22edo: Difference between revisions
Wikispaces>Andrew_Heathwaite **Imported revision 83606143 - Original comment: ** |
Wikispaces>Andrew_Heathwaite **Imported revision 83606885 - 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:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-08-07 20: | : This revision was by author [[User:Andrew_Heathwaite|Andrew_Heathwaite]] and made on <tt>2009-08-07 20:33:57 UTC</tt>.<br> | ||
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The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While [[31edo|31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like. | The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While [[31edo|31 equal temperament]] does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and [[19edo|19]], is not a [[Regular Temperaments#meantone|meantone]] system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like. | ||
See also: [[22edo Solfege]], [[22edo Tetrachords]] | See also: [[22edo Solfege]], [[22edo Tetrachords]], [[22edo Modes]] | ||
==Properties of 22 equal temperament== | ==Properties of 22 equal temperament== | ||
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The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While <a class="wiki_link" href="/31edo">31 equal temperament</a> does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and <a class="wiki_link" href="/19edo">19</a>, is not a <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.<br /> | The 22-et system is in fact the third equal division, after 12 and 19, which is capable of tolerably dealing with 5-limit music. However, there is more to it than that; unlike 12 or 19 it is able to do rough justice to the 7- and 11-limits. While <a class="wiki_link" href="/31edo">31 equal temperament</a> does much better, 22-et at least allows the use of these higher-limit harmonies. Moreover, 22-et, unlike 12 and <a class="wiki_link" href="/19edo">19</a>, is not a <a class="wiki_link" href="/Regular%20Temperaments#meantone">meantone</a> system. The net effect is that 22 allows, and to some extent even forces, the exploration of less familiar musical territory, yet is small enough that it can be used in live performances with suitably designed instruments, such as 22-tone guitars and the like.<br /> | ||
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See also: <a class="wiki_link" href="/22edo%20Solfege">22edo Solfege</a>, <a class="wiki_link" href="/22edo%20Tetrachords">22edo Tetrachords</a><br /> | See also: <a class="wiki_link" href="/22edo%20Solfege">22edo Solfege</a>, <a class="wiki_link" href="/22edo%20Tetrachords">22edo Tetrachords</a>, <a class="wiki_link" href="/22edo%20Modes">22edo Modes</a><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-Properties of 22 equal temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Properties of 22 equal temperament</h2> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h2&gt; --><h2 id="toc1"><a name="Theory-Properties of 22 equal temperament"></a><!-- ws:end:WikiTextHeadingRule:2 -->Properties of 22 equal temperament</h2> | ||
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Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''<br /> | Erlich, Paul, ''Tuning, Tonality, and Twenty-Two Tone Temperament''<br /> | ||
*[<!-- ws:start:WikiTextUrlRule: | *[<!-- ws:start:WikiTextUrlRule:66:http://66.98.148.43/~xenharmo/text/tuning22.pdf --><a class="wiki_link_ext" href="http://66.98.148.43/~xenharmo/text/tuning22.pdf" rel="nofollow">http://66.98.148.43/~xenharmo/text/tuning22.pdf</a><!-- ws:end:WikiTextUrlRule:66 -->] or <!-- ws:start:WikiTextUrlRule:67:http://lumma.org/tuning/erlich/erlich-decatonic.pdf --><a class="wiki_link_ext" href="http://lumma.org/tuning/erlich/erlich-decatonic.pdf" rel="nofollow">http://lumma.org/tuning/erlich/erlich-decatonic.pdf</a><!-- ws:end:WikiTextUrlRule:67 --><br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Theory-References"></a><!-- ws:end:WikiTextHeadingRule:6 -->References</h2> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><a name="Theory-References"></a><!-- ws:end:WikiTextHeadingRule:6 -->References</h2> | ||
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Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]<br /> | Barbour, James Murray, ''Tuning and temperament, a historical survey'', East Lansing, Michigan State College Press, 1953 [c1951]<br /> | ||
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Bosanquet, R.H.M. [<!-- ws:start:WikiTextUrlRule: | Bosanquet, R.H.M. [<!-- ws:start:WikiTextUrlRule:68:http://www.geocities.com/threesixesinarow/hindoo.htm --><a class="wiki_link_ext" href="http://www.geocities.com/threesixesinarow/hindoo.htm" rel="nofollow">http://www.geocities.com/threesixesinarow/hindoo.htm</a><!-- ws:end:WikiTextUrlRule:68 --> ''On the Hindoo division of the octave, with additions to the theory of higher orders''], Proceedings of the Royal Society of London vol. 26, 1879, pp. 272-284. Reproduced in Tagore, Sourindro Mohun, ''Hindu Music from Various Authors'', Chowkhamba Sanskrit Series, Varanasi, India, 1965<br /> | ||
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