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Approaches to Musical Tuning
Below is a partial list of currently-established theories and approaches related to tuning.
: 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.
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.
: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals.
Historical Western Temperaments
: The (somewhat forgotten) use of
in Western common practice music.
Musical traditions of indigenous, ancient, and/or non-Western cultures
Arabic, Turkish, Persian
Pre-Columbian South American
(e.g. Maya, Inca, Aztec..)
: (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
: Tunings (or better, scales) that use iterations of a generating interval, modulo a period interval, to produce scales of two step-sizes.
: 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.
: the use of divided fourths as building blocks for composition.
that represent scales in one way or another
(pretty pictures for the purpose of writing music down)
A common approach to notation
the notion of a
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
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