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List of approaches to musical tuning: 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:JlMoriart|JlMoriart]] and made on <tt>2014-07-02 13:41:59 UTC</tt>.<br>
: This revision was by author [[User:JlMoriart|JlMoriart]] and made on <tt>2014-07-07 02:31:34 UTC</tt>.<br>
: The original revision id was <tt>515447670</tt>.<br>
: The original revision id was <tt>515699632</tt>.<br>
: The revision comment was: <tt></tt><br>
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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">&lt;span style="background-color: #ffffff;"&gt;Below is a partial list of currently-established theories and approaches related to tuning.&lt;/span&gt;
<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">&lt;span style="background-color: #ffffff;"&gt;Below is a partial list of currently-established theories and approaches related to tuning.&lt;/span&gt;
* [[JustIntonation|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.
* [[JustIntonation|Just Intonation]]: The tuning of pitches so that their fundamental frequencies are related by ratios of whole numbers. An infinite world of numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.
* [[Equal Temperaments|Equal]] tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not
* [[xenharmonic/Equal Temperaments|Equal tuning]]: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals.
* In Western common practice music, the (somewhat forgotten) use of [[historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave
* [[Historical Temperaments]] The (somewhat forgotten) use of [[xenharmonic/Meantone|meantone tunings]] and [[well temperament|well temperaments]] in Western common practice music.
* Musical traditions of indigienous, ancient, and/or non-Western cultures
* Musical traditions of indigienous, ancient, and/or non-Western cultures
** [[Arabic, Turkish, Persian]]
** [[Arabic, Turkish, Persian]]
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<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Approaches to Musical Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="background-color: #ffffff;"&gt;Below is a partial list of currently-established theories and approaches related to tuning.&lt;/span&gt;&lt;br /&gt;
<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">&lt;html&gt;&lt;head&gt;&lt;title&gt;Approaches to Musical Tuning&lt;/title&gt;&lt;/head&gt;&lt;body&gt;&lt;span style="background-color: #ffffff;"&gt;Below is a partial list of currently-established theories and approaches related to tuning.&lt;/span&gt;&lt;br /&gt;
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/JustIntonation"&gt;Just Intonation&lt;/a&gt;: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Equal%20Temperaments"&gt;Equal&lt;/a&gt; tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not&lt;/li&gt;&lt;li&gt;In Western common practice music, the (somewhat forgotten) use of &lt;a class="wiki_link" href="/historical%20temperaments"&gt;historical temperaments&lt;/a&gt; (meantones, well temperaments) with 12 or more unequal notes per octave&lt;/li&gt;&lt;li&gt;Musical traditions of indigienous, ancient, and/or non-Western cultures&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic, Turkish, Persian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Indian"&gt;Indian&lt;/a&gt; (North, South)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/African"&gt;African&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Thai&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pre-Columbian%20South%20American%20Music"&gt;Pre-Columbian South American&lt;/a&gt; (e.g. Maya, Inca, Aztec..)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Indonesian"&gt;Indonesian&lt;/a&gt; (Java, Bali)&lt;/li&gt;&lt;li&gt;Ancient Greek, &lt;a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant#The_scale" rel="nofollow"&gt;Byzantine&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt; (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;Moment of Symmetry&lt;/a&gt;, a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;, a complexity measure which works well with MOS scales and rank two regular temperaments.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Empirical"&gt;Empirical&lt;/a&gt; This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/tetrachord"&gt;Tetrachordal Scales&lt;/a&gt;, which use divided fourths as building blocks for composition.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/isoharmonic%20chords"&gt;Isoharmonic chords/scales&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pretty%20Pictures"&gt;Pretty Pictures&lt;/a&gt; that represent scales in one way or another&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Notation"&gt;Notation&lt;/a&gt;(pretty pictures for a the purpose of writing music down)&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Nominal-Accidental%20Chains"&gt;Nominal-Accidental Chains&lt;/a&gt; A common approach to notation&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;the notion of a &lt;a class="wiki_link" href="/Scalesmith"&gt;Scalesmith&lt;/a&gt; who &lt;em&gt;builds&lt;/em&gt;scales, with various methods, perhaps for single occasions&lt;ul&gt;&lt;li&gt;Counter-intuitive, random, arbitrary scales&lt;/li&gt;&lt;li&gt;Numerology-based, computationally demanding scales&lt;/li&gt;&lt;li&gt;Scale stretching&lt;/li&gt;&lt;li&gt;Acoustically-based (resonant frequencies of performance space, for example)&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;(&lt;a class="wiki_link" href="/Corollaries"&gt;Corollaries&lt;/a&gt;, traces left by other reality tunnels, which by themselves are completely trivial and obvious)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Redundancy"&gt;Redundancy&lt;/a&gt; in a tuning system&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/JustIntonation"&gt;Just Intonation&lt;/a&gt;: The tuning of pitches so that their fundamental frequencies are related by ratios of whole numbers. An infinite world of numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Equal%20Temperaments"&gt;Equal tuning&lt;/a&gt;: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Historical%20Temperaments"&gt;Historical Temperaments&lt;/a&gt; The (somewhat forgotten) use of &lt;a class="wiki_link" href="http://xenharmonic.wikispaces.com/Meantone"&gt;meantone tunings&lt;/a&gt; and &lt;a class="wiki_link" href="/well%20temperament"&gt;well temperaments&lt;/a&gt; in Western common practice music.&lt;/li&gt;&lt;li&gt;Musical traditions of indigienous, ancient, and/or non-Western cultures&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian"&gt;Arabic, Turkish, Persian&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Indian"&gt;Indian&lt;/a&gt; (North, South)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/African"&gt;African&lt;/a&gt;&lt;/li&gt;&lt;li&gt;Thai&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pre-Columbian%20South%20American%20Music"&gt;Pre-Columbian South American&lt;/a&gt; (e.g. Maya, Inca, Aztec..)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Indonesian"&gt;Indonesian&lt;/a&gt; (Java, Bali)&lt;/li&gt;&lt;li&gt;Ancient Greek, &lt;a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant#The_scale" rel="nofollow"&gt;Byzantine&lt;/a&gt;&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Regular%20Temperaments"&gt;Regular Temperaments&lt;/a&gt; (including Linear Temperaments): a centuries-old practice that has recently undergone a mathematical facelift, in which Just Intonation is selectively and regularly detuned in various ways, to better meet a variety of compositional desires&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/MOSScales"&gt;Moment of Symmetry&lt;/a&gt;, a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Graham%20complexity"&gt;Graham complexity&lt;/a&gt;, a complexity measure which works well with MOS scales and rank two regular temperaments.&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Empirical"&gt;Empirical&lt;/a&gt; This is a form of hands-on, field research as opposed to a form of acoustical or scale engineering where tunings are specifically derived from listening and playing experiments carried out in the pitch continuum.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/tetrachord"&gt;Tetrachordal Scales&lt;/a&gt;, which use divided fourths as building blocks for composition.&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/isoharmonic%20chords"&gt;Isoharmonic chords/scales&lt;/a&gt;&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Pretty%20Pictures"&gt;Pretty Pictures&lt;/a&gt; that represent scales in one way or another&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Notation"&gt;Notation&lt;/a&gt;(pretty pictures for a the purpose of writing music down)&lt;ul&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Nominal-Accidental%20Chains"&gt;Nominal-Accidental Chains&lt;/a&gt; A common approach to notation&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;the notion of a &lt;a class="wiki_link" href="/Scalesmith"&gt;Scalesmith&lt;/a&gt; who &lt;em&gt;builds&lt;/em&gt;scales, with various methods, perhaps for single occasions&lt;ul&gt;&lt;li&gt;Counter-intuitive, random, arbitrary scales&lt;/li&gt;&lt;li&gt;Numerology-based, computationally demanding scales&lt;/li&gt;&lt;li&gt;Scale stretching&lt;/li&gt;&lt;li&gt;Acoustically-based (resonant frequencies of performance space, for example)&lt;/li&gt;&lt;/ul&gt;&lt;/li&gt;&lt;li&gt;(&lt;a class="wiki_link" href="/Corollaries"&gt;Corollaries&lt;/a&gt;, traces left by other reality tunnels, which by themselves are completely trivial and obvious)&lt;/li&gt;&lt;li&gt;&lt;a class="wiki_link" href="/Redundancy"&gt;Redundancy&lt;/a&gt; in a tuning system&lt;/li&gt;&lt;/ul&gt;&lt;/body&gt;&lt;/html&gt;</pre></div>
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