Returning to the Fundamentals on Temperament (In Digital Systems)

Abstract

Considering the generation of musical tunings, it is reasonable to expect that the many constructs contained in Functional programming languages may provide useful tools for exploring both conventional and new tunings. In this paper we present a number of approaches for manipulating tunings using basic mathematics. While this provides a simple foundation for describing temperament, it is fundamental enough to support a variety of approaches and further, allows the unbounded description of arbitrary tunings. It is expected that this notion will be useful in defining tunings, and by extension scales, for Digital Musical Instruments. This breaks down the physical barrier that has limited the likes of just intonations from having practical applications in the performance setting. It also enables composers to explore a variety of non traditional temperaments rapidly, without having to manually tune each note.