Just intonation: Difference between revisions

Wikispaces>hstraub
**Imported revision 9120421 - Original comment: Pages for compositions in JI**
Wikispaces>guest
**Imported revision 9236813 - 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:hstraub|hstraub]] and made on <tt>2007-10-08 06:15:52 UTC</tt>.<br>
: This revision was by author [[User:guest|guest]] and made on <tt>2007-10-10 05:39:20 UTC</tt>.<br>
: The original revision id was <tt>9120421</tt>.<br>
: The original revision id was <tt>9236813</tt>.<br>
: The revision comment was: <tt>Pages for compositions in JI</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>
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==[[OverToneSeries|Compositions]]==  
==[[OverToneSeries|Compositions]]==  


=Freestyle Just/Adaptive Just Intonation=  
=Freestyle Just=
= =
=Adaptive Just Intonation=  
Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting!
Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting!


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=Constraints=  
=Constraints=  
Create subsets of the infinitely large pool of ratios.
Create subsets of the infinitely large pool of ratios by setting constraints. Here are six ways (from Jacques Dudon, "Differential Coherence", //1/1// vol. 11, no. 2: p.1):


(insert Jacques Dudon article quote here)
//1. The principle of "[[harmonic limits]]," which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's "psycharithmes" and his ordering by complexity; Gioseffe Zarlino's five-limit "senario," and the like; Helmholtz's theory of consonance with its "blending of partials," which, like the others, results in giving priority to the lowest prime numbers).


==JI theory==
2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the "monophonic" system of Harry Partch's [[tonality diamond]]. This, incidentially, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1,3 5 7 9, 11, or their octaves.
Links to JI theory pages on [[http://moinmoin.riters.com/microtonal|another microtonal wiki]], pending transfer to this wiki:
 
3. Other theorists who, in contrast to the above, advocate the use of the products of a given set of prime numbers, such as Robert Dussaut, Ervin Wilson, and others.
 
4. Restrictions on the variety of prime numbers used within a system, for example, 3 used with only one other prime (7, 11, or 13...). This is quite common practice with Ptolemy, Ibn-Sina, Al-Farabi, and Saf-al-Din, and with numerous contemporary composers working in Just Intonation.
 
5. Restricting the denominator to one or very few values (the [[OverToneSeries|harmonic series]]).
 
6. Restricting the numerator to one or a very few values (the [[subharmonic series]] or [[aliquot scales]]).//
 
**Broken** links to JI theory pages on [[http://moinmoin.riters.com/microtonal|another microtonal wiki]], which await transfer to this wiki:
[[http://moinmoin.riters.com/microtonal/index.cgi/58Note11LimitJI|58 note 11 limit JI]] - hyper-Partchian!
[[http://moinmoin.riters.com/microtonal/index.cgi/58Note11LimitJI|58 note 11 limit JI]] - hyper-Partchian!
[[http://moinmoin.riters.com/microtonal/index.cgi/Reduction|Reduction]]
[[http://moinmoin.riters.com/microtonal/index.cgi/Reduction|Reduction]]
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[[http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance|Hahn distance]]
[[http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance|Hahn distance]]


==Scales==  
==Scalesmith's gallery of Just Intonation scales==  
[[boogiewoogiescale|Boogie woogie scale]]
[[boogiewoogiescale|Boogie woogie scale]]
[[Arnold Dreyblatt]]
[[Arnold Dreyblatt]]
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&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Overtone Series-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;a class="wiki_link" href="/OverToneSeries"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:4:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc2"&gt;&lt;a name="Overtone Series-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:4 --&gt;&lt;a class="wiki_link" href="/OverToneSeries"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Freestyle Just/Adaptive Just Intonation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Freestyle Just/Adaptive Just Intonation&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:6:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc3"&gt;&lt;a name="Freestyle Just"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:6 --&gt;Freestyle Just&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc4"&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt; &lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc5"&gt;&lt;a name="Adaptive Just Intonation"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt;Adaptive Just Intonation&lt;/h1&gt;
  Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting!&lt;br /&gt;
  Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting!&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:8:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc4"&gt;&lt;a name="Freestyle Just/Adaptive Just Intonation-Software"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:8 --&gt;Software&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Adaptive Just Intonation-Software"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;Software&lt;/h2&gt;
  &lt;ul&gt;&lt;li&gt;Chuckk Hubbard's &lt;a class="wiki_link_ext" href="http://www.badmuthahubbard.com/jisequencer.html" rel="nofollow"&gt;No-scale JI Sequencer&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.math.tu-dresden.de/%7Emutabor/" rel="nofollow"&gt;Mutabor&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
  &lt;ul&gt;&lt;li&gt;Chuckk Hubbard's &lt;a class="wiki_link_ext" href="http://www.badmuthahubbard.com/jisequencer.html" rel="nofollow"&gt;No-scale JI Sequencer&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link_ext" href="http://www.math.tu-dresden.de/%7Emutabor/" rel="nofollow"&gt;Mutabor&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:10:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc5"&gt;&lt;!-- ws:end:WikiTextHeadingRule:10 --&gt; &lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc7"&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt; &lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:12:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc6"&gt;&lt;a name="Freestyle Just/Adaptive Just Intonation-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:12 --&gt;&lt;a class="wiki_link" href="/AdaptiveJI"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
  &lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Adaptive Just Intonation-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;&lt;a class="wiki_link" href="/AdaptiveJI"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
  &lt;br /&gt;
  &lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:14:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc7"&gt;&lt;a name="Constraints"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:14 --&gt;Constraints&lt;/h1&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h1&amp;gt; --&gt;&lt;h1 id="toc9"&gt;&lt;a name="Constraints"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Constraints&lt;/h1&gt;
  Create subsets of the infinitely large pool of ratios.&lt;br /&gt;
  Create subsets of the infinitely large pool of ratios by setting constraints. Here are six ways (from Jacques Dudon, &amp;quot;Differential Coherence&amp;quot;, &lt;em&gt;1/1&lt;/em&gt; vol. 11, no. 2: p.1):&lt;br /&gt;
&lt;br /&gt;
&lt;em&gt;1. The principle of &amp;quot;&lt;a class="wiki_link" href="/harmonic%20limits"&gt;harmonic limits&lt;/a&gt;,&amp;quot; which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's &amp;quot;psycharithmes&amp;quot; and his ordering by complexity; Gioseffe Zarlino's five-limit &amp;quot;senario,&amp;quot; and the like; Helmholtz's theory of consonance with its &amp;quot;blending of partials,&amp;quot; which, like the others, results in giving priority to the lowest prime numbers).&lt;br /&gt;
&lt;br /&gt;
2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the &amp;quot;monophonic&amp;quot; system of Harry Partch's &lt;a class="wiki_link" href="/tonality%20diamond"&gt;tonality diamond&lt;/a&gt;. This, incidentially, is an eleven-limit system that only makes use of ratios of the form n:d, where n and d are drawn only from harmonics 1,3 5 7 9, 11, or their octaves.&lt;br /&gt;
&lt;br /&gt;
3. Other theorists who, in contrast to the above, advocate the use of the products of a given set of prime numbers, such as Robert Dussaut, Ervin Wilson, and others.&lt;br /&gt;
&lt;br /&gt;
4. Restrictions on the variety of prime numbers used within a system, for example, 3 used with only one other prime (7, 11, or 13...). This is quite common practice with Ptolemy, Ibn-Sina, Al-Farabi, and Saf-al-Din, and with numerous contemporary composers working in Just Intonation.&lt;br /&gt;
&lt;br /&gt;
5. Restricting the denominator to one or very few values (the &lt;a class="wiki_link" href="/OverToneSeries"&gt;harmonic series&lt;/a&gt;).&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
(insert Jacques Dudon article quote here)&lt;br /&gt;
6. Restricting the numerator to one or a very few values (the &lt;a class="wiki_link" href="/subharmonic%20series"&gt;subharmonic series&lt;/a&gt; or &lt;a class="wiki_link" href="/aliquot%20scales"&gt;aliquot scales&lt;/a&gt;).&lt;/em&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:16:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc8"&gt;&lt;a name="Constraints-JI theory"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:16 --&gt;JI theory&lt;/h2&gt;
&lt;strong&gt;Broken&lt;/strong&gt; links to JI theory pages on &lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal" rel="nofollow"&gt;another microtonal wiki&lt;/a&gt;, which await transfer to this wiki:&lt;br /&gt;
Links to JI theory pages on &lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal" rel="nofollow"&gt;another microtonal wiki&lt;/a&gt;, pending transfer to this wiki:&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/58Note11LimitJI" rel="nofollow"&gt;58 note 11 limit JI&lt;/a&gt; - hyper-Partchian!&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/58Note11LimitJI" rel="nofollow"&gt;58 note 11 limit JI&lt;/a&gt; - hyper-Partchian!&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Reduction" rel="nofollow"&gt;Reduction&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Reduction" rel="nofollow"&gt;Reduction&lt;/a&gt;&lt;br /&gt;
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&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance" rel="nofollow"&gt;Hahn distance&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance" rel="nofollow"&gt;Hahn distance&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:18:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc9"&gt;&lt;a name="Constraints-Scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:18 --&gt;Scales&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Constraints-Scalesmith's gallery of Just Intonation scales"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;Scalesmith's gallery of Just Intonation scales&lt;/h2&gt;
  &lt;a class="wiki_link" href="/boogiewoogiescale"&gt;Boogie woogie scale&lt;/a&gt;&lt;br /&gt;
  &lt;a class="wiki_link" href="/boogiewoogiescale"&gt;Boogie woogie scale&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Arnold%20Dreyblatt"&gt;Arnold Dreyblatt&lt;/a&gt;&lt;br /&gt;
&lt;a class="wiki_link" href="/Arnold%20Dreyblatt"&gt;Arnold Dreyblatt&lt;/a&gt;&lt;br /&gt;
Gallery of pentatonics&lt;br /&gt;
Gallery of pentatonics&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;!-- ws:start:WikiTextHeadingRule:20:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc10"&gt;&lt;a name="Constraints-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:20 --&gt;&lt;a class="wiki_link" href="/FiniteSubsetJI"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
&lt;!-- ws:start:WikiTextHeadingRule:22:&amp;lt;h2&amp;gt; --&gt;&lt;h2 id="toc11"&gt;&lt;a name="Constraints-Compositions"&gt;&lt;/a&gt;&lt;!-- ws:end:WikiTextHeadingRule:22 --&gt;&lt;a class="wiki_link" href="/FiniteSubsetJI"&gt;Compositions&lt;/a&gt;&lt;/h2&gt;
&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;/body&gt;&lt;/html&gt;</pre></div>