of 65/54 and its inverse</a></div> | ||
<!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 3em;"><a href="#Newer systems- | <!-- ws:end:WikiTextTocRule:52 --><!-- ws:start:WikiTextTocRule:53: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Unequal division of 65/54">Unequal division of 65/54</a></div> | ||
<!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 3em;"><a href="#Newer systems- | <!-- ws:end:WikiTextTocRule:53 --><!-- ws:start:WikiTextTocRule:54: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Equal division of the Zarlinian semitone">Equal division of the Zarlinian semitone</a></div> | ||
<!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 3em;"><a href="#Newer systems- | <!-- ws:end:WikiTextTocRule:54 --><!-- ws:start:WikiTextTocRule:55: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 54/49">Ascending/descending with 54/49</a></div> | ||
<!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 3em;"><a href="#Newer systems- | <!-- ws:end:WikiTextTocRule:55 --><!-- ws:start:WikiTextTocRule:56: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 14/13">Ascending/descending with 14/13</a></div> | ||
<!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 3em;"><a href="#Newer systems- | <!-- ws:end:WikiTextTocRule:56 --><!-- ws:start:WikiTextTocRule:57: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 11/10">Ascending/descending with 11/10</a></div> | ||
<!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 3em;"><a href="#Newer systems- | <!-- ws:end:WikiTextTocRule:57 --><!-- ws:start:WikiTextTocRule:58: --><div style="margin-left: 3em;"><a href="#Newer systems-Super-symmetrical models-Ascending/descending with 35/32">Ascending/descending with 35/32</a></div> | ||
<!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 2em;"><a href="#Newer systems-System Jacques Dudon (2006)">System Jacques Dudon (2006)</a></div> | <!-- ws:end:WikiTextTocRule:58 --><!-- ws:start:WikiTextTocRule:59: --><div style="margin-left: 2em;"><a href="#Newer systems-System Jacques Dudon (2006)">System Jacques Dudon (2006)</a></div> | ||
<!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 3em;"><a href="#Newer systems-System Jacques Dudon (2006)-Arithmetic system">Arithmetic system</a></div> | <!-- ws:end:WikiTextTocRule:59 --><!-- ws:start:WikiTextTocRule:60: --><div style="margin-left: 3em;"><a href="#Newer systems-System Jacques Dudon (2006)-Arithmetic system">Arithmetic system</a></div> | ||
| Line 481: | Line 480: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:8:&lt; | <!-- ws:start:WikiTextHeadingRule:8:&lt;h3&gt; --><h3 id="toc4"><a name="Older systems-First System J.J.Weiss-Variant with 128/119"></a><!-- ws:end:WikiTextHeadingRule:8 -->Variant with 128/119</h3> | ||
128/119: 126.2 cents<br /> | 128/119: 126.2 cents<br /> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:10:&lt; | <!-- ws:start:WikiTextHeadingRule:10:&lt;h3&gt; --><h3 id="toc5"><a name="Older systems-First System J.J.Weiss-Variant with 128/119 ascending/descending"></a><!-- ws:end:WikiTextHeadingRule:10 -->Variant with 128/119 ascending/descending</h3> | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:12:&lt; | <!-- ws:start:WikiTextHeadingRule:12:&lt;h3&gt; --><h3 id="toc6"><a name="Older systems-First System J.J.Weiss-Variant with 43/40 ascending/descending"></a><!-- ws:end:WikiTextHeadingRule:12 -->Variant with 43/40 ascending/descending</h3> | ||
43/40: 125.2 cents<br /> | 43/40: 125.2 cents<br /> | ||
XXX<br /> | XXX<br /> | ||
| Line 562: | Line 561: | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Newer systems-Symmetrical | <!-- ws:start:WikiTextHeadingRule:18:&lt;h2&gt; --><h2 id="toc9"><a name="Newer systems-Symmetrical model"></a><!-- ws:end:WikiTextHeadingRule:18 -->Symmetrical model</h2> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.<br /> | Advantage: marked contrast between Segah of Ushaq and Segah of arabic Rast.<br /> | ||
| Line 637: | Line 632: | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Newer systems- | <!-- ws:start:WikiTextHeadingRule:20:&lt;h2&gt; --><h2 id="toc10"><a name="Newer systems-Super-symmetrical models"></a><!-- ws:end:WikiTextHeadingRule:20 -->Super-symmetrical models</h2> | ||
Characteristics of super-symmetric systems: no difference between ascending and descending ratios.<br /> | |||
<br /> | |||
<!-- ws:start:WikiTextHeadingRule:22:&lt;h3&gt; --><h3 id="toc11"><a name="Newer systems-Super-symmetrical models-Equal division of 65/54 and its inverse"></a><!-- ws:end:WikiTextHeadingRule:22 -->Equal division of 65/54 and its inverse</h3> | |||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
(XXX Is that formulation correct?)<br /> | |||
Ascending/descending with 43/40 (125.2 cents).<br /> | Ascending/descending with 43/40 (125.2 cents).<br /> | ||
<br /> | <br /> | ||
| Line 649: | Line 647: | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Newer systems- | <!-- ws:start:WikiTextHeadingRule:24:&lt;h3&gt; --><h3 id="toc12"><a name="Newer systems-Super-symmetrical models-Unequal division of 65/54"></a><!-- ws:end:WikiTextHeadingRule:24 -->Unequal division of 65/54</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
<br /> | <br /> | ||
| Line 716: | Line 714: | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Newer systems- | <!-- ws:start:WikiTextHeadingRule:26:&lt;h3&gt; --><h3 id="toc13"><a name="Newer systems-Super-symmetrical models-Equal division of the Zarlinian semitone"></a><!-- ws:end:WikiTextHeadingRule:26 -->Equal division of the Zarlinian semitone</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
This is the simplest variant for luthiers...<br /> | This is the simplest variant for luthiers...<br /> | ||
| Line 852: | Line 850: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Newer systems- | <!-- ws:start:WikiTextHeadingRule:28:&lt;h3&gt; --><h3 id="toc14"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 54/49"></a><!-- ws:end:WikiTextHeadingRule:28 -->Ascending/descending with 54/49</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
<a class="wiki_link" href="/54_49">54/49</a>: 168.2 cents, Zalzal's mujannab (Al Farabi)<br /> | <a class="wiki_link" href="/54_49">54/49</a>: 168.2 cents, Zalzal's mujannab (Al Farabi)<br /> | ||
| Line 922: | Line 920: | ||
Interval table of just intervals XXX<br /> | Interval table of just intervals XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Newer systems- | <!-- ws:start:WikiTextHeadingRule:30:&lt;h3&gt; --><h3 id="toc15"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 14/13"></a><!-- ws:end:WikiTextHeadingRule:30 -->Ascending/descending with 14/13</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
<span style="color: #00000a; font-family: Tahoma;">14/13: 128.3 cents</span><br /> | <span style="color: #00000a; font-family: Tahoma;">14/13: 128.3 cents</span><br /> | ||
| Line 1,011: | Line 1,009: | ||
XXX<br /> | XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Newer systems- | <!-- ws:start:WikiTextHeadingRule:32:&lt;h3&gt; --><h3 id="toc16"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 11/10"></a><!-- ws:end:WikiTextHeadingRule:32 -->Ascending/descending with 11/10</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
11/10: 165 cents<br /> | 11/10: 165 cents<br /> | ||
| Line 1,019: | Line 1,017: | ||
Interval table XXX<br /> | Interval table XXX<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Newer systems- | <!-- ws:start:WikiTextHeadingRule:34:&lt;h3&gt; --><h3 id="toc17"><a name="Newer systems-Super-symmetrical models-Ascending/descending with 35/32"></a><!-- ws:end:WikiTextHeadingRule:34 -->Ascending/descending with 35/32</h3> | ||
J.J. Weiss<br /> | J.J. Weiss<br /> | ||
35/32: 155.14 cents<br /> | 35/32: 155.14 cents<br /> | ||