Tuning systems for qanun: Difference between revisions

Line 1:

<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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>2011-08-13 08:39:04 UTC</tt>.<br>

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-13 13:35:28 UTC</tt>.<br>

: The original revision id was <tt>~~245751113~~</tt>.<br>

: The original revision id was <tt>245775769</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>

Line 22:

=Older systems=

==First system J.J.Weiss==

Inequal subdivision of the [[2187_2048|apotome (2187/2048, 113.7 cents)]] into 7 parts (8 mandals/orabs).

Inequal subdivision of the [[2187_2048|apotome (2187/2048, 113.7 cents)]] into 7 parts (8 mandals/orabs), in the following manner:

~~Rough subdivision~~ into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|~~Zarlino~~ semitone (25/24, 70.7 cents)]] and another syntonic comma. ~~Finer~~ subdivision of ~~the~~ 25/24.

* Subdivision into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlinian semitone (25/24, 70.7 cents)]] and another syntonic comma.

~~(luthier Ejder Gulec)~~

* Further 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.

~~Positioning~~ of the mandals at: 22, 13, 13, 12, 16,|16, 22 cents.

This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.

~~Ratios~~: ~~XXX~~

Luthier: Ejder Gulec

Interval Table (cents):

Line 38:

Line 39:

Approximated just intervals:

XXX under construction

|| 1/1 || || || || || || || ||

|| 1/1 || 81/80 || || || || || || ||

|| || || || || || || || ||

Line 74:

Line 75:

<h1 id="toc1"><a name="Older systems"></a>Older systems</h1>

<h2 id="toc2"><a name="Older systems-First system J.J.Weiss"></a>First system J.J.Weiss</h2>

Inequal subdivision of the <a class="wiki_link" href="/2187_2048">apotome (2187/2048, 113.7 cents)</a> into 7 parts (8 mandals/orabs).<br />

Inequal subdivision of the <a class="wiki_link" href="/2187_2048">apotome (2187/2048, 113.7 cents)</a> into 7 parts (8 mandals/orabs), in the following manner:<br />

~~Rough subdivision~~ into one <a class="wiki_link" href="/81_80">syntonic comma (81/80, 21.5 cents)</a>, one <a class="wiki_link" href="/25_24">~~Zarlino~~ semitone (25/24, 70.7 cents)</a> and another syntonic comma. ~~Finer~~ subdivision of ~~the~~ 25/24.<br />

<ul><li>Subdivision into one <a class="wiki_link" href="/81_80">syntonic comma (81/80, 21.5 cents)</a>, one <a class="wiki_link" href="/25_24">Zarlinian semitone (25/24, 70.7 cents)</a> and another syntonic comma.</li><li>Further subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).</li><li>65/64 and 55/54 are each split into two.</li></ul><br />

~~(luthier Ejder Gulec)~~<br />

This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.<br />

<br />

Luthier: Ejder Gulec<br />

~~Positioning~~ of the mandals at: 22, 13, 13, 12, 16,|16, 22 cents.<br />

~~Ratios~~: ~~XXX~~<br />

<br />

Interval Table (cents):<br />

Line 186:

Line 185:

</td>

</td>

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 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>2011-08-13 08:39:04 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-08-13 13:35:28 UTC</tt>.<br>
-: The original revision id was <tt>245751113</tt>.<br>
+: The original revision id was <tt>245775769</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>
@@ Line 22: / Line 22: @@
 =Older systems=
 ==First system J.J.Weiss==
-Inequal subdivision of the [[2187_2048|apotome (2187/2048, 113.7 cents)]] into 7 parts (8 mandals/orabs).
+Inequal subdivision of the [[2187_2048|apotome (2187/2048, 113.7 cents)]] into 7 parts (8 mandals/orabs), in the following manner:
-Rough subdivision into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlino semitone (25/24, 70.7 cents)]] and another syntonic comma. Finer subdivision of the 25/24.
+* Subdivision into one [[81_80|syntonic comma (81/80, 21.5 cents)]], one [[25_24|Zarlinian semitone (25/24, 70.7 cents)]] and another syntonic comma.
-(luthier Ejder Gulec)
+* Further 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.
-Positioning of the mandals at: 22, 13, 13, 12, 16,|16, 22 cents.
+This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.
-Ratios: XXX
+Luthier: Ejder Gulec
 Interval Table (cents):
@@ Line 38: / Line 39: @@
 Approximated just intervals:
 XXX under construction
-|| 1/1 ||   ||   ||   ||   ||   ||   ||   ||
+|| 1/1 || 81/80 ||   ||   ||   ||   ||   ||   ||
 ||   ||   ||   ||   ||   ||   ||   ||   ||
 ||   ||   ||   ||   ||   ||   ||   ||   ||
@@ Line 74: / Line 75: @@
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Older systems"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Older systems&lt;/h1&gt;
   &lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Older systems-First system J.J.Weiss"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;First system J.J.Weiss&lt;/h2&gt;
-  Inequal subdivision of the &lt;a class="wiki_link" href="/2187_2048"&gt;apotome (2187/2048, 113.7 cents)&lt;/a&gt; into 7 parts (8 mandals/orabs).&lt;br /&gt;
+  Inequal subdivision of the &lt;a class="wiki_link" href="/2187_2048"&gt;apotome (2187/2048, 113.7 cents)&lt;/a&gt; into 7 parts (8 mandals/orabs), in the following manner:&lt;br /&gt;
-Rough subdivision into one &lt;a class="wiki_link" href="/81_80"&gt;syntonic comma (81/80, 21.5 cents)&lt;/a&gt;, one &lt;a class="wiki_link" href="/25_24"&gt;Zarlino semitone (25/24, 70.7 cents)&lt;/a&gt; and another syntonic comma. Finer subdivision of the 25/24.&lt;br /&gt;
+&lt;ul&gt;&lt;li&gt;Subdivision into one &lt;a class="wiki_link" href="/81_80"&gt;syntonic comma (81/80, 21.5 cents)&lt;/a&gt;, one &lt;a class="wiki_link" href="/25_24"&gt;Zarlinian semitone (25/24, 70.7 cents)&lt;/a&gt; and another syntonic comma.&lt;/li&gt;&lt;li&gt;Further subdivision of 25/24 into 65/64 (26 cents), 144/143 (12 cents) and 55/54 (32 cents).&lt;/li&gt;&lt;li&gt;65/64 and 55/54 are each split into two.&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
-(luthier Ejder Gulec)&lt;br /&gt;
+This gives the following interval positions of the mandals: 22, 13, 13, 12, 16, 16, 22 cents.&lt;br /&gt;
-&lt;br /&gt;
+Luthier: Ejder Gulec&lt;br /&gt;
-Positioning of the mandals at: 22, 13, 13, 12, 16,|16, 22 cents.&lt;br /&gt;
-Ratios: XXX&lt;br /&gt;
 &lt;br /&gt;
 Interval Table (cents):&lt;br /&gt;
@@ Line 186: / Line 185: @@
          &lt;td&gt;1/1&lt;br /&gt;
 &lt;/td&gt;
-         &lt;td&gt;&lt;br /&gt;
+         &lt;td&gt;81/80&lt;br /&gt;
 &lt;/td&gt;
          &lt;td&gt;&lt;br /&gt;