List of approaches to musical tuning

Musical tuning can be approached in many different ways. Here are some of the currently-established theories and approaches:

• 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.
• 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
  • 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.
• 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
• 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.
• Extensions or alterations of just intonation:
  • Homothetic just intonation
  • Xenharmonic series
• Musical traditions of indigenous, ancient, and/or non-Western cultures:
  • African
  • Ancient Greek
  • Arabic, Turkish, Persian
  • Byzantine
  • Georgian
  • Indian (e.g. North, South)
  • Indonesian (e.g. Java, Bali)
  • Pre-Columbian South American (e.g. Maya, Inca, Aztec)
  • Thai
• Historical temperaments: The (somewhat forgotten) use of Pythagorean tuning, meantone tunings and well temperaments in Western common practice music.
• Tetrachordal scales: the use of divided fourths as building blocks for composition.

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

Where to start

Xen concepts for beginners provides a solid foundation to start from in exploring this assortment of tunings.