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Chordal space: Difference between revisions

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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 23:46:35 UTC</tt>.<br>
: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2010-06-19 23:57:16 UTC</tt>.<br>
: The original revision id was <tt>149661711</tt>.<br>
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[[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 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:
{|
 
|d#
d♯ F♯ f♯ A a C c
|F#
g♯ B b D d F f
|f#
c♯ E e G g B♭ b♭
|A
f♯ A a C c E♭ e♭
|a
b D d F f A♭ a♭
|C
e G g B♭ b♭ D♭ d♭
|c
a C c E♭ e♭ G♭ g♭
|-
 
|g#
Lower case letters indicate minor key, uppercase major. This was first proposed by Vial (1767) (later Weber, Riemann, Schoenberg), the advantage over the circle of fifths being that it represents both relative and parallel major. (Lerdahl, 2001)
|B
|b
|D
|d
|F
|f
|-
|c#
|E
|e
|G
|g
|Bb
|bb
|-
|f#
|A
|a
|C
|c
|Eb
|eb
|-
|b
|D
|d
|F
|f
|Ab
|ab
|-
|e
|G
|g
|Bb
|bb
|Db
|db
|-
|a
|C
|c
|Eb
|eb
|Gb
|gb
|}
: Lower case letters indicate minor key, uppercase major. This was first proposed by Vial (1767) (later Weber, Riemann, Schoenberg), the advantage over the circle of fifths being that it represents both relative and parallel major. (Lerdahl, 2001)


== Princples of chordal space ==
== Princples of chordal space ==
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&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 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;br /&gt;
&lt;br /&gt;
|d#&lt;br /&gt;
d♯    F♯    f♯    A     a     C     c&lt;br /&gt;
|F#&lt;br /&gt;
g♯    B     b     D     d     F     f&lt;br /&gt;
|f#&lt;br /&gt;
c♯    E     e     G     g     B♭    b♭&lt;br /&gt;
|A&lt;br /&gt;
f♯    A     a     C     c     E♭    e♭&lt;br /&gt;
|a&lt;br /&gt;
b     D     d     F     f     A♭    a♭&lt;br /&gt;
|C&lt;br /&gt;
e     G     g     B♭    b♭    D♭    d♭&lt;br /&gt;
|c&lt;br /&gt;
a     C     c     E♭    e♭    G♭    g♭&lt;br /&gt;
|-&lt;br /&gt;
&lt;br /&gt;
|g#&lt;br /&gt;
Lower case letters indicate minor key, uppercase major. This was first proposed by Vial (1767) (later Weber, Riemann, Schoenberg), the advantage over the circle of fifths being that it represents both relative and parallel major. (Lerdahl, 2001)&lt;br /&gt;
|B&lt;br /&gt;
|b&lt;br /&gt;
|D&lt;br /&gt;
|d&lt;br /&gt;
|F&lt;br /&gt;
|f&lt;br /&gt;
|-&lt;br /&gt;
|c#&lt;br /&gt;
|E&lt;br /&gt;
|e&lt;br /&gt;
|G&lt;br /&gt;
|g&lt;br /&gt;
|Bb&lt;br /&gt;
|bb&lt;br /&gt;
|-&lt;br /&gt;
|f#&lt;br /&gt;
|A&lt;br /&gt;
|a&lt;br /&gt;
|C&lt;br /&gt;
|c&lt;br /&gt;
|Eb&lt;br /&gt;
|eb&lt;br /&gt;
|-&lt;br /&gt;
|b&lt;br /&gt;
|D&lt;br /&gt;
|d&lt;br /&gt;
|F&lt;br /&gt;
|f&lt;br /&gt;
|Ab&lt;br /&gt;
|ab&lt;br /&gt;
|-&lt;br /&gt;
|e&lt;br /&gt;
|G&lt;br /&gt;
|g&lt;br /&gt;
|Bb&lt;br /&gt;
|bb&lt;br /&gt;
|Db&lt;br /&gt;
|db&lt;br /&gt;
|-&lt;br /&gt;
|a&lt;br /&gt;
|C&lt;br /&gt;
|c&lt;br /&gt;
|Eb&lt;br /&gt;
|eb&lt;br /&gt;
|Gb&lt;br /&gt;
|gb&lt;br /&gt;
|}&lt;br /&gt;
: Lower case letters indicate minor key, uppercase major. This was first proposed by Vial (1767) (later Weber, Riemann, Schoenberg), the advantage over the circle of fifths being that it represents both relative and parallel major. (Lerdahl, 2001)&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Princples of chordal space"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; Princples of chordal space &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-Princples of chordal space"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt; Princples of chordal space &lt;/h2&gt;
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&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt; External links &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;a name="x-External links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt; External links &lt;/h2&gt;
&lt;br /&gt;
&lt;br /&gt;
*[&lt;!-- ws:start:WikiTextUrlRule:174:http://66.98.148.43/~xenharmo/sevlat.htm --&gt;&lt;a class="wiki_link_ext" href="http://66.98.148.43/~xenharmo/sevlat.htm" rel="nofollow"&gt;http://66.98.148.43/~xenharmo/sevlat.htm&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:174 --&gt; Seven-limit modulatory and chordal space]&lt;br /&gt;
*[&lt;!-- ws:start:WikiTextUrlRule:126:http://66.98.148.43/~xenharmo/sevlat.htm --&gt;&lt;a class="wiki_link_ext" href="http://66.98.148.43/~xenharmo/sevlat.htm" rel="nofollow"&gt;http://66.98.148.43/~xenharmo/sevlat.htm&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:126 --&gt; Seven-limit modulatory and chordal space]&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt; References &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="x-References"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt; References &lt;/h2&gt;
Retrieved from "https://en.xen.wiki/w/Chordal_space"