Counselling a better relationship between mathematics and musicology

Abstract

Mathematics and musicology have a long-standing relationship, but it is less productive than it might be. Reasons for this are explored in case studies of the ‘gap-fill’ melodic principle and of motivic analysis. In the first case, empirical results do not unequivocally support the principle, but it continues to be used by musicologists. In the second, mathematical and computational approaches are found to differ significantly from those of music analysis in their purpose and effect. Other differences between the disciplines are examined in the use of metaphor in musical discourse, and misunderstandings over the role of abstraction and estimation. Throughout, human factors are found to confound proper communication. I propose that better interdisciplinary research could arise from honesty about limitations, effort in understanding each other's disciplines, and humility about achievements.

Keywords:

• musicology
• gap-fill
• motivic analysis
• metaphor