List of approaches to musical tuning: Difference between revisions

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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.


''Below is a partial list of currently-established theories and approaches related to tuning.''
[[Xen concepts for beginners]] provides a solid foundation to start from in exploring this assortment of tunings.


*[[JustIntonation|Just Intonation]]: The tuning of pitches so that their fundamental frequencies are related by ratios of whole numbers. An infinite world of numerous models: the [[harmonic series]], integer frequency ratios, [[tonality diamond]]s, [[combination product sets]], [[Fokker blocks]] etc.
== Defined approaches ==
*[[Generalized_overtone_tuning|Generalized overtone 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.
*[[Equal_Temperaments|Equal tuning]]: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals.
*Musical traditions of historical and modern Western cultures
**[[wikipedia:Musical_system_of_ancient_Greece|Ancient Greek]], [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]
***[[Arabic, Turkish, Persian]]
**[[Russian]]
**[[Historical Western Temperaments]]: The (somewhat forgotten) use of [[Pythagorean]] and [[Meantone|meantone tunings]] and [[Circulating_Temperaments|circulating temperaments]] in Western common practice music.
*Musical traditions of indigenous, ancient, and/or non-Western cultures
**[[Indian|Indian]] (North, South)
**[[African|African]]
**Thai
**[[Pre-Columbian_South_American_Music|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)
**[[Indonesian|Indonesian]] (Java, Bali)
**[[Georgian|Georgian]]
*[[Regular_Temperaments|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]]: Tunings (or better, scales) that use iterations of a generating interval, modulo a period interval, to produce scales of two step-sizes.
*[[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]]: the use of divided fourths as building blocks for composition.
*[[isoharmonic_chords|Isoharmonic chords/scales]]
*[[Pretty_Pictures|Pretty Pictures]] that represent scales in one way or another
*[[Notation|Notation]] (pretty pictures for the purpose of writing music down)
*[[Nominal-Accidental_Chains|Nominal-Accidental Chains]] A common approach to notation
*the notion of a [[Scalesmith|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions
**Mathematically based scales
**Acoustically-based scales (resonant frequencies of performance space, for example)
**Scale transformation and stretching
**Counter-intuitive, random, arbitrary scales


[[Category:overview]]
=== Shape-based ===
[[Category:practice]]
* [[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).
[[Category:theory]]
* [[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.
[[Category:tuning]]
* [[Tetrachord|Tetrachordal scales]]: the use of divided fourths as building blocks for composition.
 
=== 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.
* [[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
* [[Historical temperaments]]: The (somewhat forgotten) use of [[Pythagorean tuning]], [[meantone]] tunings and [[well temperament]]s in Western common practice music.
* [[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 ===
* [[African]] (dozens of distinct traditions)
* [[Ancient Greek]]
* [[Arabic, Turkish, Persian|Arabic]]
* [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]
* [[Wikipedia:Music of Croatia|Croatian]] (including the [[Istrian]] scale)
* [[Music of Georgia|Georgian]]
* [[Indian]] (e.g. North, South)
* [[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 ==
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.
* [[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.
* [[Musical notation]]: Pretty pictures for the purpose of writing music down.
** [[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
** Acoustically-based scales (resonant frequencies of performance space, for example)
** Scale transformation and stretching
** Counter-intuitive, random, or [[:Category:Novelties|arbitrary]] scales
 
== See also ==
* [[Taxonomies of xen approaches]]
 
[[Category:Overview]]
[[Category:Practice]]
[[Category:Tuning]]
 
{{Todo|cleanup}}

Latest revision as of 02:28, 12 May 2025

Musical tuning can be approached in many different ways. Here are some of the currently-established theories and approaches.

Xen concepts for beginners provides a solid foundation to start from in exploring this assortment of tunings.

Defined approaches

Shape-based

  • Equal-step tunings: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals. These include edos (equal divisions of the octave), but also edonoi (equal divisions of nonoctave intervals).
  • 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.
  • Tetrachordal scales: the use of divided fourths as building blocks for composition.

Ratio-based

Musical traditions of indigenous, ancient, and/or non-Western cultures

Subjective processes

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.
  • 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.
  • 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.
    • Mathematically based scales
    • Acoustically-based scales (resonant frequencies of performance space, for example)
    • Scale transformation and stretching
    • Counter-intuitive, random, or arbitrary scales

See also

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