Meantone: Difference between revisions

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Meantone is a familar historical [[temperament]] based on a chain of fifths (or fourths), which is discussed [[Meantone family|here]] in the context of the associated family of temperaments.

=History= 
Meantone was the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various [[Well Temperament|Well Temperaments]] and eventually 12-tone [[Equal Temperament]] won in popularity.

=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 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)= 
* [[19edo|19-edo]]
* [[1-3 Syntonic Comma Meantone|1/3 Syntonic Comma Meantone]]
* [[Golden Meantone]]
* [[Quarter-comma meantone|1/4 Syntonic Comma Meantone]]
* [[31edo|31-edo]]
* [[1-5 Syntonic Comma Meantone|1/5 Syntonic Comma Meantone]]
* [[1-6 Syntonic Comma Meantone|1/6 Syntonic Comma Meantone]]
* [[12edo|12-edo]]
* [[Lucy tuning]]

=Spectrum of Meantone Tunings by Eigenmonzos=
|| Eigenmonzo || Fifth ||
|| 56/45 || 694.651 ||
|| 28/27 || 694.709 ||
|| 81/70 || 694.732 ||
|| 6/5 || 694.786 (1/3 comma) ||
|| 35/27 || 695.389 ||
|| 9/7 || 695.614 ||
|| 25/24 || 695.810 (2/7 comma) ||
|| 36/35 || 695.936 ||
|| 54/49 || 695.987 ||
|| 15/14 || 696.111 ||
|| 49/45 || 696.245 ||
|| 7/6 || 696.319 ||
|| 48/35 || 696.399 ||
|| 5/4 || 696.578 (1/4 comma) ||
|| 49/48 || 696.616 ||
|| 60/49 || 696.626 ||
|| 35/32 || 696.796 ||
|| 8/7 || 696.883 ||
|| 49/40 || 696.959 ||
|| 7/5 || 697.085 ||
|| 21/16 || 697.344 ||
|| 16/15 || 697.654 (1/5 comma) ||
|| 64/63 || 697.728 ||
|| 21/20 || 697.781 ||
|| 28/25 || 698.099 ||
|| 80/63 || 698.303 ||
|| 45/32 || 698.371 (1/6 comma) ||
|| 25/21 || 699.384 ||

=Links= 
* http://home.earthlink.net/~kgann/histune.html -- An Introduction to Historical Tunings, by [[Kyle Gann]]

Original HTML content:

<html><head><title>Meantone</title></head><body>Meantone is a familar historical <a class="wiki_link" href="/temperament">temperament</a> based on a chain of fifths (or fourths), which is discussed <a class="wiki_link" href="/Meantone%20family">here</a> in the context of the associated family of temperaments.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="History"></a><!-- ws:end:WikiTextHeadingRule:0 -->History</h1>
 Meantone was the dominant tuning used in Europe from around late 15th century to around early 18th century, after which various <a class="wiki_link" href="/Well%20Temperament">Well Temperaments</a> and eventually 12-tone <a class="wiki_link" href="/Equal%20Temperament">Equal Temperament</a> won in popularity.<br />
<br />
<!-- 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 />
<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 />
<!-- 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 />
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="Spectrum of Meantone Tunings by Eigenmonzos"></a><!-- ws:end:WikiTextHeadingRule:6 -->Spectrum of Meantone Tunings by Eigenmonzos</h1>


<table class="wiki_table">
    <tr>
        <td>Eigenmonzo<br />
</td>
        <td>Fifth<br />
</td>
    </tr>
    <tr>
        <td>56/45<br />
</td>
        <td>694.651<br />
</td>
    </tr>
    <tr>
        <td>28/27<br />
</td>
        <td>694.709<br />
</td>
    </tr>
    <tr>
        <td>81/70<br />
</td>
        <td>694.732<br />
</td>
    </tr>
    <tr>
        <td>6/5<br />
</td>
        <td>694.786 (1/3 comma)<br />
</td>
    </tr>
    <tr>
        <td>35/27<br />
</td>
        <td>695.389<br />
</td>
    </tr>
    <tr>
        <td>9/7<br />
</td>
        <td>695.614<br />
</td>
    </tr>
    <tr>
        <td>25/24<br />
</td>
        <td>695.810 (2/7 comma)<br />
</td>
    </tr>
    <tr>
        <td>36/35<br />
</td>
        <td>695.936<br />
</td>
    </tr>
    <tr>
        <td>54/49<br />
</td>
        <td>695.987<br />
</td>
    </tr>
    <tr>
        <td>15/14<br />
</td>
        <td>696.111<br />
</td>
    </tr>
    <tr>
        <td>49/45<br />
</td>
        <td>696.245<br />
</td>
    </tr>
    <tr>
        <td>7/6<br />
</td>
        <td>696.319<br />
</td>
    </tr>
    <tr>
        <td>48/35<br />
</td>
        <td>696.399<br />
</td>
    </tr>
    <tr>
        <td>5/4<br />
</td>
        <td>696.578 (1/4 comma)<br />
</td>
    </tr>
    <tr>
        <td>49/48<br />
</td>
        <td>696.616<br />
</td>
    </tr>
    <tr>
        <td>60/49<br />
</td>
        <td>696.626<br />
</td>
    </tr>
    <tr>
        <td>35/32<br />
</td>
        <td>696.796<br />
</td>
    </tr>
    <tr>
        <td>8/7<br />
</td>
        <td>696.883<br />
</td>
    </tr>
    <tr>
        <td>49/40<br />
</td>
        <td>696.959<br />
</td>
    </tr>
    <tr>
        <td>7/5<br />
</td>
        <td>697.085<br />
</td>
    </tr>
    <tr>
        <td>21/16<br />
</td>
        <td>697.344<br />
</td>
    </tr>
    <tr>
        <td>16/15<br />
</td>
        <td>697.654 (1/5 comma)<br />
</td>
    </tr>
    <tr>
        <td>64/63<br />
</td>
        <td>697.728<br />
</td>
    </tr>
    <tr>
        <td>21/20<br />
</td>
        <td>697.781<br />
</td>
    </tr>
    <tr>
        <td>28/25<br />
</td>
        <td>698.099<br />
</td>
    </tr>
    <tr>
        <td>80/63<br />
</td>
        <td>698.303<br />
</td>
    </tr>
    <tr>
        <td>45/32<br />
</td>
        <td>698.371 (1/6 comma)<br />
</td>
    </tr>
    <tr>
        <td>25/21<br />
</td>
        <td>699.384<br />
</td>
    </tr>
</table>

<br />
<!-- ws:start:WikiTextHeadingRule:8:&lt;h1&gt; --><h1 id="toc4"><a name="Links"></a><!-- ws:end:WikiTextHeadingRule:8 -->Links</h1>
 <ul><li><!-- ws:start:WikiTextUrlRule:295: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:295 --> -- An Introduction to Historical Tunings, by <a class="wiki_link" href="/Kyle%20Gann">Kyle Gann</a></li></ul></body></html>

Meantone: Difference between revisions

Revision as of 19:22, 1 November 2012

IMPORTED REVISION FROM WIKISPACES

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