From categories to continua for composition and improvisation: manipulating distributions of pitch intervals in prime number tuning systems

Abstract

I have recently codified and analysed general and potentially valuable approaches to finding novel musical vehicles for expression. One of these is the process of gradually converting any set of categorical elements of musical structure into a continuum, assessing the utility and expressive applicability of each gradation. The purpose of this article is to illustrate this with respect to pitch structures, starting from normal Western tuning such as that of the piano, and moving towards continuous pitch structures, in this case emphasising intermediaries based on prime number systems, one from my earlier work, others created for the article. I provide pointers towards the perceptual and cognitive aspects of pitch structures, alongside the consideration of their utility for performance.  I complement the article by providing examples of ensemble and keyboard music made with some of the graded tuning intermediaries.