List of approaches to musical tuning: Difference between revisions

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<span style="display: block; text-align: right;"><span style="background-color: #ffffff;">[[調律方法|日本語]]</span>
{{interwiki
| en = List of approaches to musical tuning
| de =
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| 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.


</span>
[[Xen concepts for beginners]] provides a solid foundation to start from in exploring this assortment of tunings.


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


<ul><li>[[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 diamonds, eikosany, Fokker blocks etc.</li><li>[[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.</li><li>[[Equal_Temperaments|Equal tuning]]: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals.</li><li>[[Historical_Western_Temperaments|Historical Western Temperaments]]: The (somewhat forgotten) use of [[Meantone|meantone tunings]] and [[Circulating_Temperaments|circulating temperaments]] in Western common practice music.</li><li>Musical traditions of indigenous, ancient, and/or non-Western cultures<ul><li>[[Arabic,_Turkish,_Persian|Arabic, Turkish, Persian]]</li><li>[[Indian|Indian]] (North, South)</li><li>[[African|African]]</li><li>Thai</li><li>[[Pre-Columbian_South_American_Music|Pre-Columbian South American]] (e.g. Maya, Inca, Aztec..)</li><li>[[Indonesian|Indonesian]] (Java, Bali)</li><li>Ancient Greek, [http://orthodoxwiki.org/Byzantine_Chant#The_scale Byzantine]</li><li>[[Georgian|Georgian]]</li></ul></li><li>[[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</li><li>[[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.</li><li>[[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.</li><li>[[tetrachord|Tetrachordal Scales]]: the use of divided fourths as building blocks for composition.</li><li>[[isoharmonic_chords|Isoharmonic chords/scales]]</li><li>[[Pretty_Pictures|Pretty Pictures]] that represent scales in one way or another</li><li>[[Notation|Notation]] (pretty pictures for the purpose of writing music down)<ul><li>[[Nominal-Accidental_Chains|Nominal-Accidental Chains]] A common approach to notation</li></ul></li><li>the notion of a [[Scalesmith|Scalesmith]] who ''builds'' scales, with various methods, perhaps for single occasions<ul><li>Mathematically based scales</li><li>Acoustically-based scales (resonant frequencies of performance space, for example)</li><li>Scale transformation and stretching</li><li>Counter-intuitive, random, arbitrary scales</li></ul></li></ul>      [[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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