Tuning systems for qanun: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

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: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-29 16:20:23 UTC</tt>.

: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-29 16:21:47 UTC</tt>.

: The original revision id was <tt>~~259752572~~</tt>.

: The original revision id was <tt>259753064</tt>.

: The revision comment was: <tt></tt>

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The empty strings of the qanun are tuned to a pythagorean diatonic scale, with a major third of [[81_80|81/80]], a major sixth of [[27_16|27/16]] and a major seventh of [[243_128|243/128]].

The possible pitches of a string obtained via raising/lowering the mandals lie within two [[2187_2048|apotomes (2187/2048, 113.7 cents)]]. The base note is assumed in the middle and ~~can be raised and lowered~~ by maximally one apotome.

The possible pitches of a string obtained via raising/lowering the mandals lie within two [[2187_2048|apotomes (2187/2048, 113.7 cents)]]. The base note is assumed in the middle. The mandals allow raising and lowering this note by maximally one apotome.

One apotome is divided into 7 parts, which requires 14 mandals per string (one apotome up and down). The first rough subdivision of the apotome is always 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. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.

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The empty strings of the qanun are tuned to a pythagorean diatonic scale, with a major third of <a class="wiki_link" href="/81_80">81/80</a>, a major sixth of <a class="wiki_link" href="/27_16">27/16</a> and a major seventh of <a class="wiki_link" href="/243_128">243/128</a>.

The possible pitches of a string obtained via raising/lowering the mandals lie within two <a class="wiki_link" href="/2187_2048">apotomes (2187/2048, 113.7 cents)</a>. The base note is assumed in the middle and ~~can be raised and lowered~~ by maximally one apotome.

The possible pitches of a string obtained via raising/lowering the mandals lie within two <a class="wiki_link" href="/2187_2048">apotomes (2187/2048, 113.7 cents)</a>. The base note is assumed in the middle. The mandals allow raising and lowering this note by maximally one apotome.

One apotome is divided into 7 parts, which requires 14 mandals per string (one apotome up and down). The first rough subdivision of the apotome is always 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. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.

@@ 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>2011-09-29 16:20:23 UTC</tt>.<br>
+: This revision was by author [[User:hstraub|hstraub]] and made on <tt>2011-09-29 16:21:47 UTC</tt>.<br>
-: The original revision id was <tt>259752572</tt>.<br>
+: The original revision id was <tt>259753064</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 16: / Line 16: @@
 The empty strings of the qanun are tuned to a pythagorean diatonic scale, with a major third of [[81_80|81/80]], a major sixth of [[27_16|27/16]] and a major seventh of [[243_128|243/128]].
-The possible pitches of a string obtained via raising/lowering the mandals lie within two [[2187_2048|apotomes (2187/2048, 113.7 cents)]]. The base note is assumed in the middle and can be raised and lowered by maximally one apotome.
+The possible pitches of a string obtained via raising/lowering the mandals lie within two [[2187_2048|apotomes (2187/2048, 113.7 cents)]]. The base note is assumed in the middle. The mandals allow raising and lowering this note by maximally one apotome.
 One apotome is divided into 7 parts, which requires 14 mandals per string (one apotome up and down). The first rough subdivision of the apotome is always 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. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.
@@ Line 171: / Line 172: @@
 &lt;br /&gt;
 The empty strings of the qanun are tuned to a pythagorean diatonic scale, with a major third of &lt;a class="wiki_link" href="/81_80"&gt;81/80&lt;/a&gt;, a major sixth of &lt;a class="wiki_link" href="/27_16"&gt;27/16&lt;/a&gt; and a major seventh of &lt;a class="wiki_link" href="/243_128"&gt;243/128&lt;/a&gt;.&lt;br /&gt;
-The possible pitches of a string obtained via raising/lowering the mandals lie within two &lt;a class="wiki_link" href="/2187_2048"&gt;apotomes (2187/2048, 113.7 cents)&lt;/a&gt;. The base note is assumed in the middle and can be raised and lowered by maximally one apotome.&lt;br /&gt;
+&lt;br /&gt;
+The possible pitches of a string obtained via raising/lowering the mandals lie within two &lt;a class="wiki_link" href="/2187_2048"&gt;apotomes (2187/2048, 113.7 cents)&lt;/a&gt;. The base note is assumed in the middle. The mandals allow raising and lowering this note by maximally one apotome.&lt;br /&gt;
 &lt;br /&gt;
 One apotome is divided into 7 parts, which requires 14 mandals per string (one apotome up and down). The first rough subdivision of the apotome is always 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. The middle part (25/24, Zarlinian semitone) is then further subdivided into 5 (unequal or equal) parts. The various systems differ mainly in the division of the middle part.&lt;br /&gt;