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List of approaches to musical tuning: Difference between revisions

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m Moved just intonation higher on the list again. Removed "frequency integer ratios" from the list of just intonation examples because isn't that what all just intonation is by definition anyway?
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{{interwiki
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| en = List of approaches to musical tuning
| de =  
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| en = Approaches to Musical Tuning
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| ja = 調律方法
| ja = 調律方法
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Musical [[tuning]] can be approached in many different ways. Here are some of the currently-established theories and approaches:
Musical [[tuning]] can be approached in many different ways. Here are some of the currently-established theories and approaches.


* [[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 many [[nonoctave]] tunings (sometimes called [[edonoi]]).
[[Xen concepts for beginners]] provides a solid foundation to start from in exploring this assortment of tunings.
* [[Regular temperament]]s (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
 
*[[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.
== Defined approaches ==
*[[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]]
=== Shape-based ===
** The [[harmonic series]]
* [[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).
**[[Fokker blocks]]
* [[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.
**[[Overtone scale]]s & [[primodality]]
* [[Tetrachord|Tetrachordal scales]]: the use of divided fourths as building blocks for composition.
**[[Tonality diamond]]s
 
=== 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:
** [[Adaptive just intonation]]
** [[Combination product sets]]
** [[Detempering]] (including [[ringer scale]]s)
** [[Fokker blocks]]
** The [[harmonic series]] and [[subharmonic series]]
** [[Harmonic limits]]
** [[Isoharmonic chord]]s
** [[Just intonation subgroup]]s
** [[NEJI]] scales (near-equal just intonation)
** [[Overtone scale]]s/[[AFDO]]s
** [[Primodality]]
** [[Tonality diamond]]s
** [[Tritriadic scale]]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.
* Musical traditions of indigenous, ancient, and/or non-Western cultures:
* [[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
**[[African]]
* [[Historical temperaments]]: The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and [[well temperament]]s in Western common practice music.
**[[Wikipedia:Musical_system_of_ancient_Greece|Ancient Greek]]
* [[Xenharmonic series]]: Just intonation but the entire matrix of just intervals is stretched, squished or otherwise warped or manipulated for interesting effect.
**[[Arabic, Turkish, Persian]]
 
** [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]
=== Musical traditions of indigenous, ancient, and/or non-Western cultures ===
**[[Music of Georgia|Georgian]]
* [[African]] (dozens of distinct traditions)
**[[Indian]] (North, South)
* [[Ancient Greek]]
**[[Indonesian]] (Java, Bali)
* [[Arabic, Turkish, Persian|Arabic]]
**[[Pre-Columbian South American Music|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)
* [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]
**[[Wikipedia:Music of Thailand|Thai]]
* [[Wikipedia:Music of Croatia|Croatian]] (including the [[Istrian]] scale)
*[[Historical temperaments|Historical western temperaments]]: The (somewhat forgotten) use of [[Pythagorean]] and [[meantone]] tunings and [[well temperament]]s in Western common practice music.
* [[Music of Georgia|Georgian]]
*[[Tetrachord|Tetrachordal scales]]: the use of divided fourths as building blocks for composition.
* [[Indian]] (e.g. North, South)
*[[Isoharmonic chords]]: the use of chords with an equal harmonic difference between the pitches as building blocks for scales.
* [[Indonesian]] (most famously [[gamelan]])
* [[Arabic, Turkish, Persian|Iranian (Persian)]]
* [[Pre-Columbian South American Music|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec)
* [[Wikipedia:Music of Thailand|Thai]]
* [[Arabic, Turkish, Persian|Turkish]]
* Many that use an [[equipentatonic]] or [[equiheptatonic]] scale


== Subjective processes ==
== Subjective processes ==
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:


* [[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.
* [[Contextual Xenharmonics]]: The exploration of why things sound the way they do to some and not others.
* [[Pretty Pictures]] that represent scales in one way or another
* [[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.
* [[Notation]] (pretty pictures for the purpose of writing music down)
* [[Pretty Pictures]] that represent scales in one way or another.
* [[Nominal-Accidental Chains]] A common approach to notation
* [[Musical notation]]: Pretty pictures for the purpose of writing music down.
* The notion of a [[Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions
** [[Nominal-Accidental Chains]]: The most common approach to notation
* 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)
** Scale transformation and stretching
** Scale transformation and stretching
** Counter-intuitive, random, arbitrary scales
** Counter-intuitive, random, or [[:Category:Novelties|arbitrary]] scales
 
== See also ==
* [[Taxonomies of xen approaches]]


[[Category:Overview]]
[[Category:Overview]]
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