96edo: Difference between revisions
Wikispaces>genewardsmith **Imported revision 235887448 - Original comment: ** |
Wikispaces>genewardsmith **Imported revision 235890936 - 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:genewardsmith|genewardsmith]] and made on <tt>2011-06-10 | : This revision was by author [[User:genewardsmith|genewardsmith]] and made on <tt>2011-06-10 23:35:40 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>235890936</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> | ||
<h4>Original Wikitext content:</h4> | <h4>Original Wikitext content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html"> | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;white-space: pre-wrap ! important" class="old-revision-html">[[toc|flat]] | ||
=Properties= | |||
The 96 equal division divides the octave into 96 equal parts of exactly 12.5 cents each. As a [[5-limit]] system, it can be characterized by the fact that it tempers out both the Pythagorean comma, 531441/524288, and Wuerschmidt's comma, 393216/390625. It therefore has the same familiar 700 cent fifth as [[12edo]], and has a best major third of 387.5 cents, a bit over a cent sharp. There is therefore nothing to complain of with its representation of the 5-limit and it can be recommended as an approach to the [[Wuerschmidt family]] of temperaments. | |||
=[[http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html|Julian Carrillo and the 13th Sound a microtonal musical system]] | In the [[7-limit]], 96 has two possible mappings for 7/4, a sharp one of 975 cents and a flat one of 962.5 cents. Using the sharp mapping, 96 tempers out 225/224 and supports wurschmidt temperament, and using the flat mapping it tempers out 126/125 and supports worschmidt temperament. We can also dispense with 7 altogether, and use it as a no-sevens system, where it tempers out 243/242 in the 11-limit and 676/675 in the 13-limit. If we include 7, then the sharp mapping tempers out 99/98 and 176/175 in the 11-limit, and 169/168 in the 13-limit. With the flat 7 it tempers out 385/384 in the 11-limit and 196/195 and 364/363 in the 13-limit. | ||
=History= | |||
96 equal divisions of the octave was first used by the Mexican composer and theorist [[http://en.wikipedia.org/wiki/Juli%C3%A1n_Carrillo|Julián Carrillo]]. It has subsequently been used by a number of other composers. | |||
=Links=[[http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html|Julian Carrillo and the 13th Sound a microtonal musical system]] | |||
English & Spanish, by Ernesto Solís Winkler. | English & Spanish, by Ernesto Solís Winkler. | ||
[[http://brahms.ircam.fr/textes/c00000454/|Julián Carrillo]] (Centre George Pompidou) - French | |||
[[http://www.cenart.gob.mx/centros/cenidim/eventos/M_julian_carrillo.htm|National Cetre for investigation, Documentation and Musical Information - Spanish]] | |||
[[http://www.myspace.com/juliancarrillo|Julián Carrillo at My Space - Spanish ]] | |||
[[http://www.smf.mx/boletin/Jul-96/articles/son13.html|Sonido 13: Towards the musical Infinite - Spanish]] by J.R. Martínez y S. Palomares-Sánchez. | |||
Two movements from //Suite Improntus//, for guitar in quatertones [[http://www.xs4all.nl/~huygensf/english/music.html|Stichting Huygens-Fokker Centrum voor Microtonale Muziek]] | |||
[[http://www.cnca.gob.mx/cnca/nuevo/diarias/051199/testimon.html|Julián Carrillo: Testimonio de una vida]] About the book edited by the council of San Luis Potosí in 1992. (Gabriel Ríos) - Spanish | |||
[[http://www.jornada.unam.mx/2005/07/10/a02n2cul.php|Article from the journal 'La Jornada' - Spanish ]] | |||
[[http://sepiensa.org.mx/contenidos/menu_arte/l_mexXX/sigloxx/carrillo/1.htm|Sonido 13 - An easy explannation by Jesús Herrera - Spanish.]] | |||
[[http://www.gimenezcacho.com/indexF.htm|Performer Jimena Giménez Cacho performs works by Carrillo on the Cello> ]] | |||
[[http://cronica.diputados.gob.mx/DDebates/34/1er/Ord/19301121.html|Mexican Houses of Parliament about Carrillo - Cámara de Diputados. - México, D.F. a 21 de noviembre de 1930]] | |||
[[http://www.epdlp.com/compclasico.php?id=973|El Poder de la Palabra. Short bibliography of Julián Carrillo]] | |||
[[http://www.guije.com/cosas/folk/carrillo.htm|Eduardo Sánchez, La Habana 1928]] | |||
[[http://www.jornada.unam.mx/2005/12/11/sem-cacho.html|La Jornada, Jimena Jiménez, December 2005 - article in Spanish]] | |||
OTHER COMPOSERS | OTHER COMPOSERS | ||
Works for the [[http://www.sauter-pianos.de/english/pianos/microtone.html|Sauter's 1/16tone microtone piano]] by the composers [[http://presence.or.at/einklang/Archiv/archiv_Komponisten_E.htm#flammer|Ernest Helmuth Flammer]], Marc Kilchenmann, Bernfried E. G. Pröve, Martin Imholz, Franck Cristoph Yeznikian, Werner Grimmel, and [[http://www.moderecords.com/catalog/120_121bancquart.html|Alain Bancquart]], are recompilated on this CD: [[http://www.zeitklang.de/cd_thecarrillo.htm|'The Carrillo tone piano']] | Works for the [[http://www.sauter-pianos.de/english/pianos/microtone.html|Sauter's 1/16tone microtone piano]] by the composers [[http://presence.or.at/einklang/Archiv/archiv_Komponisten_E.htm#flammer|Ernest Helmuth Flammer]], Marc Kilchenmann, Bernfried E. G. Pröve, Martin Imholz, Franck Cristoph Yeznikian, Werner Grimmel, and [[http://www.moderecords.com/catalog/120_121bancquart.html|Alain Bancquart]], are recompilated on this CD: [[http://www.zeitklang.de/cd_thecarrillo.htm|'The Carrillo tone piano']] | ||
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[[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Carrillo/Cromometrofon%eda%20%231.mp3|Cromometrofonía #1]] by [[Julián Carrillo]]</pre></div> | [[http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Carrillo/Cromometrofon%eda%20%231.mp3|Cromometrofonía #1]] by [[Julián Carrillo]]</pre></div> | ||
<h4>Original HTML content:</h4> | <h4>Original HTML content:</h4> | ||
<div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>96edo</title></head><body>96 equal | <div style="width:100%; max-height:400pt; overflow:auto; background-color:#f8f9fa; border: 1px solid #eaecf0; padding:0em"><pre style="margin:0px;border:none;background:none;word-wrap:break-word;width:200%;white-space: pre-wrap ! important" class="old-revision-html"><html><head><title>96edo</title></head><body><!-- ws:start:WikiTextTocRule:6:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:6 --><!-- ws:start:WikiTextTocRule:7: --><a href="#Properties">Properties</a><!-- ws:end:WikiTextTocRule:7 --><!-- ws:start:WikiTextTocRule:8: --> | <a href="#History">History</a><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --> | <a href="#Music">Music</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | ||
<!-- ws:end:WikiTextTocRule:10 --><br /> | |||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Properties"></a><!-- ws:end:WikiTextHeadingRule:0 -->Properties</h1> | |||
The 96 equal division divides the octave into 96 equal parts of exactly 12.5 cents each. As a <a class="wiki_link" href="/5-limit">5-limit</a> system, it can be characterized by the fact that it tempers out both the Pythagorean comma, 531441/524288, and Wuerschmidt's comma, 393216/390625. It therefore has the same familiar 700 cent fifth as <a class="wiki_link" href="/12edo">12edo</a>, and has a best major third of 387.5 cents, a bit over a cent sharp. There is therefore nothing to complain of with its representation of the 5-limit and it can be recommended as an approach to the <a class="wiki_link" href="/Wuerschmidt%20family">Wuerschmidt family</a> of temperaments.<br /> | |||
<br /> | <br /> | ||
In the <a class="wiki_link" href="/7-limit">7-limit</a>, 96 has two possible mappings for 7/4, a sharp one of 975 cents and a flat one of 962.5 cents. Using the sharp mapping, 96 tempers out 225/224 and supports wurschmidt temperament, and using the flat mapping it tempers out 126/125 and supports worschmidt temperament. We can also dispense with 7 altogether, and use it as a no-sevens system, where it tempers out 243/242 in the 11-limit and 676/675 in the 13-limit. If we include 7, then the sharp mapping tempers out 99/98 and 176/175 in the 11-limit, and 169/168 in the 13-limit. With the flat 7 it tempers out 385/384 in the 11-limit and 196/195 and 364/363 in the 13-limit.<br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="History"></a><!-- ws:end:WikiTextHeadingRule:2 -->History</h1> | ||
96 equal divisions of the octave was first used by the Mexican composer and theorist <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Juli%C3%A1n_Carrillo" rel="nofollow">Julián Carrillo</a>. It has subsequently been used by a number of other composers.<br /> | |||
<br /> | <br /> | ||
=Links=<a class="wiki_link_ext" href="http://paginas.tol.itesm.mx/campus/L00280370/carrillo.html" rel="nofollow">Julian Carrillo and the 13th Sound a microtonal musical system</a><br /> | |||
< | English &amp; Spanish, by Ernesto Solís Winkler.<br /> | ||
<a class="wiki_link_ext" href="http://brahms.ircam.fr/textes/c00000454/" rel="nofollow">Julián Carrillo</a> (Centre George Pompidou) - French <br /> | |||
<a class="wiki_link_ext" href="http://www.cenart.gob.mx/centros/cenidim/eventos/M_julian_carrillo.htm" rel="nofollow">National Cetre for investigation, Documentation and Musical Information - Spanish</a><br /> | |||
<a class="wiki_link_ext" href="http://www.myspace.com/juliancarrillo" rel="nofollow">Julián Carrillo at My Space - Spanish </a><br /> | |||
<a class="wiki_link_ext" href="http://www.smf.mx/boletin/Jul-96/articles/son13.html" rel="nofollow">Sonido 13: Towards the musical Infinite - Spanish</a> by J.R. Martínez y S. Palomares-Sánchez. <br /> | |||
Two movements from <em>Suite Improntus</em>, for guitar in quatertones <a class="wiki_link_ext" href="http://www.xs4all.nl/~huygensf/english/music.html" rel="nofollow">Stichting Huygens-Fokker Centrum voor Microtonale Muziek</a><br /> | |||
<a class="wiki_link_ext" href="http://www.cnca.gob.mx/cnca/nuevo/diarias/051199/testimon.html" rel="nofollow">Julián Carrillo: Testimonio de una vida</a> About the book edited by the council of San Luis Potosí in 1992. (Gabriel Ríos) - Spanish <br /> | |||
<a class="wiki_link_ext" href="http://www.jornada.unam.mx/2005/07/10/a02n2cul.php" rel="nofollow">Article from the journal 'La Jornada' - Spanish </a><br /> | |||
<a class="wiki_link_ext" href="http://sepiensa.org.mx/contenidos/menu_arte/l_mexXX/sigloxx/carrillo/1.htm" rel="nofollow">Sonido 13 - An easy explannation by Jesús Herrera - Spanish.</a><br /> | |||
<a class="wiki_link_ext" href="http://www.gimenezcacho.com/indexF.htm" rel="nofollow">Performer Jimena Giménez Cacho performs works by Carrillo on the Cello&gt; </a><br /> | |||
<a class="wiki_link_ext" href="http://cronica.diputados.gob.mx/DDebates/34/1er/Ord/19301121.html" rel="nofollow">Mexican Houses of Parliament about Carrillo - Cámara de Diputados. - México, D.F. a 21 de noviembre de 1930</a><br /> | |||
<a class="wiki_link_ext" href="http://www.epdlp.com/compclasico.php?id=973" rel="nofollow">El Poder de la Palabra. Short bibliography of Julián Carrillo</a><br /> | |||
<a class="wiki_link_ext" href="http://www.guije.com/cosas/folk/carrillo.htm" rel="nofollow">Eduardo Sánchez, La Habana 1928</a><br /> | |||
<a class="wiki_link_ext" href="http://www.jornada.unam.mx/2005/12/11/sem-cacho.html" rel="nofollow">La Jornada, Jimena Jiménez, December 2005 - article in Spanish</a><br /> | |||
OTHER COMPOSERS<br /> | |||
Works for the <a class="wiki_link_ext" href="http://www.sauter-pianos.de/english/pianos/microtone.html" rel="nofollow">Sauter's 1/16tone microtone piano</a> by the composers <a class="wiki_link_ext" href="http://presence.or.at/einklang/Archiv/archiv_Komponisten_E.htm#flammer" rel="nofollow">Ernest Helmuth Flammer</a>, Marc Kilchenmann, Bernfried E. G. Pröve, Martin Imholz, Franck Cristoph Yeznikian, Werner Grimmel, and <a class="wiki_link_ext" href="http://www.moderecords.com/catalog/120_121bancquart.html" rel="nofollow">Alain Bancquart</a>, are recompilated on this CD: <a class="wiki_link_ext" href="http://www.zeitklang.de/cd_thecarrillo.htm" rel="nofollow">'The Carrillo tone piano'</a><br /> | Works for the <a class="wiki_link_ext" href="http://www.sauter-pianos.de/english/pianos/microtone.html" rel="nofollow">Sauter's 1/16tone microtone piano</a> by the composers <a class="wiki_link_ext" href="http://presence.or.at/einklang/Archiv/archiv_Komponisten_E.htm#flammer" rel="nofollow">Ernest Helmuth Flammer</a>, Marc Kilchenmann, Bernfried E. G. Pröve, Martin Imholz, Franck Cristoph Yeznikian, Werner Grimmel, and <a class="wiki_link_ext" href="http://www.moderecords.com/catalog/120_121bancquart.html" rel="nofollow">Alain Bancquart</a>, are recompilated on this CD: <a class="wiki_link_ext" href="http://www.zeitklang.de/cd_thecarrillo.htm" rel="nofollow">'The Carrillo tone piano'</a><br /> | ||
<a class="wiki_link_ext" href="http://www.96edo.com/" rel="nofollow">Mohajeri, Shaahin</a><br /> | <a class="wiki_link_ext" href="http://www.96edo.com/" rel="nofollow">Mohajeri, Shaahin</a><br /> | ||
| Line 58: | Line 79: | ||
<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow">Georg Friedrich Haas</a>, &quot;flow and friction&quot;<br /> | <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Georg_Friedrich_Haas" rel="nofollow">Georg Friedrich Haas</a>, &quot;flow and friction&quot;<br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="Music"></a><!-- ws:end:WikiTextHeadingRule:4 -->Music</h1> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/4gahforbrass-880821.mp3" rel="nofollow">4gah for brass</a> by <a class="wiki_link" href="/Shahiin%20Mohajeri">Shahiin Mohajeri</a><br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/4gahforbrass-880821.mp3" rel="nofollow">4gah for brass</a> by <a class="wiki_link" href="/Shahiin%20Mohajeri">Shahiin Mohajeri</a><br /> | ||
<a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Endless%20life.mp3" rel="nofollow">Endless life</a> by Shahiin Mohajeri<br /> | <a class="wiki_link_ext" href="http://clones.soonlabel.com/public/micro/gene_ward_smith/Others/Mohajeri/Endless%20life.mp3" rel="nofollow">Endless life</a> by Shahiin Mohajeri<br /> | ||