Approaches to musical tuning
Musical tuning can be approached in many different ways. Here are some of the currently-established theories and approaches.
- 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, combination product sets, Fokker blocks, primodality, etc.
- 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-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 many nonoctave tunings (sometimes called edonoi).
- Historical western temperaments: The (somewhat forgotten) use of Pythagorean and meantone tunings and well temperaments in Western common practice music.
- Musical traditions of indigenous, ancient, and/or non-Western cultures
- 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
- 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.
- Isoharmonic chords: the use of chords with an equal harmonic difference between the pitches as building blocks for scales.
The following approaches describe the subjective exploration process or its representations rather than its objective, audible result:
- 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.
- Pretty Pictures that represent scales in one way or another
- Notation (pretty pictures for the purpose of writing music down)
- Nominal-Accidental Chains A 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