Just intonation: Difference between revisions
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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:xenjacob|xenjacob]] and made on <tt>2007-10-10 06:23:38 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>9237531</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">=Just Intonation | <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">=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. | 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). | //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). | ||
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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. | 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. | 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 (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. | 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]]). | 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]]).// | 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: | **Broken** links to JI theory pages on [[http://moinmoin.riters.com/microtonal|another microtonal wiki]], which await transfer to this wiki: | ||
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[[boogiewoogiescale|Boogie woogie scale]] | [[boogiewoogiescale|Boogie woogie scale]] | ||
[[Arnold Dreyblatt]] | [[Arnold Dreyblatt]] | ||
Gallery of pentatonics | [[Gallery of pentatonics]] | ||
[[FiniteSubsetJI]]</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>Just intonation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Just Intonation | <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>Just intonation</title></head><body><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><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 /> | 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 /> | <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 /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><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 /> | |||
<!-- ws:start:WikiTextHeadingRule: | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:4:&lt;h2&gt; --><h2 id="toc2"><a name="Just Intonation used-Free Style Just"></a><!-- ws:end:WikiTextHeadingRule:4 -->Free Style Just</h2> | ||
<!-- ws:start:WikiTextHeadingRule:6:&lt;h1&gt; --><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 -&gt; <a class="wiki_link" href="/FreeStyleJI">FreeStyleJI</a><br /> | |||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:8:&lt;h2&gt; --><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, &quot;Differential Coherence&quot;, <em>1/1</em> vol. 11, no. 2: p.1):<br /> | |||
<br /> | <br /> | ||
<em>1. The principle of &quot;<a class="wiki_link" href="/harmonic%20limits">harmonic limits</a>,&quot; which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's &quot;psycharithmes&quot; and his ordering by complexity; Gioseffe Zarlino's five-limit &quot;senario,&quot; and the like; Helmholtz's theory of consonance with its &quot;blending of partials,&quot; which, like the others, results in giving priority to the lowest prime numbers).<br /> | <em>1. The principle of &quot;<a class="wiki_link" href="/harmonic%20limits">harmonic limits</a>,&quot; which sets a threshold in order to place a limit on the largest prime number in any ratio (cf: Tanner's &quot;psycharithmes&quot; and his ordering by complexity; Gioseffe Zarlino's five-limit &quot;senario,&quot; and the like; Helmholtz's theory of consonance with its &quot;blending of partials,&quot; which, like the others, results in giving priority to the lowest prime numbers).<br /> | ||
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2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the &quot;monophonic&quot; 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 /> | 2. Restrictions on the combinations of numbers that make up the numerator and denominator of the ratios under consideration, such as the &quot;monophonic&quot; 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 /> | <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 /> | 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 /> | <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 /> | 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 /> | <br /> | ||
5. Restricting the denominator to one or very few values (the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>).<br /> | 5. Restricting the denominator to one or very few values (the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>).<br /> | ||
<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 /> | 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:&lt;h1&gt; --><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:&lt;h1&gt; --><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 /> | <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 /> | <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 /> | ||
| Line 93: | Line 94: | ||
<a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance" rel="nofollow">Hahn distance</a><br /> | <a class="wiki_link_ext" href="http://moinmoin.riters.com/microtonal/index.cgi/Hahn_20distance" rel="nofollow">Hahn distance</a><br /> | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule: | <!-- ws:start:WikiTextHeadingRule:14:&lt;h2&gt; --><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="/boogiewoogiescale">Boogie woogie scale</a><br /> | ||
<a class="wiki_link" href="/Arnold%20Dreyblatt">Arnold Dreyblatt</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></pre></div> | |||
</body></html></pre></div> | |||