Paratactical Tuning: An Agenda for the Use of Computers in Experimental Intonation

Several factors have significantly affected, and perhaps more importantly, limited, the choice and usage of intonational strategies in music. Recognition of the existence of these limitations, as well as a discussion of procedures adopted to circumvent them, may help us to design computer-based tuning systems with greater flexibility and increased experimental possibilities. One of these limiting factors is the classification of instruments into two categories: those of fixed pitch (like keyboards) and those of variable pitch (like unfretted strings). Even though most instruments do not securely fit into either category (like the fretted strings, the keyed winds, or countless other instruments from around the world), it has been a consistent tendency among composers, theorists, and musicians to assume that they do. Or it has been assumed that their idiomatic usages preclude the possibility of performance in the mode of the other category. For example, it is generally conceded that string quartets and vocal ensembles develop sophisticated intonational adjustment procedures because of the nondiscrete pitch scale available to them, while other ensembles of so-called fixed-pitch instruments (those with a presumed limited set of pitches available, like the piano) have a simpler set of procedures for intonational performance. (In modern Western music, this is assumed to be twelve-tone equal temperament.) Although most contemporary Western performers on fixedpitch instruments have developed methods of extending the pitch resources of the instruments' twelve-tone equal design, these methods are not