Meantone: Difference between revisions
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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]] <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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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Theory and Classification"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory and Classification</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Theory and Classification"></a><!-- ws:end:WikiTextHeadingRule:2 -->Theory and Classification</h1> | ||
Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a <a class="wiki_link" href="/Regular%20Temperaments">rank-2 temperament</a>. 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.<br /> | Meantone temperaments are based on two generating intervals; the octave and the fifth, from which all pitches are composed. This qualifies it as a <a class="wiki_link" href="/Regular%20Temperaments">rank-2 temperament</a>. 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.<br /> | ||
<br /> | |||
<a class="wiki_link" href="/Meantone%20intervals">Intervals in meantone</a> have standard names based on the number of steps of the diatonic scale they span (this corresponds to the <a class="wiki_link" href="/val">val</a> &lt;7 11 16|), with a modifier {...&quot;double diminished&quot;, &quot;diminished&quot;, &quot;minor&quot;, &quot;major&quot;, &quot;augmented&quot;, &quot;double augmented&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.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Common Meantone Temperaments (ie, tunings)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Common Meantone Temperaments (ie, tunings)</h1> | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Common Meantone Temperaments (ie, tunings)"></a><!-- ws:end:WikiTextHeadingRule:4 -->Common Meantone Temperaments (ie, tunings)</h1> | ||
<ul><li><a class="wiki_link" href="/19edo">19-edo</a></li><li><a class="wiki_link" href="/1-3%20Syntonic%20Comma%20Meantone">1/3 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/Golden%20Meantone">Golden Meantone</a></li><li><a class="wiki_link" href="/Quarter-comma%20meantone">1/4 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/31edo">31-edo</a></li><li><a class="wiki_link" href="/1-5%20Syntonic%20Comma%20Meantone">1/5 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/1-6%20Syntonic%20Comma%20Meantone">1/6 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/12edo">12-edo</a></li><li><a class="wiki_link" href="/Lucy%20tuning">Lucy tuning</a></li></ul><br /> | <ul><li><a class="wiki_link" href="/19edo">19-edo</a></li><li><a class="wiki_link" href="/1-3%20Syntonic%20Comma%20Meantone">1/3 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/Golden%20Meantone">Golden Meantone</a></li><li><a class="wiki_link" href="/Quarter-comma%20meantone">1/4 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/31edo">31-edo</a></li><li><a class="wiki_link" href="/1-5%20Syntonic%20Comma%20Meantone">1/5 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/1-6%20Syntonic%20Comma%20Meantone">1/6 Syntonic Comma Meantone</a></li><li><a class="wiki_link" href="/12edo">12-edo</a></li><li><a class="wiki_link" href="/Lucy%20tuning">Lucy tuning</a></li></ul><br /> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:6 -->Links</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:6 -->Links</h1> | ||
<ul><li><!-- ws:start:WikiTextUrlRule: | <ul><li><!-- ws:start:WikiTextUrlRule:58:http://home.earthlink.net/~kgann/histune.html --><a class="wiki_link_ext" href="http://home.earthlink.net/~kgann/histune.html" rel="nofollow">http://home.earthlink.net/~kgann/histune.html</a><!-- ws:end:WikiTextUrlRule:58 --> -- An Introduction to Historical Tunings, by <a class="wiki_link" href="/Kyle%20Gann">Kyle Gann</a></li></ul></body></html></pre></div> | ||