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List of approaches to musical tuning: Difference between revisions

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=== Shape-based ===
=== Shape-based ===
* '''[[Equal-step tuning]]s''': Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals. These include [[edo]]s (equal divisions of the octave), but also [[edonoi]] (equal divisions of [[nonoctave]] intervals).
* [[Equal-step tuning]]s: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals. These include [[edo]]s (equal divisions of the octave), but also [[edonoi]] (equal divisions of [[nonoctave]] intervals).
* '''[[MOS scale|Moment of symmetry (MOS)]]''': Tunings (or better, scales) that use iterations of a generating interval, modulo a period interval, to produce scales of two step-sizes.
* [[MOS scale|Moment of symmetry (MOS)]]: Tunings (or better, scales) that use iterations of a generating interval, modulo a period interval, to produce scales of two step-sizes.
* '''[[Tetrachord|Tetrachordal scales]]''': the use of divided fourths as building blocks for composition.
* [[Tetrachord|Tetrachordal scales]]: the use of divided fourths as building blocks for composition.


=== Ratio-based ===
=== Ratio-based ===
* '''[[Just intonation]]''': The tuning of pitches so that their fundamental frequencies are related by ratios of whole numbers. An infinite world of numerous models:
* [[Just intonation]]: The tuning of pitches so that their fundamental frequencies are related by ratios of whole numbers. An infinite world of numerous models:
** [[Combination product sets]]
** [[Combination product sets]]
** [[Detempering]] (including [[ringer scale]]s)
** [[Detempering]] (including [[ringer scale]]s)
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** Undertone scales/[[IFDO]]s
** Undertone scales/[[IFDO]]s
** etc.
** etc.
* '''[[Timbral tuning]]''': An approach similar to just intonation, but using an instrument's actual, non-harmonic overtone spectrum (e.g. the partials of a metal bar, drum head, or synthesized timbre) to relate frequencies instead of the harmonic series.
* [[Timbral tuning]]: An approach similar to just intonation, but using an instrument's actual, non-harmonic overtone spectrum (e.g. the partials of a metal bar, drum head, or synthesized timbre) to relate frequencies instead of the harmonic series.
* '''[[Regular temperament]]s''' (including [[linear temperament]]s): 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
* [[Regular temperament]]s (including [[linear temperament]]s): 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
* '''[[Historical temperaments]]''': The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and [[well temperament]]s in Western common practice music.
* [[Historical temperaments]]: The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and [[well temperament]]s in Western common practice music.
* '''[[Homothetic just intonation]]''': Just intonation with extra tones added in between according to a specific method.
* [[Homothetic just intonation]]: Just intonation with extra tones added in between according to a specific method.
* '''[[Xenharmonic series]]''': Just intonation but the entire matrix of just intervals is stretched, squished or otherwise warped or manipulated for interesting effect.
* [[Xenharmonic series]]: Just intonation but the entire matrix of just intervals is stretched, squished or otherwise warped or manipulated for interesting effect.


=== Musical traditions of indigenous, ancient, and/or non-Western cultures ===
=== Musical traditions of indigenous, ancient, and/or non-Western cultures ===
* '''[[African]]''' (dozens of distinct traditions)
* [[African]] (dozens of distinct traditions)
* '''[[Ancient Greek]]'''
* [[Ancient Greek]]
* '''[[Arabic, Turkish, Persian|Arabic]]'''
* [[Arabic, Turkish, Persian|Arabic]]
* '''[http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]'''
* [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]
* '''[[Georgian]]'''
* [[Georgian]]
* '''[[Indian]] (e.g. North, South)'''
* [[Indian]] (e.g. North, South)
* '''[[Indonesian]] (e.g. Java, Bali)'''
* [[Indonesian]] (e.g. Java, Bali)
* '''[[Arabic, Turkish, Persian|Iranian (Persian)]]'''
* [[Arabic, Turkish, Persian|Iranian (Persian)]]
* '''[[Pre-Columbian South American Music|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec)'''
* [[Pre-Columbian South American Music|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec)
* '''[[Wikipedia:Music of Thailand|Thai]]'''
* [[Wikipedia:Music of Thailand|Thai]]
* '''[[Arabic, Turkish, Persian|Turkish]]'''
* [[Arabic, Turkish, Persian|Turkish]]
* Many that use an [[equipentatonic]] or [[equiheptatonic]] scale
* Many that use an [[equipentatonic]] or [[equiheptatonic]] scale


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The following approaches describe the subjective exploration process or its representations rather than its objective, audible result:
The following approaches describe the subjective exploration process or its representations rather than its objective, audible result:


* '''[[Contextual Xenharmonics]]''': The exploration of why things sound the way they do to some and not others.
* [[Contextual Xenharmonics]]: The exploration of why things sound the way they do to some and not others.
* '''[[Empirical]]''': 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.
* [[Empirical]]: 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.
* '''[[Pretty Pictures]]''' that represent scales in one way or another.
* [[Pretty Pictures]] that represent scales in one way or another.
* '''[[Musical notation]]''': Pretty pictures for the purpose of writing music down.
* [[Musical notation]]: Pretty pictures for the purpose of writing music down.
** [[Nominal-Accidental Chains]]: The most common approach to notation
** [[Nominal-Accidental Chains]]: The most common approach to notation
* 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.
** Mathematically based scales
** Mathematically based scales
** Acoustically-based scales (resonant frequencies of performance space, for example)
** Acoustically-based scales (resonant frequencies of performance space, for example)
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