Chordal space: Difference between revisions

Wikispaces>genewardsmith
**Imported revision 149662389 - Original comment: **
Wikispaces>genewardsmith
**Imported revision 149723393 - Original comment: **
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<h2>IMPORTED REVISION FROM WIKISPACES</h2>
<h2>IMPORTED REVISION FROM WIKISPACES</h2>
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== History of chordal space ==
== History of chordal space ==


Historically, chordal space goes back to [[http://en.wikipedia.org/wiki/Johann_David_Heinichen|Johann David Heinichen]] in 1728;  
One of the earliest graphical models of chord-relationships was devised by [[http://en.wikipedia.org/wiki/Johann_David_Heinichen|Johann David Heinichen]] in 1728;  
he proposed placing the major and minor chords in a circular arrangement of twenty-four chords arranged according to the circle of fifths; reading clockwise, ... F, d, C, a, G, ... (Lerdahl, 2001). The currently more popular major on the outside relative minor on the inside format was proposed by [[http://en.wikipedia.org/wiki/David_Kellner|David Kellner]]  (1737).  
he proposed placing the major and minor chords in a circular arrangement of twenty-four chords arranged according to the circle of fifths; reading clockwise, ... F, d, C, a, G, ... (Lerdahl, 2001). The currently more popular major on the outside relative minor on the inside format was proposed by [[http://en.wikipedia.org/wiki/David_Kellner|David Kellner]]  (1737).  


[[http://en.wikipedia.org/wiki/Gottfried_Weber|Gottfried Weber]]  and S. G. Vial suggested a [[http://en.wikipedia.org/wiki/Lattice_graph|grid graph]] or [[http://en.wikipedia.org/wiki/Square_lattice|square lattice]] model of chordal space; Weber's "regional chart" centered on C major, is:
[[http://en.wikipedia.org/wiki/Gottfried_Weber|Gottfried Weber]]  and F. G. Vial suggested a [[http://en.wikipedia.org/wiki/Lattice_graph|grid graph]] or [[http://en.wikipedia.org/wiki/Square_lattice|square lattice]] model of chordal space; Weber's "regional chart" centered on C major, is:


d♯ F♯ f♯ A a C c
d♯ F♯ f♯ A a C c
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&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-History of chordal space"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; History of chordal space &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-History of chordal space"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt; History of chordal space &lt;/h2&gt;
&lt;br /&gt;
&lt;br /&gt;
Historically, chordal space goes back to &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Johann_David_Heinichen" rel="nofollow"&gt;Johann David Heinichen&lt;/a&gt; in 1728; &lt;br /&gt;
One of the earliest graphical models of chord-relationships was devised by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Johann_David_Heinichen" rel="nofollow"&gt;Johann David Heinichen&lt;/a&gt; in 1728; &lt;br /&gt;
he proposed placing the major and minor chords in a circular arrangement of twenty-four chords arranged according to the circle of fifths; reading clockwise, ... F, d, C, a, G, ... (Lerdahl, 2001). The currently more popular major on the outside relative minor on the inside format was proposed by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/David_Kellner" rel="nofollow"&gt;David Kellner&lt;/a&gt;  (1737). &lt;br /&gt;
he proposed placing the major and minor chords in a circular arrangement of twenty-four chords arranged according to the circle of fifths; reading clockwise, ... F, d, C, a, G, ... (Lerdahl, 2001). The currently more popular major on the outside relative minor on the inside format was proposed by &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/David_Kellner" rel="nofollow"&gt;David Kellner&lt;/a&gt;  (1737). &lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Gottfried_Weber" rel="nofollow"&gt;Gottfried Weber&lt;/a&gt;  and S. G. Vial suggested a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_graph" rel="nofollow"&gt;grid graph&lt;/a&gt; or &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_lattice" rel="nofollow"&gt;square lattice&lt;/a&gt; model of chordal space; Weber's &amp;quot;regional chart&amp;quot; centered on C major, is:&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Gottfried_Weber" rel="nofollow"&gt;Gottfried Weber&lt;/a&gt;  and F. G. Vial suggested a &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_graph" rel="nofollow"&gt;grid graph&lt;/a&gt; or &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_lattice" rel="nofollow"&gt;square lattice&lt;/a&gt; model of chordal space; Weber's &amp;quot;regional chart&amp;quot; centered on C major, is:&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
d♯    F♯    f♯    A    a    C    c&lt;br /&gt;
d♯    F♯    f♯    A    a    C    c&lt;br /&gt;