Musical Vectors and Spaces

Candace Carroll, J. X. Carteret

(1. Department of Mathematics, Computer Science, and Engineering, Gordon State College, USA;

2. Department of Fine and Performing Arts, Gordon State College, USA)

Abstract: A vector is a quantity which has both magnitude and direction. In music, since an interval has both magnitude and direction, an interval is a vector. In his seminal work Generalized Musical Intervals and Transformations, David Lewin depicts an interval i as an arrow or vector from a point s to a point t in musical space. Using Lewin’s text as a point of departure, this article discusses the notion of musical vectors in musical spaces.

Key words: Pitch space, pitch class space, chord space, vector space, affine space