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 16:30:56 UTC</tt>.

: This revision was by author [[User:guest|guest]] and made on <tt>2011-09-29 16:33:06 UTC</tt>.

: The original revision id was <tt>~~259756138~~</tt>.

: The original revision id was <tt>259756812</tt>.

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Each apotome is divided into 7 parts, which requires 14 mandals per string. 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.

The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, ~~The~~ first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).

The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).

An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one [[32805_32768|schisma (2 cents)]]. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.

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Each apotome is divided into 7 parts, which requires 14 mandals per string. 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.

The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, ~~The~~ first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).

The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).

An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one <a class="wiki_link" href="/32805_32768">schisma (2 cents)</a>. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.

@@ 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 16:30:56 UTC</tt>.<br>
+: This revision was by author [[User:guest|guest]] and made on <tt>2011-09-29 16:33:06 UTC</tt>.<br>
-: The original revision id was <tt>259756138</tt>.<br>
+: The original revision id was <tt>259756812</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 21: / Line 21: @@
 Each apotome is divided into 7 parts, which requires 14 mandals per string. 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.
-The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, The first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).
+The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).
 An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one [[32805_32768|schisma (2 cents)]]. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.
@@ Line 176: / Line 176: @@
 Each apotome is divided into 7 parts, which requires 14 mandals per string. 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;
 &lt;br /&gt;
-The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, The first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).&lt;br /&gt;
+The tuning systems are all described by a series of cent values, which describe the subdivision of one apotome. According to the system sketched above, the first and the last value are always 22 cents (or 21.5 cents). This subdivision pattern occurs twice on each string (one apotome up and one down), alltogether 14 times per octave. This is followed by listings of some important rational intervals that are possible in this tuning (XXX STILL TO DO).&lt;br /&gt;
 &lt;br /&gt;
 An notable property (of all systems) is that the second-highest mandal position of, say, the C string is 114-22=92 cents, while the lowest mandal position on the following string (D in the example) is 214 (one wholetone above C) - 114 = 90 cents - we have two notes differing by one &lt;a class="wiki_link" href="/32805_32768"&gt;schisma (2 cents)&lt;/a&gt;. So the interval of the schisma is present and can be played on a qanun in any of the tuning systems described here.&lt;br /&gt;