Just intonation: Difference between revisions
Wikispaces>Sarzadoce **Imported revision 296269396 - Original comment: ** |
Wikispaces>xenwolf **Imported revision 510001036 - Original comment: merged contents from the JI fork** |
||
| Line 1: | Line 1: | ||
<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:xenwolf|xenwolf]] and made on <tt>2014-05-20 02:41:15 UTC</tt>.<br> | ||
: The original revision id was <tt> | : The original revision id was <tt>510001036</tt>.<br> | ||
: The revision comment was: <tt></tt><br> | : The revision comment was: <tt>merged contents from the JI fork</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> | ||
| Line 9: | Line 9: | ||
---- | ---- | ||
=Just Intonation explained= | =Just Intonation explained= | ||
JI, or [[Just Intonation]] describes [[Gallery of Just Intervals|intervals]] between pitches by specifying ratios (of [[http://en.wikipedia.org/wiki/Rational_number|rational numbers]]) between the frequencies of pitches. This is sometimes distinguished from //rational intonation// by requiring that the ratios be ones of low complexity (as for example measured by [[Benedetti height]]) but there is no clear dividing line. The matter is partially a question of intent. The rank two tuning system in which all intervals are given as combinations of the just perfect fourth, 4/3, and the just minor third, 6/5, would seem to be a nonoctave 5-limit just intonation system by definition. In practice, it can hardly be used except as a rank two 7-limit [[Microtempering|microtempering]] system because of certain very accurate approximations to the octave and to seven limit intervals: (6/5)^2/(4/3) = 27/25, the semitone maximus or just minor second; and (27/25)^9 is less than a cent short of an octave, while (27/25)^2 is almost precisely 7/6, the [[http://en.wikipedia.org/wiki/Septimal_minor_third|septimal minor third]]. | |||
If you are used to speaking only in note names, you may need to study the relation between frequency and [[http://en.wikipedia.org/wiki/Pitch_%28music%29|pitch]]. Kyle Gann's //[[http://www.kylegann.com/tuning.html|Just Intonation Explained]]// is one good reference. A transparent illustration and one of just intonation's acoustic bases is the [[OverToneSeries|harmonic series]]. | |||
"Just Intonation", as we find it commonly used today, describes [[Gallery of Just Intervals|intervals]] between pitches by specifying ratios ([[http://en.wikipedia.org/wiki/Rational_number|rational numbers]]) of pitch frequencies. | "Just Intonation", as we find it commonly used today, describes [[Gallery of Just Intervals|intervals]] between pitches by specifying ratios ([[http://en.wikipedia.org/wiki/Rational_number|rational numbers]]) of pitch frequencies. | ||
In languages other than English, the original conceptions of "Just Intonation" are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, | In languages other than English, the original conceptions of "Just Intonation" are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, ??????????? ????? in Ukrainian and Gamme naturelle in French, (both referring to the "natural scale", that is, intervals derived from the harmonic series), Intonazione naturale (natural intonation, once again intervals derived from harmonic series) in Italian, and so on. | ||
In the English language, the term "just" referred to "true, correct", and is still used today in this sense, in the crafts. In printing, to "justify" a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as "natural". | In the English language, the term "just" referred to "true, correct", and is still used today in this sense, in the crafts. In printing, to "justify" a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as "natural". | ||
| Line 104: | Line 108: | ||
* [[http://www.kylegann.com/Octave.html|Anatomy of an Octave]] by Kyle Gann [[http://www.webcitation.org/5xe30LCev|Permalink]] | * [[http://www.kylegann.com/Octave.html|Anatomy of an Octave]] by Kyle Gann [[http://www.webcitation.org/5xe30LCev|Permalink]] | ||
* [[http://www.dbdoty.com/Words/What-is-Just-Intonation.html|What is Just Intonation?]] by David B. Doty [[http://www.webcitation.org/5xe3MeWVq|Permalink]] | * [[http://www.dbdoty.com/Words/What-is-Just-Intonation.html|What is Just Intonation?]] by David B. Doty [[http://www.webcitation.org/5xe3MeWVq|Permalink]] | ||
* [[http://lumma.org/tuning/faq/#whatisJI|What is "just intonation"?]] by Carl Lumma [[http://www.webcitation.org/65NwFAKLh|Permalink]] | |||
* [[http://www.dbdoty.com/Words/werntz.html|A Response to Julia Werntz]] by David B. Doty [[http://www.webcitation.org/5xe38KWx4|Permalink]] | * [[http://www.dbdoty.com/Words/werntz.html|A Response to Julia Werntz]] by David B. Doty [[http://www.webcitation.org/5xe38KWx4|Permalink]] | ||
* [[http://lumma.org/tuning/gws/commaseq.htm|Comma Sequences]] by Gene Ward Smith [[http://www.webcitation.org/5xe4rPLZ0|Permalink]]</pre></div> | * [[http://lumma.org/tuning/gws/commaseq.htm|Comma Sequences]] by Gene Ward Smith [[http://www.webcitation.org/5xe4rPLZ0|Permalink]]</pre></div> | ||
| Line 110: | Line 115: | ||
<!-- ws:end:WikiTextTocRule:25 --><hr /> | <!-- ws:end:WikiTextTocRule:25 --><hr /> | ||
<!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Just Intonation explained"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just Intonation explained</h1> | <!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Just Intonation explained"></a><!-- ws:end:WikiTextHeadingRule:0 -->Just Intonation explained</h1> | ||
&quot;Just Intonation&quot;, as we find it commonly used today, describes <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">intervals</a> between pitches by specifying ratios (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rational_number" rel="nofollow">rational numbers</a>) of pitch frequencies.<br /> | JI, or <a class="wiki_link" href="/Just%20Intonation">Just Intonation</a> describes <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">intervals</a> 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. This is sometimes distinguished from <em>rational intonation</em> by requiring that the ratios be ones of low complexity (as for example measured by <a class="wiki_link" href="/Benedetti%20height">Benedetti height</a>) but there is no clear dividing line. The matter is partially a question of intent. The rank two tuning system in which all intervals are given as combinations of the just perfect fourth, 4/3, and the just minor third, 6/5, would seem to be a nonoctave 5-limit just intonation system by definition. In practice, it can hardly be used except as a rank two 7-limit <a class="wiki_link" href="/Microtempering">microtempering</a> system because of certain very accurate approximations to the octave and to seven limit intervals: (6/5)^2/(4/3) = 27/25, the semitone maximus or just minor second; and (27/25)^9 is less than a cent short of an octave, while (27/25)^2 is almost precisely 7/6, the <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Septimal_minor_third" rel="nofollow">septimal minor third</a>.<br /> | ||
<br /> | |||
If you are used to speaking only in note names, you may need to study the relation between frequency and <a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Pitch_%28music%29" rel="nofollow">pitch</a>. Kyle Gann's <em><a class="wiki_link_ext" href="http://www.kylegann.com/tuning.html" rel="nofollow">Just Intonation Explained</a></em> is one good reference. A transparent illustration and one of just intonation's acoustic bases is the <a class="wiki_link" href="/OverToneSeries">harmonic series</a>.<br /> | |||
<br /> | |||
&quot;Just Intonation&quot;, as we find it commonly used today, describes <a class="wiki_link" href="/Gallery%20of%20Just%20Intervals">intervals</a> between pitches by specifying ratios (<a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Rational_number" rel="nofollow">rational numbers</a>) of pitch frequencies.<br /> | |||
<br /> | <br /> | ||
In languages other than English, the original conceptions of &quot;Just Intonation&quot; are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, | In languages other than English, the original conceptions of &quot;Just Intonation&quot; are more obviously retained in the terms used in those languages: Reine Stimmung (pure, that is, beatless, tuning) in German, ??????????? ????? in Ukrainian and Gamme naturelle in French, (both referring to the &quot;natural scale&quot;, that is, intervals derived from the harmonic series), Intonazione naturale (natural intonation, once again intervals derived from harmonic series) in Italian, and so on.<br /> | ||
<br /> | <br /> | ||
In the English language, the term &quot;just&quot; referred to &quot;true, correct&quot;, and is still used today in this sense, in the crafts. In printing, to &quot;justify&quot; a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as &quot;natural&quot;.<br /> | In the English language, the term &quot;just&quot; referred to &quot;true, correct&quot;, and is still used today in this sense, in the crafts. In printing, to &quot;justify&quot; a line of type is to fit it precisely to a certain measure, for example. The original sense, then, was similar to that sense which is clearly retained in other languages as &quot;natural&quot;.<br /> | ||
| Line 200: | Line 209: | ||
<br /> | <br /> | ||
<!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Articles"></a><!-- ws:end:WikiTextHeadingRule:14 -->Articles</h1> | <!-- ws:start:WikiTextHeadingRule:14:&lt;h1&gt; --><h1 id="toc7"><a name="Articles"></a><!-- ws:end:WikiTextHeadingRule:14 -->Articles</h1> | ||
<ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Just_intonation" rel="nofollow">Wikipedia article on just intonation</a></li><li><a class="wiki_link_ext" href="http://nowitzky.hostwebs.com/justint/" rel="nofollow">Just Intonation</a> by Mark Nowitzky <a class="wiki_link_ext" href="http://www.webcitation.org/5xeAm2lPL" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/tuning.html" rel="nofollow">Just Intonation Explained</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe2iC7Nq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow">Anatomy of an Octave</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe30LCev" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/What-is-Just-Intonation.html" rel="nofollow">What is Just Intonation?</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe3MeWVq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/werntz.html" rel="nofollow">A Response to Julia Werntz</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe38KWx4" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/gws/commaseq.htm" rel="nofollow">Comma Sequences</a> by Gene Ward Smith <a class="wiki_link_ext" href="http://www.webcitation.org/5xe4rPLZ0" rel="nofollow">Permalink</a></li></ul></body></html></pre></div> | <ul><li><a class="wiki_link_ext" href="http://en.wikipedia.org/wiki/Just_intonation" rel="nofollow">Wikipedia article on just intonation</a></li><li><a class="wiki_link_ext" href="http://nowitzky.hostwebs.com/justint/" rel="nofollow">Just Intonation</a> by Mark Nowitzky <a class="wiki_link_ext" href="http://www.webcitation.org/5xeAm2lPL" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/tuning.html" rel="nofollow">Just Intonation Explained</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe2iC7Nq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.kylegann.com/Octave.html" rel="nofollow">Anatomy of an Octave</a> by Kyle Gann <a class="wiki_link_ext" href="http://www.webcitation.org/5xe30LCev" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/What-is-Just-Intonation.html" rel="nofollow">What is Just Intonation?</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe3MeWVq" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/faq/#whatisJI" rel="nofollow">What is &quot;just intonation&quot;?</a> by Carl Lumma <a class="wiki_link_ext" href="http://www.webcitation.org/65NwFAKLh" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://www.dbdoty.com/Words/werntz.html" rel="nofollow">A Response to Julia Werntz</a> by David B. Doty <a class="wiki_link_ext" href="http://www.webcitation.org/5xe38KWx4" rel="nofollow">Permalink</a></li><li><a class="wiki_link_ext" href="http://lumma.org/tuning/gws/commaseq.htm" rel="nofollow">Comma Sequences</a> by Gene Ward Smith <a class="wiki_link_ext" href="http://www.webcitation.org/5xe4rPLZ0" rel="nofollow">Permalink</a></li></ul></body></html></pre></div> | ||