MicrotonalTheory: Difference between revisions
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=Theory: Inventions that shape understanding= | =Theory: Inventions that shape understanding= | ||
Theories are [[http://grace.evergreen.edu/%7Earunc/texts/cybernetics/heinz/disorder.pdf|not discoveries but inventions]] of humans, 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.) | 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= | =Reality tunnels into microtonality= | ||
* [[JustIntonation|Just Intonation]]: an infinite world of rational numbers and numerous models: the harmonic series, tonality diamonds, eikosany, etc. | * [[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 | * [[Equal Temperaments|Equal]] tunings: each one 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 | * 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]] | ** [[Arabic, Turkish, Persian]] | ||
** [[Indian]] (North, South) | ** [[Indian]] (North, South) | ||
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** Indonesian (Java, Bali) | ** Indonesian (Java, Bali) | ||
** Ancient Greek, [[http://orthodoxwiki.org/Byzantine_Chant#The_scale|Byzantine]] | ** Ancient Greek, [[http://orthodoxwiki.org/Byzantine_Chant#The_scale|Byzantine]] | ||
* [[Regular Temperaments]] (including Linear Temperaments): a | * [[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]], | * [[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 | ||
* [[Empirical]] | * [[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. | * [[tetrachord|Tetrachordal Scales]], which use divided fourths as building blocks for composition. | ||
* [[isoharmonic chords|Isoharmonic chords/scales]] | * [[isoharmonic chords|Isoharmonic chords/scales]] | ||
* [[Pretty Pictures]] that represent scales in one way or another | * [[Pretty Pictures]] that represent scales in one way or another | ||
* [[Notation]] (pretty pictures for a the purpose of writing music down) | * [[Notation]] (pretty pictures for a the purpose of writing music down) | ||
* the notion of a [[Scalesmith]] who //builds// scales, with various methods, perhaps for single occasions | * the notion of a [[Scalesmith]] who //builds//scales, with various methods, perhaps for single occasions | ||
** Counter-intuitive, random, arbitrary scales | ** Counter-intuitive, random, arbitrary scales | ||
** Numerology-based, computationally demanding scales | ** Numerology-based, computationally demanding scales | ||
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<br /> | <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, 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.)<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 /> | <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> | <!-- 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, tonality diamonds, eikosany, etc.</li><li><a class="wiki_link" href="/Equal%20Temperaments">Equal</a> tunings: each one a subtle monoculture of intervals</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> | <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</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>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</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)</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: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> | <!-- 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></pre></div> | <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></pre></div> | ||