List of approaches to musical tuning
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This is an easily accessed page that is intended to serve as a portal to the pedagogical enrichment of newcomers to the xenharmonic community as well as of more established members who are unaware of certain bodies of knowledge. As a result, it has been semi-protected to prevent vandalism.
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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:
- Adaptive just intonation
- 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
- Croatian (including the Istrian scale)
- 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