MicrotonalTheory

IMPORTED REVISION FROM WIKISPACES

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

This revision was by author Sarzadoce and made on 2011-08-19 21:09:44 UTC.

The original revision id was 247092965.

The revision comment was:

The revision contents are below, presented both in the original Wikispaces Wikitext format, and in HTML exactly as Wikispaces rendered it.

Original Wikitext content:

[[toc|flat]]
=Theory: Inventions that shape understanding= 

Theories are [[http://grace.evergreen.edu/%7Earunc/texts/cybernetics/heinz/disorder.pdf|not discoveries but inventions]] of humans, usually meant to formally describe regularities in experience, which often bring forth //new ways of experiencing//. (The music-making itself ('practice'), if at odds with existing theories, may provoke the creation of new theories; it is thus important to recognize that theory and practice mutually and reciprocally influence each other.)

There is a great deal of theory around the creation and/or discovering of tunings, scales, and temperaments, but whether it is useful to bother learning any of them is a matter of personal decision. (It is always possible to load up a random tuning on your retunable instrument of choice and explore it through music, without bothering to understand the theoretical considerations that led to the construction and/or discovery of said tuning.) Below you will find a partial list of currently-established theories related to alternative intonations.

=Reality tunnels into microtonality= 
* [[JustIntonation|Just Intonation]]: an infinite world of rational numbers and 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
* In Western common practice music, the (somewhat forgotten) use of [[historical temperaments]] (meantones, well temperaments) with 12 or more unequal notes per octave
* Musical traditions of indigienous, ancient, and/or non-Western cultures
** [[Arabic, Turkish, Persian]]
** [[Indian]] (North, South)
** African
** Thai
** [[Pre-Columbian South American Music|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)
** Indonesian (Java, Bali)
** Ancient Greek, [[http://orthodoxwiki.org/Byzantine_Chant#The_scale|Byzantine]]
* [[Regular Temperaments]] (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
* [[MOSScales|Moment of Symmetry]], 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
** [[Graham complexity]], a complexity measure which works well with MOS scales and rank two regular temperaments.
* [[Empirical]] 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.
* [[tetrachord|Tetrachordal Scales]], which use divided fourths as building blocks for composition.
* [[isoharmonic chords|Isoharmonic chords/scales]]
* [[Pretty Pictures]] that represent scales in one way or another
* [[Notation]](pretty pictures for a the purpose of writing music down)
** [[Nominal-Accidental Chains]] A common approach to notation
* the notion of a [[Scalesmith]] who //builds//scales, with various methods, perhaps for single occasions
** Counter-intuitive, random, arbitrary scales
** Numerology-based, computationally demanding scales
** Scale stretching
** Acoustically-based (resonant frequencies of performance space, for example)
* ([[Corollaries]], traces left by other reality tunnels, which by themselves are completely trivial and obvious)
* [[Redundancy]] in a tuning system

=External links= 
== == 
* Tonalsoft [[http://www.tonalsoft.com/enc/encyclopedia.aspx|Encyclopedia of microtonal music theory]] - a whole sea of information on the topic, covering both historical tuning theories and modern developments
* [[http://microtonalismo.com|Microtonalismo]] - Web microtonal
* [[http://www.bikexprt.com/music/tunebibl.htm|A bibliography on musical tunings and temperaments]], compiled by John S. Allen
* [[Huygens-Fokker]] Foundation's [[http://www.xs4all.nl/%7Ehuygensf/doc/bib.html|Tuning & temperament bibliography]], hyperlinked and updated by Manuel op de Coul
* The [[http://www.untwelve.org|UnTwelve]] website has some pages of theoretical interest, including a [[http://www.untwelve.org/what.html|fascinating article]] authored by Margo Schulter

Original HTML content:

<html><head><title>MicrotonalTheory</title></head><body><!-- ws:start:WikiTextTocRule:8:&lt;img id=&quot;wikitext@@toc@@flat&quot; class=&quot;WikiMedia WikiMediaTocFlat&quot; title=&quot;Table of Contents&quot; src=&quot;/site/embedthumbnail/toc/flat?w=100&amp;h=16&quot;/&gt; --><!-- ws:end:WikiTextTocRule:8 --><!-- ws:start:WikiTextTocRule:9: --><a href="#Theory: Inventions that shape understanding">Theory: Inventions that shape understanding</a><!-- ws:end:WikiTextTocRule:9 --><!-- ws:start:WikiTextTocRule:10: --> | <a href="#Reality tunnels into microtonality">Reality tunnels into microtonality</a><!-- ws:end:WikiTextTocRule:10 --><!-- ws:start:WikiTextTocRule:11: --> | <a href="#External links">External links</a><!-- ws:end:WikiTextTocRule:11 --><!-- ws:start:WikiTextTocRule:12: --><!-- ws:end:WikiTextTocRule:12 --><!-- ws:start:WikiTextTocRule:13: -->
<!-- ws:end:WikiTextTocRule:13 --><!-- ws:start:WikiTextHeadingRule:0:&lt;h1&gt; --><h1 id="toc0"><a name="Theory: Inventions that shape understanding"></a><!-- ws:end:WikiTextHeadingRule:0 -->Theory: Inventions that shape understanding</h1>
 <br />
Theories are <a class="wiki_link_ext" href="http://grace.evergreen.edu/%7Earunc/texts/cybernetics/heinz/disorder.pdf" rel="nofollow">not discoveries but inventions</a> of humans, usually meant to formally describe regularities in experience, which often bring forth <em>new ways of experiencing</em>. (The music-making itself ('practice'), if at odds with existing theories, may provoke the creation of new theories; it is thus important to recognize that theory and practice mutually and reciprocally influence each other.)<br />
<br />
There is a great deal of theory around the creation and/or discovering of tunings, scales, and temperaments, but whether it is useful to bother learning any of them is a matter of personal decision. (It is always possible to load up a random tuning on your retunable instrument of choice and explore it through music, without bothering to understand the theoretical considerations that led to the construction and/or discovery of said tuning.) Below you will find a partial list of currently-established theories related to alternative intonations.<br />
<br />
<!-- ws:start:WikiTextHeadingRule:2:&lt;h1&gt; --><h1 id="toc1"><a name="Reality tunnels into microtonality"></a><!-- ws:end:WikiTextHeadingRule:2 -->Reality tunnels into microtonality</h1>
 <ul><li><a class="wiki_link" href="/JustIntonation">Just Intonation</a>: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.</li><li><a class="wiki_link" href="/Equal%20Temperaments">Equal</a> tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not</li><li>In Western common practice music, the (somewhat forgotten) use of <a class="wiki_link" href="/historical%20temperaments">historical temperaments</a> (meantones, well temperaments) with 12 or more unequal notes per octave</li><li>Musical traditions of indigienous, ancient, and/or non-Western cultures<ul><li><a class="wiki_link" href="/Arabic%2C%20Turkish%2C%20Persian">Arabic, Turkish, Persian</a></li><li><a class="wiki_link" href="/Indian">Indian</a> (North, South)</li><li>African</li><li>Thai</li><li><a class="wiki_link" href="/Pre-Columbian%20South%20American%20Music">Pre-Columbian South American</a> (e.g. Maya, Inca, Aztec..)</li><li>Indonesian (Java, Bali)</li><li>Ancient Greek, <a class="wiki_link_ext" href="http://orthodoxwiki.org/Byzantine_Chant#The_scale" rel="nofollow">Byzantine</a></li></ul></li><li><a class="wiki_link" href="/Regular%20Temperaments">Regular Temperaments</a> (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</li><li><a class="wiki_link" href="/MOSScales">Moment of Symmetry</a>, 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<ul><li><a class="wiki_link" href="/Graham%20complexity">Graham complexity</a>, a complexity measure which works well with MOS scales and rank two regular temperaments.</li></ul></li><li><a class="wiki_link" href="/Empirical">Empirical</a> 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.</li><li><a class="wiki_link" href="/tetrachord">Tetrachordal Scales</a>, which use divided fourths as building blocks for composition.</li><li><a class="wiki_link" href="/isoharmonic%20chords">Isoharmonic chords/scales</a></li><li><a class="wiki_link" href="/Pretty%20Pictures">Pretty Pictures</a> that represent scales in one way or another</li><li><a class="wiki_link" href="/Notation">Notation</a>(pretty pictures for a the purpose of writing music down)<ul><li><a class="wiki_link" href="/Nominal-Accidental%20Chains">Nominal-Accidental Chains</a> A common approach to notation</li></ul></li><li>the notion of a <a class="wiki_link" href="/Scalesmith">Scalesmith</a> who <em>builds</em>scales, with various methods, perhaps for single occasions<ul><li>Counter-intuitive, random, arbitrary scales</li><li>Numerology-based, computationally demanding scales</li><li>Scale stretching</li><li>Acoustically-based (resonant frequencies of performance space, for example)</li></ul></li><li>(<a class="wiki_link" href="/Corollaries">Corollaries</a>, traces left by other reality tunnels, which by themselves are completely trivial and obvious)</li><li><a class="wiki_link" href="/Redundancy">Redundancy</a> in a tuning system</li></ul><br />
<!-- ws:start:WikiTextHeadingRule:4:&lt;h1&gt; --><h1 id="toc2"><a name="External links"></a><!-- ws:end:WikiTextHeadingRule:4 -->External links</h1>
 <!-- ws:start:WikiTextHeadingRule:6:&lt;h2&gt; --><h2 id="toc3"><!-- ws:end:WikiTextHeadingRule:6 --> </h2>
 <ul><li>Tonalsoft <a class="wiki_link_ext" href="http://www.tonalsoft.com/enc/encyclopedia.aspx" rel="nofollow">Encyclopedia of microtonal music theory</a> - a whole sea of information on the topic, covering both historical tuning theories and modern developments</li><li><a class="wiki_link_ext" href="http://microtonalismo.com" rel="nofollow">Microtonalismo</a> - Web microtonal</li><li><a class="wiki_link_ext" href="http://www.bikexprt.com/music/tunebibl.htm" rel="nofollow">A bibliography on musical tunings and temperaments</a>, compiled by John S. Allen</li><li><a class="wiki_link" href="/Huygens-Fokker">Huygens-Fokker</a> Foundation's <a class="wiki_link_ext" href="http://www.xs4all.nl/%7Ehuygensf/doc/bib.html" rel="nofollow">Tuning &amp; temperament bibliography</a>, hyperlinked and updated by Manuel op de Coul</li><li>The <a class="wiki_link_ext" href="http://www.untwelve.org" rel="nofollow">UnTwelve</a> website has some pages of theoretical interest, including a <a class="wiki_link_ext" href="http://www.untwelve.org/what.html" rel="nofollow">fascinating article</a> authored by Margo Schulter</li></ul></body></html>