72edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 502325974 - Original comment: ** |
Wikispaces>hstraub **Imported revision 527592214 - 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: | : This revision was by author [[User:hstraub|hstraub]] and made on <tt>2014-10-22 02:25:39 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>527592214</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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72 is an excellent tuning for [[xenharmonic/Gamelismic clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament [[xenharmonic/Marvel family#Prodigy|prodigy]], and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic. | 72 is an excellent tuning for [[xenharmonic/Gamelismic clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament [[xenharmonic/Marvel family#Prodigy|prodigy]], and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic. | ||
=Commas and Temperaments= | =Commas and Temperaments= | ||
72et tempers out the Pythagorean comma, 531441/524288, in the 3-limit and the kleisma, 15625/15552, the ampersand, 34171875/33554432 = |-25 7 6>, the graviton, 129140163/128000000 = |-13 17 -6>, the and the ennealimma, 7629394531250/7625597484987 = |1 -27 18> in the 5-limit. The 7-limit commas include 225/224, 1029/1024, 16875/16807, 19683/19600, 420175/419904, 2401/2400, 4375/4374 and 250047/250000. 72et shines in the 11-limit, with commas 243/242, 385/384, 441/440, 540/539, 1375/1372, 6250/6237, 4000/3993, 3025/3024 and 9801/9800. For the 13-limit, it tempers out 169/168, 325/324, 351/350, 364/363, 625/624, 676/675, 729/728, 1001/1000, 1575/1573, 1716/1715, 2080/2079 and 6656/6655. It provides the optimal patent val for miracle and wizard in the 7-limit, miracle, catakleismic, bikleismic, compton, ennealimnic, ennealiminal, enneaportent, marvolo and catalytic in the 11-limit, and catakleismic, bikleismic, compton, comptone, enneaportent, ennealim, catalytic, marvolo, manna, hendec, lizard, neominor, hours, and semimiracle in the 13-limit. | 72et tempers out the Pythagorean comma, 531441/524288, in the 3-limit and the kleisma, 15625/15552, the ampersand, 34171875/33554432 = |-25 7 6>, the graviton, 129140163/128000000 = |-13 17 -6>, the and the ennealimma, 7629394531250/7625597484987 = |1 -27 18> in the 5-limit. The 7-limit commas include 225/224, 1029/1024, 16875/16807, 19683/19600, 420175/419904, 2401/2400, 4375/4374 and 250047/250000. 72et shines in the 11-limit, with commas 243/242, 385/384, 441/440, 540/539, 1375/1372, 6250/6237, 4000/3993, 3025/3024 and 9801/9800. For the 13-limit, it tempers out 169/168, 325/324, 351/350, 364/363, 625/624, 676/675, 729/728, 1001/1000, 1575/1573, 1716/1715, 2080/2079 and 6656/6655. It provides the optimal patent val for miracle and wizard in the 7-limit, miracle, catakleismic, bikleismic, compton, ennealimnic, ennealiminal, enneaportent, marvolo and catalytic in the 11-limit, and catakleismic, bikleismic, compton, comptone, enneaportent, ennealim, catalytic, marvolo, manna, hendec, lizard, neominor, hours, and semimiracle in the 13-limit. | ||
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* [[http://en.wikipedia.org/wiki/Joe_Maneri|Wikipedia article on Joe Maneri (1927-2009)]] | * [[http://en.wikipedia.org/wiki/Joe_Maneri|Wikipedia article on Joe Maneri (1927-2009)]] | ||
* [[http://www.ekmelic-music.org/en/|Ekmelic Music Society/Gesellschaft für Ekmelische Musik]], a group of composers and researchers dedicated to 72edo music | * [[http://www.ekmelic-music.org/en/|Ekmelic Music Society/Gesellschaft für Ekmelische Musik]], a group of composers and researchers dedicated to 72edo music | ||
* [[http:// | * [[http://72note.com/site/original.html|Rick Tagawa's 72edo site]], including theory and composers' list | ||
* [[@http://www.myspace.com/dawier|Danny Wier, composer and musician who specializes in 72-edo]]</pre></div> | * [[@http://www.myspace.com/dawier|Danny Wier, composer and musician who specializes in 72-edo]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
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<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Commas and Temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Commas and Temperaments</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Commas and Temperaments"></a><!-- ws:end:WikiTextHeadingRule:0 -->Commas and Temperaments</h1> | ||
72et tempers out the Pythagorean comma, 531441/524288, in the 3-limit and the kleisma, 15625/15552, the ampersand, 34171875/33554432 = |-25 7 6&gt;, the graviton, 129140163/128000000 = |-13 17 -6&gt;, the and the ennealimma, 7629394531250/7625597484987 = |1 -27 18&gt; in the 5-limit. The 7-limit commas include 225/224, 1029/1024, 16875/16807, 19683/19600, 420175/419904, 2401/2400, 4375/4374 and 250047/250000. 72et shines in the 11-limit, with commas 243/242, 385/384, 441/440, 540/539, 1375/1372, 6250/6237, 4000/3993, 3025/3024 and 9801/9800. For the 13-limit, it tempers out 169/168, 325/324, 351/350, 364/363, 625/624, 676/675, 729/728, 1001/1000, 1575/1573, 1716/1715, 2080/2079 and 6656/6655. It provides the optimal patent val for miracle and wizard in the 7-limit, miracle, catakleismic, bikleismic, compton, ennealimnic, ennealiminal, enneaportent, marvolo and catalytic in the 11-limit, and catakleismic, bikleismic, compton, comptone, enneaportent, ennealim, catalytic, marvolo, manna, hendec, lizard, neominor, hours, and semimiracle in the 13-limit.<br /> | 72et tempers out the Pythagorean comma, 531441/524288, in the 3-limit and the kleisma, 15625/15552, the ampersand, 34171875/33554432 = |-25 7 6&gt;, the graviton, 129140163/128000000 = |-13 17 -6&gt;, the and the ennealimma, 7629394531250/7625597484987 = |1 -27 18&gt; in the 5-limit. The 7-limit commas include 225/224, 1029/1024, 16875/16807, 19683/19600, 420175/419904, 2401/2400, 4375/4374 and 250047/250000. 72et shines in the 11-limit, with commas 243/242, 385/384, 441/440, 540/539, 1375/1372, 6250/6237, 4000/3993, 3025/3024 and 9801/9800. For the 13-limit, it tempers out 169/168, 325/324, 351/350, 364/363, 625/624, 676/675, 729/728, 1001/1000, 1575/1573, 1716/1715, 2080/2079 and 6656/6655. It provides the optimal patent val for miracle and wizard in the 7-limit, miracle, catakleismic, bikleismic, compton, ennealimnic, ennealiminal, enneaportent, marvolo and catalytic in the 11-limit, and catakleismic, bikleismic, compton, comptone, enneaportent, ennealim, catalytic, marvolo, manna, hendec, lizard, neominor, hours, and semimiracle in the 13-limit.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Harmonic Scale"></a><!-- ws:end:WikiTextHeadingRule:2 -->Harmonic Scale</h1> | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Harmonic Scale"></a><!-- ws:end:WikiTextHeadingRule:2 -->Harmonic Scale</h1> | ||
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<!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:16 -->External links</h1> | <!-- ws:start:WikiTextHeadingRule:16:&lt;h1&gt; --><h1 id="toc8"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:16 -->External links</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/72_tone_equal_temperament" rel="nofollow">Wikipedia article on 72edo</a></li><li><a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant" rel="nofollow">OrthodoxWiki Article on Byzantine chant, which uses 72edo</a></li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joe_Maneri" rel="nofollow">Wikipedia article on Joe Maneri (1927-2009)</a></li><li><a class="wiki_link_ext" href="http://www.ekmelic-music.org/en/" rel="nofollow">Ekmelic Music Society/Gesellschaft für Ekmelische Musik</a>, a group of composers and researchers dedicated to 72edo music</li><li><a class="wiki_link_ext" href="http:// | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/72_tone_equal_temperament" rel="nofollow">Wikipedia article on 72edo</a></li><li><a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant" rel="nofollow">OrthodoxWiki Article on Byzantine chant, which uses 72edo</a></li><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Joe_Maneri" rel="nofollow">Wikipedia article on Joe Maneri (1927-2009)</a></li><li><a class="wiki_link_ext" href="http://www.ekmelic-music.org/en/" rel="nofollow">Ekmelic Music Society/Gesellschaft für Ekmelische Musik</a>, a group of composers and researchers dedicated to 72edo music</li><li><a class="wiki_link_ext" href="http://72note.com/site/original.html" rel="nofollow">Rick Tagawa's 72edo site</a>, including theory and composers' list</li><li><a class="wiki_link_ext" href="http://www.myspace.com/dawier" rel="nofollow" target="_blank">Danny Wier, composer and musician who specializes in 72-edo</a></li></ul></body></html></pre></div> | ||