7/4: Difference between revisions

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<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:~~xenwolf~~|~~xenwolf~~]] and made on <tt>2011-05-31 17:24:11 UTC</tt>.<br>

: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-31 21:21:46 UTC</tt>.<br>

: The original revision id was <tt>~~233284800~~</tt>.<br>

: The original revision id was <tt>233336070</tt>.<br>

: The revision comment was: <tt>~~re-ordered after relative delta (in relative cents)~~</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>

<h4>Original Wikitext content:</h4>

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=Meantone Augmented Sixth=

In [[Meantone family|meantone systems]] -- which are generated by repeatedly stacking a slightly flatted (from just) [[perfect fifth]] such that four fifths gives a near-just [[major third]] -- there is sometimes a good approximation of the harmonic seventh in the form of an "augmented sixth". Quarter-comma meantone (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the "augmented sixth chord," and is treated as a rare and special dissonance. The so-called "German Sixth," in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).

In [[Meantone family|meantone systems]] -- which are generated by repeatedly stacking a slightly flatted (from just) [[perfect fifth]] such that four fifths gives a near-just [[major third]] -- there is sometimes a good approximation of the harmonic seventh in the form of an "augmented sixth". [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the "augmented sixth chord," and is treated as a rare and special dissonance. The so-called "German Sixth," in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).

Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance.

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<br />

<h1 id="toc1"><a name="Meantone Augmented Sixth"></a>Meantone Augmented Sixth</h1>

In <a class="wiki_link" href="/Meantone%20family">meantone systems</a> -- which are generated by repeatedly stacking a slightly flatted (from just) <a class="wiki_link" href="/perfect%20fifth">perfect fifth</a> such that four fifths gives a near-just <a class="wiki_link" href="/major%20third">major third</a> -- there is sometimes a good approximation of the harmonic seventh in the form of an &quot;augmented sixth&quot;. Quarter-comma meantone (aurally identical, for most intents and purposes, to <a class="wiki_link" href="/31edo">31edo</a>) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the &quot;augmented sixth chord,&quot; and is treated as a rare and special dissonance. The so-called &quot;German Sixth,&quot; in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).<br />

In <a class="wiki_link" href="/Meantone%20family">meantone systems</a> -- which are generated by repeatedly stacking a slightly flatted (from just) <a class="wiki_link" href="/perfect%20fifth">perfect fifth</a> such that four fifths gives a near-just <a class="wiki_link" href="/major%20third">major third</a> -- there is sometimes a good approximation of the harmonic seventh in the form of an &quot;augmented sixth&quot;. <a class="wiki_link" href="/Quarter-comma%20meantone">Quarter-comma meantone</a> (aurally identical, for most intents and purposes, to <a class="wiki_link" href="/31edo">31edo</a>) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the &quot;augmented sixth chord,&quot; and is treated as a rare and special dissonance. The so-called &quot;German Sixth,&quot; in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).<br />

<br />

Note that a good approximation of the harmonic seventh is not available in every meantone system. In <a class="wiki_link" href="/19edo">19edo</a> (aurally identical, more or less, to 1/3-comma meantone), the &quot;augmented sixth&quot; is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance.<br />

@@ 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:xenwolf|xenwolf]] and made on <tt>2011-05-31 17:24:11 UTC</tt>.<br>
+: This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-05-31 21:21:46 UTC</tt>.<br>
-: The original revision id was <tt>233284800</tt>.<br>
+: The original revision id was <tt>233336070</tt>.<br>
-: The revision comment was: <tt>re-ordered after relative delta (in relative cents)</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>
 <h4>Original Wikitext content:</h4>
@@ Line 30: / Line 30: @@
 =Meantone Augmented Sixth=
-In [[Meantone family|meantone systems]] -- which are generated by repeatedly stacking a slightly flatted (from just) [[perfect fifth]] such that four fifths gives a near-just [[major third]] -- there is sometimes a good approximation of the harmonic seventh in the form of an "augmented sixth". Quarter-comma meantone (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the "augmented sixth chord," and is treated as a rare and special dissonance. The so-called "German Sixth," in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).
+In [[Meantone family|meantone systems]] -- which are generated by repeatedly stacking a slightly flatted (from just) [[perfect fifth]] such that four fifths gives a near-just [[major third]] -- there is sometimes a good approximation of the harmonic seventh in the form of an "augmented sixth". [[Quarter-comma meantone]] (aurally identical, for most intents and purposes, to [[31edo]]) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the "augmented sixth chord," and is treated as a rare and special dissonance. The so-called "German Sixth," in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).
 Note that a good approximation of the harmonic seventh is not available in every meantone system. In [[19edo]] (aurally identical, more or less, to 1/3-comma meantone), the "augmented sixth" is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance.
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 &lt;br /&gt;
 &lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Meantone Augmented Sixth"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Meantone Augmented Sixth&lt;/h1&gt;
-  In &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone systems&lt;/a&gt; -- which are generated by repeatedly stacking a slightly flatted (from just) &lt;a class="wiki_link" href="/perfect%20fifth"&gt;perfect fifth&lt;/a&gt; such that four fifths gives a near-just &lt;a class="wiki_link" href="/major%20third"&gt;major third&lt;/a&gt; -- there is sometimes a good approximation of the harmonic seventh in the form of an &amp;quot;augmented sixth&amp;quot;. Quarter-comma meantone (aurally identical, for most intents and purposes, to &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the &amp;quot;augmented sixth chord,&amp;quot; and is treated as a rare and special dissonance. The so-called &amp;quot;German Sixth,&amp;quot; in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).&lt;br /&gt;
+  In &lt;a class="wiki_link" href="/Meantone%20family"&gt;meantone systems&lt;/a&gt; -- which are generated by repeatedly stacking a slightly flatted (from just) &lt;a class="wiki_link" href="/perfect%20fifth"&gt;perfect fifth&lt;/a&gt; such that four fifths gives a near-just &lt;a class="wiki_link" href="/major%20third"&gt;major third&lt;/a&gt; -- there is sometimes a good approximation of the harmonic seventh in the form of an &amp;quot;augmented sixth&amp;quot;. &lt;a class="wiki_link" href="/Quarter-comma%20meantone"&gt;Quarter-comma meantone&lt;/a&gt; (aurally identical, for most intents and purposes, to &lt;a class="wiki_link" href="/31edo"&gt;31edo&lt;/a&gt;) is one such system. In quarter-comma meantone, the interval of C to A# approximates a harmonic seventh, and is a distinct interval from C to Bb, a meantone minor seventh (falling somewhere between 16:9 and 9:5). The augmented sixth appears in tonal harmony in the &amp;quot;augmented sixth chord,&amp;quot; and is treated as a rare and special dissonance. The so-called &amp;quot;German Sixth,&amp;quot; in quarter-comma meantone, would approximate the harmonic seventh chord of 4:5:6:7(:8).&lt;br /&gt;
 &lt;br /&gt;
 Note that a good approximation of the harmonic seventh is not available in every meantone system. In &lt;a class="wiki_link" href="/19edo"&gt;19edo&lt;/a&gt; (aurally identical, more or less, to 1/3-comma meantone), the &amp;quot;augmented sixth&amp;quot; is an interval of 947 cents -- about 22 cents flat of 7:4, and so less effective as a consonance.&lt;br /&gt;