Computation and Musical Applications of Discrete and Continuous Rhythmic Phase-shifting Techniques

Abstract

This paper describes how to implement rhythm phase shifting in a computational way in order to shift the phase of a rhythm in a controlled but expanded way. It is mainly divided into two methods, discrete phase-shifting which can be implemented through the shifting of the sample delay, and continuous phase-shifting through the adjustment of the playback speed. The latter is again divided into two techniques depending on whether the playback speed is fixed or variable. It also deals with the mixing of these various techniques. For each technique, we discuss the process and the related mathematical formula that must be computed to align the phase-interval in rhythmic units of the current BPM.