Real-time synchronization of independently controlled phasors

Abstract

Phasors have a wide variety of uses in music and sound synthesis. At audio signal rates, phasors can be used as indexing functions for table oscillators. At control rates, phasors can be used as clocks to control tempo and trigger events. When simultaneous control over multiple phasors or oscillators is desired, there arises a conflict between the need to control their individual frequencies, and the need to coordinate the phase relationships between the different phasors. The problem is particularly acute in real-time systems where a flexible mechanism for negotiating between local and global control is necessary. This paper presents a spline technique for quasi-independent control over phasor frequency and phase, discusses the objects and interfaces in an implementation, and presents several examples to illustrate the utility of the system for signal and event generation, and for synchronization in real-time networked music environments.