Two approaches to tuning and pitch systems

Abstract

This paper attempts to sort out some distinctions important to the understanding of tuning and pitch systems. Two different approaches are distinguished, the acoustic approach and the structural approach. In the acoustic approach, intervals are defined as whole‐number ratios, and a pitch system considered as a collection of ratios, some interrelated, some incommensurable. On the structural approach, the system is taken as prior to the intervals that compose it; intervals, then, become elements in a system with properties at least partially determined by the system. In the acoustic approach, what the intervals are and how they are tuned amount to the same thing, so it makes no sense to distinguish between a pitch system and a tuning scheme. But the structural approach distinguishes sharply between the pitch system as an abstract template or structure, and a tuning scheme as a strategy for mapping the template to specific frequency relations. Acoustic and structural views of tonality and microtonality will be presented, including examples of pitch systems constructed on both approaches. The present terminology will be applied to diverse instances of musical thought and practice, and implications of the two approaches for future evolution of pitch systems will be discussed.