A new perspective on David Lewin's interval function : the symmetrical IFUNC array
This paper expands on the work of David Lewin, whose seminal work Generalized Musical Intervals and Transformations proposes, among other functions, the interval function or IFUNC. The interval function catalogs the type and number of directed pitchclass intervals between two different pitch-class sets. This paper proposes the concept of the IFUNC array, an ordered sequence of twelve digits representing the IFUNC values for an interval i = 0–11, reading either left to right or clockwise around a circle. It explores features of the interval function, including symmetry in the IFUNC array, and includes analysis of several excerpts from Anton Webern’s early atonal works. The paper addresses axes of symmetry, both in pitch-class sets and in interval functions.