72edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 264024823 - Original comment: ** |
Wikispaces>keenanpepper **Imported revision 267798768 - 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:keenanpepper|keenanpepper]] and made on <tt>2011-10-24 02:03:56 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>267798768</tt>.<br> | ||
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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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Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo|96-edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri. | Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with [[96edo|96-edo]]), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri. | ||
72-tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, and is the ninth [[The Riemann Zeta Function and Tuning#Zeta | 72-tone equal temperament approximates [[11-limit|11-limit just intonation]] exceptionally well, and is the ninth [[The Riemann Zeta Function and Tuning#Zeta%20EDO%20lists|Zeta integral tuning]]. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33. | ||
72 is an excellent tuning for [[Gamelismic clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament [[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 [[Gamelismic clan|miracle temperament]], especially the 11-limit version, and the related rank three temperament [[Marvel family#Prodigy|prodigy]], and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic. | ||
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=External links= | =External links= | ||
* [[http://en.wikipedia.org/wiki/72_tone_equal_temperament|Wikipedia article on 72edo]] | * [[http://en.wikipedia.org/wiki/72_tone_equal_temperament|Wikipedia article on 72edo]] | ||
* [[http:// | * [[http://orthodoxwiki.org/Byzantine_Chant|OrthodoxWiki Article on Byzantine chant, which uses 72edo]] | ||
* [[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/index.htmmusik/|Ekmelic Music Society/Gesellschaft für Ekmelische Musik]], a group of composers and researchers dedicated to 72edo music | * [[http://www.ekmelic-music.org/en/index.htmmusik/|Ekmelic Music Society/Gesellschaft für Ekmelische Musik]], a group of composers and researchers dedicated to 72edo music | ||
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Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with <a class="wiki_link" href="/96edo">96-edo</a>), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri.<br /> | Composers that used 72-tone include Alois Hába, Ivan Wyschnegradsky, Julián Carillo (who is better associated with <a class="wiki_link" href="/96edo">96-edo</a>), Iannis Xenakis, Ezra Sims, James Tenney and the jazz musician Joe Maneri.<br /> | ||
<br /> | <br /> | ||
72-tone equal temperament approximates <a class="wiki_link" href="/11-limit">11-limit just intonation</a> exceptionally well, and is the ninth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta | 72-tone equal temperament approximates <a class="wiki_link" href="/11-limit">11-limit just intonation</a> exceptionally well, and is the ninth <a class="wiki_link" href="/The%20Riemann%20Zeta%20Function%20and%20Tuning#Zeta%20EDO%20lists">Zeta integral tuning</a>. The octave, fifth and fourth are the same size as they would be in 12-tone, 72, 42 and 30 steps respectively, but the major third (5/4) measures 23 steps, not 24, and other major intervals are one step flat of 12-et while minor ones are one step sharp. The septimal minor seventh (7/4) is 58 steps, while the undecimal semiaugmented fourth (11/8) is 33.<br /> | ||
<br /> | <br /> | ||
72 is an excellent tuning for <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>, especially the 11-limit version, and the related rank three temperament <a class="wiki_link" href="/Marvel%20family#Prodigy">prodigy</a>, and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic.<br /> | 72 is an excellent tuning for <a class="wiki_link" href="/Gamelismic%20clan">miracle temperament</a>, especially the 11-limit version, and the related rank three temperament <a class="wiki_link" href="/Marvel%20family#Prodigy">prodigy</a>, and is a good tuning for other temperaments and scales, including wizard, harry, catakleismic, compton, unidec and tritikleismic.<br /> | ||
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<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:6 -->External links</h1> | <!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><h1 id="toc3"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:6 -->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:// | <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/index.htmmusik/" 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://sonic-arts.org/tagawa/72edo.htm" rel="nofollow">Rick Tagawa's 72edo site</a>, including theory and composers' list</li><li><a class="wiki_link_ext" href="http://dannywier.ucoz.com" rel="nofollow">Danny Wier, composer and musician who specializes in 72-edo</a></li></ul></body></html></pre></div> | ||