List of approaches to musical tuning

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<span style="background-color: #ffffff;">Below is a partial list of currently-established theories and approaches related to tuning.</span>
* [[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

Original HTML content:

<html><head><title>Approaches to Musical Tuning</title></head><body><span style="background-color: #ffffff;">Below is a partial list of currently-established theories and approaches related to tuning.</span><br />
<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><a class="wiki_link" href="/African">African</a></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><a class="wiki_link" href="/Indonesian">Indonesian</a> (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></body></html>
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