Michael Buchler
University of Iowa
Most similarity measures for pitch-class sets (pcsets) have utilized a comparison of either interval class vectors (ICVs) or total abstract subset content. In this paper, I will begin by describing some of the criticisms that have been leveled against both traditional approaches, and I will posit a fundamentally different methodology that examines the way a pcset is partitioned with respect to the six distinct interval-cycles. (Because interval 7- through 11-cycles may be understood as retrogrades of interval 5- through 1-cycles, they are not considered distinct.)
This information serves as the basis for a new weighted six-argument vector that resembles the interval-class vector (ICV) in function (at least in its function as data for similarity indices), but not in design. Each argument of the vector represents the degree to which instances of corresponding interval-class i are found in unbroken i-cyclic adjacencies. The assumption behind the weighting process is that, for any SC X, the more that instances of interval-class i form a particular i-cycle, the more likely that realizations of X will project interval-class i. This new vector class and its associated similarity index will be explained methodically, and their usefulness will be illustrated through a series of analytic vignettes.