Meantone: Difference between revisions

Wikispaces>hstraub
**Imported revision 237355761 - Original comment: **
Wikispaces>keenanpepper
**Imported revision 271803632 - 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:hstraub|hstraub]] and made on <tt>2011-06-17 15:31:38 UTC</tt>.<br>
: This revision was by author [[User:keenanpepper|keenanpepper]] and made on <tt>2011-11-04 01:06:36 UTC</tt>.<br>
: The original revision id was <tt>237355761</tt>.<br>
: The original revision id was <tt>271803632</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>
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=Theory and Classification=  
=Theory and Classification=  
Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a [[Regular Temperaments|rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few cents narrower than pure. The rationale for narrowing the fifth is to temper out the syntonic comma. This means that stacking four fifths (such as C-G-D-A-E) results in a major third (C-E) that is close to just.
Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a [[Regular Temperaments|rank-2 temperament]]. The octave is typically pure or close to pure, and the fifth is a few cents narrower than pure. The rationale for narrowing the fifth is to temper out the syntonic comma. This means that stacking four fifths (such as C-G-D-A-E) results in a major third (C-E) that is close to just.
[[Meantone intervals|Intervals in meantone]] have standard names based on the number of steps of the diatonic scale they span (this corresponds to the [[val]] &lt;7 11 16|), with a modifier {..."double diminished", "diminished", "minor", "major", "augmented", "double augmented"...} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.


=Common Meantone Temperaments (ie, tunings)=  
=Common Meantone Temperaments (ie, tunings)=  
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&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Theory and Classification"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory and Classification&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:2:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc1"&gt;&lt;a name="Theory and Classification"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:2 --&gt;Theory and Classification&lt;/h1&gt;
  Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;rank-2 temperament&lt;/a&gt;. The octave is typically pure or close to pure, and the fifth is a few cents narrower than pure. The rationale for narrowing the fifth is to temper out the syntonic comma. This means that stacking four fifths (such as C-G-D-A-E) results in a major third (C-E) that is close to just.&lt;br /&gt;
  Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a &lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;rank-2 temperament&lt;/a&gt;. The octave is typically pure or close to pure, and the fifth is a few cents narrower than pure. The rationale for narrowing the fifth is to temper out the syntonic comma. This means that stacking four fifths (such as C-G-D-A-E) results in a major third (C-E) that is close to just.&lt;br /&gt;
&lt;br /&gt;
&lt;a class="wiki_link" href="/Meantone%20intervals"&gt;Intervals in meantone&lt;/a&gt; have standard names based on the number of steps of the diatonic scale they span (this corresponds to the &lt;a class="wiki_link" href="/val"&gt;val&lt;/a&gt; &amp;lt;7 11 16|), with a modifier {...&amp;quot;double diminished&amp;quot;, &amp;quot;diminished&amp;quot;, &amp;quot;minor&amp;quot;, &amp;quot;major&amp;quot;, &amp;quot;augmented&amp;quot;, &amp;quot;double augmented&amp;quot;...} that tells you the specific interval in increments of a chromatic semitone. Note that in a general meantone system, all of these intervals are distinct. For example, a diminished fourth is a different interval from a major third.&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Common Meantone Temperaments (ie, tunings)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Common Meantone Temperaments (ie, tunings)&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc2"&gt;&lt;a name="Common Meantone Temperaments (ie, tunings)"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;Common Meantone Temperaments (ie, tunings)&lt;/h1&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/19edo"&gt;19-edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/1-3%20Syntonic%20Comma%20Meantone"&gt;1/3 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Golden%20Meantone"&gt;Golden Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Quarter-comma%20meantone"&gt;1/4 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/31edo"&gt;31-edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/1-5%20Syntonic%20Comma%20Meantone"&gt;1/5 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/1-6%20Syntonic%20Comma%20Meantone"&gt;1/6 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/12edo"&gt;12-edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Lucy%20tuning"&gt;Lucy tuning&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/19edo"&gt;19-edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/1-3%20Syntonic%20Comma%20Meantone"&gt;1/3 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Golden%20Meantone"&gt;Golden Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Quarter-comma%20meantone"&gt;1/4 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/31edo"&gt;31-edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/1-5%20Syntonic%20Comma%20Meantone"&gt;1/5 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/1-6%20Syntonic%20Comma%20Meantone"&gt;1/6 Syntonic Comma Meantone&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/12edo"&gt;12-edo&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Lucy%20tuning"&gt;Lucy tuning&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Links&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Links"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Links&lt;/h1&gt;
  &lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:54:http://home.earthlink.net/~kgann/histune.html --&gt;&lt;a class="wiki_link_ext" href="http://home.earthlink.net/~kgann/histune.html" rel="nofollow"&gt;http://home.earthlink.net/~kgann/histune.html&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:54 --&gt; -- An Introduction to Historical Tunings, by &lt;a class="wiki_link" href="/Kyle%20Gann"&gt;Kyle Gann&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
  &lt;ul&gt;&lt;li&gt;&lt;!-- ws:start:WikiTextUrlRule:58:http://home.earthlink.net/~kgann/histune.html --&gt;&lt;a class="wiki_link_ext" href="http://home.earthlink.net/~kgann/histune.html" rel="nofollow"&gt;http://home.earthlink.net/~kgann/histune.html&lt;/a&gt;&lt;!-- ws:end:WikiTextUrlRule:58 --&gt; -- An Introduction to Historical Tunings, by &lt;a class="wiki_link" href="/Kyle%20Gann"&gt;Kyle Gann&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>