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List of approaches to musical tuning: Difference between revisions

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{{interwiki
{{Interwiki
| de =
| en = List of approaches to musical tuning
| en = List of approaches to musical tuning
| de =
| es = Orientación general
| es =  
| ja = 調律方法
| ja = 調律方法
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* [[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 or fifths as building blocks for composition.


=== Frequency ratio-based ===
=== Frequency 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:
** [[Adaptive just intonation]]
** [[Adaptive just intonation]]
** [[Combination product sets]]
** [[Combination product set]]s
** [[Detempering]] (including [[ringer scale]]s)
** [[Detempering]] (including [[ringer scale]]s)
** [[Fokker blocks]]
** [[Fokker blocks]]
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** 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, regularly and consistently detuned in various ways to better meet a variety of compositional desires; most often making JI easier to navigate by [[tempering out]] [[Comma basis|commas]] to equate similarly sized pitches.
* [[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 historic [[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.
* [[Xenharmonic series]]: Just intonation but the entire matrix of just intervals is stretched, squished or otherwise warped or manipulated for interesting effect.


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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.
* [[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.
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