Just intonation
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=Just Intonation defined= Describe intervals between pitches by specifying ratios (of [[http://en.wikipedia.org/wiki/Rational_number|rational numbers]]) between the frequencies of pitches, and you will be speaking Just Intonation. =Overtone Series= (Insert theory/description here...) ==[[OverToneSeries|Compositions]]== =Freestyle Just= = = =Adaptive Just Intonation= Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting! ==Software== * Chuckk Hubbard's [[http://www.badmuthahubbard.com/jisequencer.html|No-scale JI Sequencer]] * [[http://www.math.tu-dresden.de/%7Emutabor/|Mutabor]] == == ==[[AdaptiveJI|Compositions]]== =Constraints= 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): //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). 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. 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/Reduction|Reduction]] [[http://moinmoin.riters.com/microtonal/index.cgi/Comma_20sequences|Comma sequences]] [[http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance|Hahn distance]] ==Scalesmith's gallery of Just Intonation scales== [[boogiewoogiescale|Boogie woogie scale]] [[Arnold Dreyblatt]] Gallery of pentatonics ==[[FiniteSubsetJI|Compositions]]==
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<html><head><title>Just intonation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Just Intonation defined"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just Intonation defined</h1> Describe intervals between pitches by specifying ratios (of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rational_number" rel="nofollow">rational numbers</a>) between the frequencies of pitches, and you will be speaking Just Intonation.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Overtone Series"></a><!-- ws:end:WikiTextHeadingRule:2 -->Overtone Series</h1> (Insert theory/description here...)<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Overtone Series-Compositions"></a><!-- ws:end:WikiTextHeadingRule:4 --><a class="wiki_link" href="/OverToneSeries">Compositions</a></h2> <br /> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><a name="Freestyle Just"></a><!-- ws:end:WikiTextHeadingRule:6 -->Freestyle Just</h1> <!-- ws:start:WikiTextHeadingRule:8:<h1> --><h1 id="toc4"><!-- ws:end:WikiTextHeadingRule:8 --> </h1> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Adaptive Just Intonation"></a><!-- ws:end:WikiTextHeadingRule:10 -->Adaptive Just Intonation</h1> Compose music such that each pitch you choose is chosen from the infinitely large pool of rational numbers. Daunting!<br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h2> --><h2 id="toc6"><a name="Adaptive Just Intonation-Software"></a><!-- ws:end:WikiTextHeadingRule:12 -->Software</h2> <ul><li>Chuckk Hubbard's <a class="wiki_link_ext" href="http://www.badmuthahubbard.com/jisequencer.html" rel="nofollow">No-scale JI Sequencer</a></li><li><a class="wiki_link_ext" href="http://www.math.tu-dresden.de/%7Emutabor/" rel="nofollow">Mutabor</a></li></ul><br /> <!-- ws:start:WikiTextHeadingRule:14:<h2> --><h2 id="toc7"><!-- ws:end:WikiTextHeadingRule:14 --> </h2> <!-- ws:start:WikiTextHeadingRule:16:<h2> --><h2 id="toc8"><a name="Adaptive Just Intonation-Compositions"></a><!-- ws:end:WikiTextHeadingRule:16 --><a class="wiki_link" href="/AdaptiveJI">Compositions</a></h2> <br /> <!-- ws:start:WikiTextHeadingRule:18:<h1> --><h1 id="toc9"><a name="Constraints"></a><!-- ws:end:WikiTextHeadingRule:18 -->Constraints</h1> Create subsets of the infinitely large pool of ratios by setting constraints. Here are six ways (from Jacques Dudon, "Differential Coherence", <em>1/1</em> vol. 11, no. 2: p.1):<br /> <br /> <em>1. The principle of "<a class="wiki_link" href="/harmonic%20limits">harmonic limits</a>," 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).<br /> <br /> 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 <a class="wiki_link" href="/tonality%20diamond">tonality diamond</a>. 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.<br /> <br /> 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.<br /> <br /> 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.<br /> <br /> 5. Restricting the denominator to one or very few values (the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>).<br /> <br /> 6. Restricting the numerator to one or a very few values (the <a class="wiki_link" href="/subharmonic%20series">subharmonic series</a> or <a class="wiki_link" href="/aliquot%20scales">aliquot scales</a>).</em><br /> <br /> <strong>Broken</strong> links to JI theory pages on <a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal" rel="nofollow">another microtonal wiki</a>, which await transfer to this wiki:<br /> <a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/58Note11LimitJI" rel="nofollow">58 note 11 limit JI</a> - hyper-Partchian!<br /> <a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Reduction" rel="nofollow">Reduction</a><br /> <a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Comma_20sequences" rel="nofollow">Comma sequences</a><br /> <a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance" rel="nofollow">Hahn distance</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:20:<h2> --><h2 id="toc10"><a name="Constraints-Scalesmith's gallery of Just Intonation scales"></a><!-- ws:end:WikiTextHeadingRule:20 -->Scalesmith's gallery of Just Intonation scales</h2> <a class="wiki_link" href="/boogiewoogiescale">Boogie woogie scale</a><br /> <a class="wiki_link" href="/Arnold%20Dreyblatt">Arnold Dreyblatt</a><br /> Gallery of pentatonics<br /> <br /> <!-- ws:start:WikiTextHeadingRule:22:<h2> --><h2 id="toc11"><a name="Constraints-Compositions"></a><!-- ws:end:WikiTextHeadingRule:22 --><a class="wiki_link" href="/FiniteSubsetJI">Compositions</a></h2> </body></html>