Stacked chord: Difference between revisions

Wikispaces>kentaku
**Imported revision 450584140 - Original comment: **
Wikispaces>kentaku
**Imported revision 450883782 - 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:kentaku|kentaku]] and made on <tt>2013-09-12 10:24:25 UTC</tt>.<br>
: This revision was by author [[User:kentaku|kentaku]] and made on <tt>2013-09-13 10:29:19 UTC</tt>.<br>
: The original revision id was <tt>450584140</tt>.<br>
: The original revision id was <tt>450883782</tt>.<br>
: The revision comment was: <tt></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>
The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.<br>
<h4>Original Wikitext content:</h4>
<h4>Original Wikitext content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">In Music, &lt;span class="adtext"&gt;stacked&lt;/span&gt; chords are a set of well-defined pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain on interval.
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">In Music, &lt;span class="adtext"&gt;stacked&lt;/span&gt; chords are a set of well-&lt;span class="adtext"&gt;defined&lt;/span&gt; pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain on interval.


==5-limit tertiary harmonic triads==  
==5-limit tertiary harmonic triads==  


|| **Name** || **Divides interval** || **Chord Formula** || **&lt;span class="adtext"&gt;Harmonic&lt;/span&gt; State** ||
|| **Name** || **Divides interval** || **Chord Formula** || **Odd Limit** ||
|| &lt;span class="adtext"&gt;Major&lt;/span&gt; || 3/2 || 5/4 + 6/5 or M3 + m3 || Stable ||
|| &lt;span class="adtext"&gt;Major&lt;/span&gt; || 3/2 || 5/4 + 6/5 or M3 + m3 || 5 ||
|| Minor || 3/2 || 6/5 + 5/4 or m3 + M3 || Stable ||
|| Minor || 3/2 || 6/5 + 5/4 or m3 + M3 || 5 ||
|| Augmented || 25/16 || 5/4 + 5/4 or M3 + M3 || Unstable ||
|| Augmented || 25/16 || 5/4 + 5/4 or M3 + M3 || 25 ||
|| &lt;span class="adtext"&gt;Diminished&lt;/span&gt; || 25/18 || 6/5 + 6/5 or m3 + m3 || Unstable ||
|| &lt;span class="adtext"&gt;Diminished&lt;/span&gt; || 25/18 || 6/5 + 6/5 or m3 + m3 || 25 ||
==5-limit tertiary harmonic tetrads==
 
|| **Name** || **Divides interval** || **Chord Formula** || **Odd Limit** ||
|| &lt;span class="adtext"&gt;Major&lt;/span&gt; || 3/2 || 5/4 + 6/5 or M3 + m3 || 5 ||
|| Minor || 3/2 || 6/5 + 5/4 or m3 + M3 || 5 ||
|| Augmented || 25/16 || 5/4 + 5/4 or M3 + M3 || 25 ||
|| &lt;span class="adtext"&gt;Diminished&lt;/span&gt; || 25/18 || 6/5 + 6/5 or m3 + m3 || 25 ||
 


==7-limit tertiary harmonic triads==  
==7-limit tertiary harmonic triads==  


|| **&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;** || **&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;** || **Chord Formula** || **Harmonic State** ||
|| **&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;** || **&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;** || **Chord Formula** || **Odd Limit** ||
|| Septimal Major || 3/2 || 9/7 + 7/6 or 7M3 + 7m3 || Stable ||
|| Septimal Major || 3/2 || 9/7 + 7/6 or 7M3 + 7m3 || 9 ||
|| Septimal Minor || 3/2 || 7/6 + 9/7 or 7m3 + 7M3 || Stable ||
|| Septimal Minor || 3/2 || 7/6 + 9/7 or 7m3 + 7M3 || 9 ||
||  ||  ||  ||  ||
||  ||  ||  ||  ||
||  ||  ||  ||  ||
||  ||  ||  ||  ||
==11-limit tertiary harmonic triads==  
==11-limit tertiary harmonic triads==  


|| **&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;** || **&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;** || **Chord Formula** || **Isolate State** ||
|| **&lt;span style="line-height: 1.5;"&gt;Name&lt;/span&gt;** || **&lt;span style="line-height: 1.5;"&gt;Divides interval&lt;/span&gt;** || **Chord Formula** || **Odd Limit** ||
|| Neutral || 3/2 || 11/9 + 11/9 || Semi-stable ||
|| Neutral || 3/2 || 11/9 + 11/9 || 11 ||
|| Super Major || 3/2 ||  || Semi-stable ||</pre></div>
||   ||   ||  ||   ||</pre></div>
<h4>Original HTML content:</h4>
<h4>Original HTML content:</h4>
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Stacked Chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In Music, &lt;span class="adtext"&gt;stacked&lt;/span&gt; chords are a set of well-defined pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain on interval.&lt;br /&gt;
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html">&lt;html&gt;&lt;head&gt;&lt;title&gt;Stacked Chords&lt;/title&gt;&lt;/head&gt;&lt;body&gt;In Music, &lt;span class="adtext"&gt;stacked&lt;/span&gt; chords are a set of well-&lt;span class="adtext"&gt;defined&lt;/span&gt; pitches sounding together consisting of a stack of varying flavors or qualities of the same numerical interval. The most common stacked chords comprise of splitting a 3/2 or perfect fifth into two varying sizes of thirds. Stacked chords must be at least triadic as dyadic can only contain on interval.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-5-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit tertiary harmonic triads&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:0:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc0"&gt;&lt;a name="x-5-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:0 --&gt;5-limit tertiary harmonic triads&lt;/h2&gt;
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         &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;&lt;span class="adtext"&gt;Harmonic&lt;/span&gt; State&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span class="adtext"&gt;Major&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4 + 6/5 or M3 + m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Minor&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;3/2&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5 + 5/4 or m3 + M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;Augmented&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/16&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;5/4 + 5/4 or M3 + M3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;span class="adtext"&gt;Diminished&lt;/span&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25/18&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;6/5 + 6/5 or m3 + m3&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
    &lt;/tr&gt;
&lt;/table&gt;
 
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc1"&gt;&lt;a name="x-5-limit tertiary harmonic tetrads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;5-limit tertiary harmonic tetrads&lt;/h2&gt;
&lt;br /&gt;
 
 
&lt;table class="wiki_table"&gt;
    &lt;tr&gt;
        &lt;td&gt;&lt;strong&gt;Name&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Divides interval&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
        &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;5/4 + 6/5 or M3 + m3&lt;br /&gt;
         &lt;td&gt;5/4 + 6/5 or M3 + m3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Stable&lt;br /&gt;
         &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;6/5 + 5/4 or m3 + M3&lt;br /&gt;
         &lt;td&gt;6/5 + 5/4 or m3 + M3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Stable&lt;br /&gt;
         &lt;td&gt;5&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;5/4 + 5/4 or M3 + M3&lt;br /&gt;
         &lt;td&gt;5/4 + 5/4 or M3 + M3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Unstable&lt;br /&gt;
         &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;6/5 + 6/5 or m3 + m3&lt;br /&gt;
         &lt;td&gt;6/5 + 6/5 or m3 + m3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Unstable&lt;br /&gt;
         &lt;td&gt;25&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&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-7-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;7-limit tertiary harmonic triads&lt;/h2&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-7-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;7-limit tertiary harmonic triads&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;


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         &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;Harmonic State&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;9/7 + 7/6 or 7M3 + 7m3&lt;br /&gt;
         &lt;td&gt;9/7 + 7/6 or 7M3 + 7m3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Stable&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;7/6 + 9/7 or 7m3 + 7M3&lt;br /&gt;
         &lt;td&gt;7/6 + 9/7 or 7m3 + 7M3&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Stable&lt;br /&gt;
         &lt;td&gt;9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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&lt;/table&gt;
&lt;/table&gt;


&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="x-11-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;11-limit tertiary harmonic triads&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc3"&gt;&lt;a name="x-11-limit tertiary harmonic triads"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;11-limit tertiary harmonic triads&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;


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         &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Chord Formula&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;strong&gt;Isolate State&lt;/strong&gt;&lt;br /&gt;
         &lt;td&gt;&lt;strong&gt;Odd Limit&lt;/strong&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
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         &lt;td&gt;11/9 + 11/9&lt;br /&gt;
         &lt;td&gt;11/9 + 11/9&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Semi-stable&lt;br /&gt;
         &lt;td&gt;11&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;
     &lt;tr&gt;
     &lt;tr&gt;
         &lt;td&gt;Super Major&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;3/2&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
         &lt;td&gt;Semi-stable&lt;br /&gt;
         &lt;td&gt;&lt;br /&gt;
&lt;/td&gt;
&lt;/td&gt;
     &lt;/tr&gt;
     &lt;/tr&gt;