Just intonation: Difference between revisions

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<h2>IMPORTED REVISION FROM WIKISPACES</h2>

This is an imported revision from Wikispaces. The revision metadata is included below for reference:

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-21 11:11:04 UTC</tt>.

: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-21 13:04:41 UTC</tt>.

: The original revision id was <tt>~~602713864~~</tt>.

: The original revision id was <tt>602719196</tt>.

: The revision comment was: <tt></tt>

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One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this.

There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals ~~were~~ the concern, understanding and defining "Just" was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...

There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals was the concern, understanding and defining "Just" was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...

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//1. The principle of "[[Harmonic Limit|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). See [[3-limit]], [[5-limit]], [[7-limit]], [[11-limit]], [[13-limit]].//

//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 [[http://en.wikipedia.org/wiki/Harry_Partch|Harry Partch]]'s [[http://en.wikipedia.org/wiki/Pitch_%28music%29|tonality diamond]]. This, incidentally, 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 [[http://en.wikipedia.org/wiki/Harry_Partch|Harry Partch]]'s [[http://en.wikipedia.org/wiki/Pitch_%28music%29|tonality diamond]]. This, incidentally, 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 [[http://en.wikipedia.org/wiki/Hexany|products sets]] of given arrays of prime numbers, such as [[http://en.wikipedia.org/wiki/Erv_Wilson|Ervin Wilson]], Robert Dussaut, and others.//

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One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this.

There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals ~~were~~ the concern, understanding and defining &quot;Just&quot; was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...

There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals was the concern, understanding and defining &quot;Just&quot; was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...

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1. The principle of &quot;<a class="wiki_link" href="/Harmonic%20Limit">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). See <a class="wiki_link" href="/3-limit">3-limit</a>, <a class="wiki_link" href="/5-limit">5-limit</a>, <a class="wiki_link" href="/7-limit">7-limit</a>, <a class="wiki_link" href="/11-limit">11-limit</a>, <a class="wiki_link" href="/13-limit">13-limit</a>.

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 <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch" rel="nofollow">Harry Partch</a>'s <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pitch_%28music%29" rel="nofollow">tonality diamond</a>. This, incidentally, 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 &quot;monophonic&quot; system of <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch" rel="nofollow">Harry Partch</a>'s <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pitch_%28music%29" rel="nofollow">tonality diamond</a>. This, incidentally, 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 <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexany" rel="nofollow">products sets</a> of given arrays of prime numbers, such as <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Erv_Wilson" rel="nofollow">Ervin Wilson</a>, Robert Dussaut, and others.

@@ Line 1: / Line 1: @@
 <h2>IMPORTED REVISION FROM WIKISPACES</h2>
 This is an imported revision from Wikispaces. The revision metadata is included below for reference:<br>
-: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-21 11:11:04 UTC</tt>.<br>
+: This revision was by author [[User:JosephRuhf|JosephRuhf]] and made on <tt>2016-12-21 13:04:41 UTC</tt>.<br>
-: The original revision id was <tt>602713864</tt>.<br>
+: The original revision id was <tt>602719196</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>
@@ Line 46: / Line 46: @@
 One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this.
-There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals were the concern, understanding and defining "Just" was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...
+There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals was the concern, understanding and defining "Just" was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...
@@ Line 64: / Line 64: @@
 //1. The principle of "[[Harmonic Limit|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). See [[3-limit]], [[5-limit]], [[7-limit]], [[11-limit]], [[13-limit]].//
-//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 [[http://en.wikipedia.org/wiki/Harry_Partch|Harry Partch]]'s [[http://en.wikipedia.org/wiki/Pitch_%28music%29|tonality diamond]]. This, incidentally, 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 [[http://en.wikipedia.org/wiki/Harry_Partch|Harry Partch]]'s [[http://en.wikipedia.org/wiki/Pitch_%28music%29|tonality diamond]]. This, incidentally, 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 [[http://en.wikipedia.org/wiki/Hexany|products sets]] of given arrays of prime numbers, such as [[http://en.wikipedia.org/wiki/Erv_Wilson|Ervin Wilson]], Robert Dussaut, and others.//
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 One does not need to know of the harmonic series, nor even know how to read, or even count, to sing this.&lt;br /&gt;
 &lt;br /&gt;
-There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals were the concern, understanding and defining &amp;quot;Just&amp;quot; was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...&lt;br /&gt;
+There is more to it than this, of course, but the basic principles of Just Intonation are very simple. Hundreds of years ago, when the intonation of a few well-known intervals was the concern, understanding and defining &amp;quot;Just&amp;quot; was not difficult. These days, though, and going on from these basics, it can get a bit more complicated...&lt;br /&gt;
 &lt;br /&gt;
 &lt;br /&gt;
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 &lt;em&gt;1. The principle of &amp;quot;&lt;a class="wiki_link" href="/Harmonic%20Limit"&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). See &lt;a class="wiki_link" href="/3-limit"&gt;3-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/5-limit"&gt;5-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/7-limit"&gt;7-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/11-limit"&gt;11-limit&lt;/a&gt;, &lt;a class="wiki_link" href="/13-limit"&gt;13-limit&lt;/a&gt;.&lt;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
-&lt;em&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 &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch" rel="nofollow"&gt;Harry Partch&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pitch_%28music%29" rel="nofollow"&gt;tonality diamond&lt;/a&gt;. This, incidentally, 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;/em&gt;&lt;br /&gt;
+&lt;em&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 &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Harry_Partch" rel="nofollow"&gt;Harry Partch&lt;/a&gt;'s &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pitch_%28music%29" rel="nofollow"&gt;tonality diamond&lt;/a&gt;. This, incidentally, 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;/em&gt;&lt;br /&gt;
 &lt;br /&gt;
 &lt;em&gt;3. Other theorists who, in contrast to the above, advocate the use of &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Hexany" rel="nofollow"&gt;products sets&lt;/a&gt; of given arrays of prime numbers, such as &lt;a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Erv_Wilson" rel="nofollow"&gt;Ervin Wilson&lt;/a&gt;, Robert Dussaut, and others.&lt;/em&gt;&lt;br /&gt;