Yi-Cheng Daniel Wu

A Reconsideration of Interval-Class Spacethrough the Perspective of Joseph Straus’s Evenness and Spaciousness

In his 2005 article, Joseph Straus’s ‘offset number' derived from his ‘fuzzy transformational voice leading’ implies ic 6 as the most “even, spacious” ic among ics 1 to 6 (2005, 67).  However, to define ic 6 as the most even, we must locate it in the larger space of an octave, for it equally divides an octave into two even halves.  But the ic representing an octave—ic 0 — is missing in Straus’s discussion.  To satisfy Straus’s notion of evenness, we must consider ic 0.  However, how do we know ic 0 only ever represents an octave?  Also, once we consider ic 0, ic 6 no longer projects the most spacious ic, for ic 0— the octave— has a bigger space than that of ic 6.  Prompted by this paradox, I propose a theory re-conceptualizing the space of all ic’s. 

I set up two rules to measure the space of all ic’s in a clock-image used by most theorists to represent a pc-space: (1) no pc ever remains stationary, and (2) we measure the shortest distance between two pcs.  These two rules allow us to perceive ic 0 as the most spatial ic projected by the full circle progression around the clock, and ic 6 as the most even ic dividing the clock into two equal semi-circles.  Based on this new definition of the space of all ics, I refine Straus’s ‘offset number’, which reveals a truer picture of the ‘degree of chromaticness’ of a chord.  To show the practical advantage of my harmonic measurement, my presentation concludes with analyses of Kürtag’s Chamber Song Op. 37 and Crawford’s String Quartet.