Just intonation
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=Just Intonation explained= 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. To understand this, you need first to understand the relation of [[FrequencyPitchTutorial|frequency and pitch]]. Kyle Gann is a good thing to read. A transparent illustration and one of just intonation's acoustic bases is the [[OverToneSeries|harmonic series]]. =Just Intonation used= The use of just intonation could be divided into these two flavors: ==Free Style Just== = = Lou Harrison used this term; it means that you choose just-intonation pitches, from the set of all possible just intervals (not from a mode or scale), as you use them in music. Dedicated page -> [[FreeStyleJI]] ==Constrained Just== (In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (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 [[CombinationProductSet|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 ([[3and7JI|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]]).// =Just Intonation Propaganda= //Insert fair discussion of JI proselytizing and psychoacoustics psychobabble right here!// =Variations on 'Just'= [[Regular Temperaments]] are just intonation systems of various [[harmonic limits]] with certain commas tempered out [[AdaptiveJI|Adaptive JI]] schemes usually temper out these commas over time, resulting in **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]]
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<html><head><title>Just intonation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:<h1> --><h1 id="toc0"><a name="Just Intonation explained"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just Intonation explained</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 /> To understand this, you need first to understand the relation of <a class="wiki_link" href="/FrequencyPitchTutorial">frequency and pitch</a>. Kyle Gann is a good thing to read. A transparent illustration and one of just intonation's acoustic bases is the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>.<br /> <br /> <!-- ws:start:WikiTextHeadingRule:2:<h1> --><h1 id="toc1"><a name="Just Intonation used"></a><!-- ws:end:WikiTextHeadingRule:2 -->Just Intonation used</h1> The use of just intonation could be divided into these two flavors:<br /> <br /> <!-- ws:start:WikiTextHeadingRule:4:<h2> --><h2 id="toc2"><a name="Just Intonation used-Free Style Just"></a><!-- ws:end:WikiTextHeadingRule:4 -->Free Style Just</h2> <!-- ws:start:WikiTextHeadingRule:6:<h1> --><h1 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h1> Lou Harrison used this term; it means that you choose just-intonation pitches, from the set of all possible just intervals (not from a mode or scale), as you use them in music. Dedicated page -> <a class="wiki_link" href="/FreeStyleJI">FreeStyleJI</a><br /> <br /> <!-- ws:start:WikiTextHeadingRule:8:<h2> --><h2 id="toc4"><a name="Just Intonation used-Constrained Just"></a><!-- ws:end:WikiTextHeadingRule:8 -->Constrained Just</h2> (In need of a better name maybe) Here are six ways that musicians and theorists have constrained the field of potential just ratios (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 <a class="wiki_link" href="/CombinationProductSet">products</a> 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 (<a class="wiki_link" href="/3and7JI">7</a>, 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 /> <!-- ws:start:WikiTextHeadingRule:10:<h1> --><h1 id="toc5"><a name="Just Intonation Propaganda"></a><!-- ws:end:WikiTextHeadingRule:10 -->Just Intonation Propaganda</h1> <br /> <em>Insert fair discussion of JI proselytizing and psychoacoustics psychobabble right here!</em><br /> <br /> <!-- ws:start:WikiTextHeadingRule:12:<h1> --><h1 id="toc6"><a name="Variations on 'Just'"></a><!-- ws:end:WikiTextHeadingRule:12 -->Variations on 'Just'</h1> <a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a> are just intonation systems of various <a class="wiki_link" href="/harmonic%20limits">harmonic limits</a> with certain commas tempered out<br /> <a class="wiki_link" href="/AdaptiveJI">Adaptive JI</a> schemes usually temper out these commas over time, resulting in<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:14:<h2> --><h2 id="toc7"><a name="Variations on 'Just'-Scalesmith's gallery of Just Intonation scales"></a><!-- ws:end:WikiTextHeadingRule:14 -->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 /> <a class="wiki_link" href="/Gallery%20of%20pentatonics">Gallery of pentatonics</a><br /> <a class="wiki_link" href="/FiniteSubsetJI">FiniteSubsetJI</a></body></html>