Dynamic tonality

Dynamic tonality is a paradigm for tuning and timbre which generalizes the special relationship between just intonation and the harmonic series to apply to a wider set of pseudo-just tunings and related pseudo-harmonic timbres. The main limitation of Dynamic Tonality is that it is best used with compatible isomorphic keyboard instruments and compatible synthesizers or with voices and instruments whose sounds are transformed in real time via compatible digital tools. A vibrating string, a column or air, and the human voice all emit a specific pattern of partials corresponding to the harmonic series. The degree of correspondence varies, depending on the physical characteristics of the emitter. "Partials" are also called "harmonics" or "overtones." Each musical instrument's unique sound is called its timbre, so an instrument's timbre can be called a "harmonic timbre" if its partials correspond closely to the harmonic series. Just intonation is a system of tuning that adjusts a tuning's notes to maximize their alignment with a harmonic timbre's partials. This alignment maximizes the consonance of music's tonal intervals. The harmonic series and just intonation share an infinitely-complex—i.e., rank-∞—pattern that is determined by the infinite series of prime numbers. A temperament is an attempt to reduce this complexity by mapping this rank-∞ pattern to a simpler—i.e., lower rank—pattern. Throughout history, the pattern of notes in a tuning could be altered (that is, "tempered") by humans but the pattern of partials sounded by an acoustic musical instrument was largely determined by the physics of their sound production. The resulting misalignment between "pseudo-just" tempered tunings and untempered timbres made temperament "a battleground for the great minds of Western civilization." This misalignment, in any tuning that is not fully Just (and hence infinitely complex), is the defining characteristic of the Static Timbre Paradigm.