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> | ||
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:genewardsmith|genewardsmith]] and made on <tt>2010-06-19 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-20 19:01:19 UTC</tt>.<br> | ||
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== History of chordal space == | == History of chordal space == | ||
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 | [[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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<!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-History of chordal space"></a><!-- ws:end:WikiTextHeadingRule:0 --> History of chordal space </h2> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h2&gt; --><h2 id="toc0"><a name="x-History of chordal space"></a><!-- ws:end:WikiTextHeadingRule:0 --> History of chordal space </h2> | ||
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One of the earliest graphical models of chord-relationships was devised by <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Johann_David_Heinichen" rel="nofollow">Johann David Heinichen</a> in 1728; <br /> | |||
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 <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/David_Kellner" rel="nofollow">David Kellner</a> (1737). <br /> | 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 <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/David_Kellner" rel="nofollow">David Kellner</a> (1737). <br /> | ||
<br /> | <br /> | ||
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Gottfried_Weber" rel="nofollow">Gottfried Weber</a> and | <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Gottfried_Weber" rel="nofollow">Gottfried Weber</a> and F. G. Vial suggested a <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Lattice_graph" rel="nofollow">grid graph</a> or <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Square_lattice" rel="nofollow">square lattice</a> model of chordal space; Weber's &quot;regional chart&quot; centered on C major, is:<br /> | ||
<br /> | <br /> | ||
d♯ F♯ f♯ A a C c<br /> | d♯ F♯ f♯ A a C c<br /> | ||