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) | ||
Revision as of 08:08, 17 November 2024
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
- 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
- Detempering (including ringer scales)
- Fokker blocks
- The harmonic series and subharmonic series
- Harmonic limits
- Isoharmonic chords
- Just intonation subgroups
- NEJI scales (near-equal just intonation)
- Overtone scales/AFDOs
- Primodality
- Tonality diamonds
- Tritriadic scales
- Undertone scales/IFDOs
- 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 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
- Historical temperaments: The (somewhat forgotten) use of Pythagorean tuning, meantone tunings and well temperaments in Western common practice music.
- 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.
Musical traditions of indigenous, ancient, and/or non-Western cultures
- African (dozens of distinct traditions)
- Ancient Greek
- Arabic
- Byzantine
- Georgian
- Indian (e.g. North, South)
- Indonesian (e.g. Java, Bali)
- Iranian (Persian)
- Pre-Columbian South American (e.g. Maya, Inca, Aztec)
- Thai
- 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, arbitrary scales