List of approaches to musical tuning

Below is a partial list of currently-established theories and approaches related to tuning.

• 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 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 tuning: Tunings that use a single interval (and combinations thereof) to form a subtle monoculture of intervals.
• Musical traditions of historical and modern Western cultures
  • Ancient Greek, Byzantine
    • Arabic, Turkish, Persian
  • Russian
  • Historical Western Temperaments: The (somewhat forgotten) use of Pythagorean and meantone tunings and circulating temperaments in Western common practice music.
• Musical traditions of indigenous, ancient, and/or non-Western cultures
  • Indian (North, South)
  • African
  • Thai
  • Pre-Columbian South American (e.g. Maya, Inca, Aztec..)
  • Indonesian (Java, Bali)
  • Georgian
• 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: Tunings (or better, scales) that use iterations of a generating interval, modulo a period interval, to produce scales of two step-sizes.
• 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.
• Tetrachordal Scales: the use of divided fourths as building blocks for composition.
• Isoharmonic chords/scales
• 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