Pitches in bach

Traditionally, most computer-aided composition environments represent a pitch via a number (typically a MIDI note number or its value in midicents), flattening the enharmonic information onto a single real-valued parameter. Although this choice is convenient in many applications, it can be very limiting in any context where diatonicism, to some degree, matters. The latest release of bach, a library for Max dedicated to musical representation and computer-aided composition, introduces a new `pitch' data type, designed to overcome this limitation by representing both diatonic pitches and intervals and supporting standard arithmetic operations. In this article we motivate and detail its implementation and its syntax. As an application, we introduce a new respelling algorithm, also implemented in ach, designed to provide an easy-to-read spelling of notes. Differently from most existing pitch spelling algorithms, tailored on the tonal repertoire, our algorithm is targeted to produce a musician-friendly representation of non-tonal music.