Exploding the Monochord: An intuitive spatial representation of microtonal relational structures

Abstract

Microtonality appears in a wide range of historical and ethnomusicological contexts, particularly in theoretical aspects of tuning systems and as intonation in performance. Theoretical concepts of microtonality can be inaccessible due to difficulties arising in the reconciliation of mathematical and musical approaches. The development of sophisticated geometrical representations of pitch cognition has largely been focused on the Western tonal tradition with limited incorporation of microtonality. This paper presents a spatial model of microtonal intervals and their relational structures. The model enhances accessibility of microtonal-theoretic concepts through a visually intuitive representation. It also acts as a unifying framework with respect to the comparative assessment of microtonal schemes and the integration of the different dimensions of pitch cognition. The integrative characteristics of the model demonstrate the psychological emergence of cognitive structures and their potential isomorphism with algorithmic approaches. The comparative features of the model may provide the basis for computational applications of broader scope than a culturally specific model can provide, while the intuitive spatial aspects may inspire improvements in the human-computer interaction of such applications. © 2011 Springer-Verlag.