Theory: Inventions that shape understanding
Theories are not discoveries but inventions of humans, usually meant to formally describe regularities in experience, which often bring forth new ways of experiencing. (The music-making itself ('practice'), if at odds with existing theories, may provoke the creation of new theories; it is thus important to recognize that theory and practice mutually and reciprocally influence each other.)
There is a great deal of theory around the creation and/or discovering of tunings, scales, and temperaments, but whether it is useful to bother learning any of them is a matter of personal decision. (It is always possible to load up a random tuning on your retunable instrument of choice and explore it through music, without bothering to understand the theoretical considerations that led to the construction and/or discovery of said tuning.) Below you will find a partial list of currently-established theories related to alternative intonations.
Reality tunnels into microtonality
- Just Intonation: an infinite world of rational numbers and numerous models: the harmonic series, integer frequency ratios, tonality diamonds, eikosany, etc.
- Equal tunings: each one a subtle monoculture of intervals. May be treated as temperaments, or not
- In Western common practice music, the (somewhat forgotten) use of historical temperaments (meantones, well temperaments) with 12 or more unequal notes per octave
- 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, a means of iterating a single generative interval, modulo a period interval, to produce scales of two step-sizes. Brought to you by Erv Wilson
- Graham complexity, a complexity measure which works well with MOS scales and rank two regular temperaments.
- 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, which use divided fourths as building blocks for composition.
- Isoharmonic chords/scales
- Pretty Pictures that represent scales in one way or another
- Notation(pretty pictures for a 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
- Counter-intuitive, random, arbitrary scales
- Numerology-based, computationally demanding scales
- Scale stretching
- Acoustically-based (resonant frequencies of performance space, for example)
- (Corollaries, traces left by other reality tunnels, which by themselves are completely trivial and obvious)
- Redundancy in a tuning system
- Tonalsoft Encyclopedia of microtonal music theory - a whole sea of information on the topic, covering both historical tuning theories and modern developments
- Microtonalismo - Web microtonal
- A bibliography on musical tunings and temperaments, compiled by John S. Allen
- Huygens-Fokker Foundation's Tuning & temperament bibliography, hyperlinked and updated by Manuel op de Coul
- The UnTwelve website has some pages of theoretical interest, including a fascinating article authored by Margo Schulter
- German sister wiki "Xenharmonie"