On Pitch or Rhythm: Interpretations of Orderings of and in Pitch and Time
John Rahn · Perspectives of New Music · 1975
The meat of this paper consists of a system of relations among types of interpreted orderings. I first stumbled into these kinds of relations while composing a song cycle entitled Peanut Butter Defies Gravity. Any value that this system of relations has for us must reside in its demonstrated usefulness in the understanding and composition of music. I regret that the mere exposition of the bare bones of these relations here will occupy only too much of your time and attention, leaving but scanty orts of their more interesting compositional flesh here to be chewed over. Much of the background for this paper is either assumed or explicit in Milton Babbitt's article, Twelve-Tone Rhythmic Structure and the Electronic Medium, which appeared originally in Perspectives of New Music, Fall 1962. Nevertheless the early part of this paper will review this background material in the hope of getting all of our heads on the same track, at least initially. This preliminary review will not raise the issue of what many feel to be potentially serious problems concerning the general perception of structures of 12-modular timepoint-classes (TC) analogous to 12-modular pitch-classes (PC). Temporarily, then, ignoring the differences which can be found in our perceptions in the dimensions of time and pitch, let us proceed as far as possible to set up formal similarities between them by considering a common model. For this model, take a which has a direction-for example, the real number line (Ex. 1). Such a may model either dimension, with an arbitrary assignment of direction. In this example higher pitch is correlated with later time.