One Cognitive Psychologist's Quest for the Structural Grounds of Music Cognition

ABSTRACT-Here, I describe how I came to believe that the musical scales and tonal systems of diverse human cultures reflect both (a) underlying, universal principles of cognition, including a modality-general time-distance law, and (b) underlying cognitive structures corresponding to geometrically regular helical and toroidal configurations in higher-dimensional spaces. I review supportive evidence obtained, first, by means of methods (which I and my associates developed at the Bell Labs) of multidimensional scaling and of synthesizing tones that form the height-suppressed chroma circle and, second, by means of the probe-tone method (which Krumhansl and I developed at Stanford) for quantifying tonal hierarchies. I argue that two quite independent kinds of considerations-acoustical and abstract structural-converge in establishing the perceptual-cognitive optimality of the extended (12-tone) diatonic system. I then venture some speculations about the sources of the emotional power of music. At the end, I append an annotated list of my former students, coworkers, and associates who contributed to the work described here. PRELIMINARY REMARK Since retiring from Stanford and closing my psychological laboratory some dozen years ago, I have focused my professional endeavors on thinking and writing about more theoretical and philosophical issues of cognitive science (see Shepard, 2001, 2004, 2008). Accordingly, instead of presenting any new empirical findings of my own, I shall attempt to do two things: The first is to offer some reminiscences about how I have off and on sought to extend my general approach to cognitive science on to the investigation, specifically, of music perception and cognition. The second is to provide a relatively coherent overview of what I retrospectively regard as the most significant conclusions to be drawn from the work that my students and associates (at the Bell Labs and at Stanford) have carried out relating to auditory perception and music cognition. THE EMERGENCE OF MY INTERESTS IN SCIENCE, GEOMETRY, AND MUSIC My early scholastic record was not promising - from the first grade (which I was required to repeat) through my freshman year of college (from which I was required to take a two-quarter leave before being granted a probationary re-entry). I was always fascinated by things mechanical and geometrical and loved to tinker, to draw, and to explore the wonderful sounds produced by depressing various combinations of keys on the piano. But I was typically unable to tear myself away from these interests to undertake the less interesting work assigned by my teachers. I found the obligatory elementary school music class to be wholly devoid of intellectual content, and I was too shy and disdainful to join in the singing of what I regarded as silly songs. All of this changed following my probationary period at Stanford, when I was finally permitted to register for more advanced courses whose subject matters - particularly in science, math, and philosophy - did finally inspire me to work toward conceptual mastery and to explore various implications, extensions, and applications on my own. (These included the construction and study of two- and three-dimensional tessellations of constant curvature and of three- and four-dimensional regular polytopes.) I also began attending the Tuesday afternoon organ concerts in Stanford's Memorial Church (by Stanford's organist Herbert Nanny and by other, visiting organists). I was immediately enthralled by the architectonic grandeur of Bach's preludes, toccatas, and fugues and by the harmonically rich and splendorously driving 19th- and 20th-century organ music of Franck, Vierne, Widor, Dupre, and others of the "French" school. Later, while a graduate student in psychology at Yale, I became spellbound by the late string quartets of Beethoven and, soon thereafter, the quartets of Bartok. At an abstract level, it was the structural elegance and symmetries that appealed to me both in such geometrical objects as regular tessellations and polytopes and in contrapuntal music. …