A typology of binary relationships between sequences of durations.

Abstract

In this paper I present a typology of musical binary relationships between sequences of durations. First, I define some theoretical concepts. These relationships are classified in two main categories: total match and similarity. In the first group there is identity, permutation, pseudo-permutation, delta (augmentation-diminution) division and addition. Similarity relationshlps exist when we found total match relationships between subsequences. Then we present an implementation or this theory in Common Lisp. wc show the analysis functions that correspond to cvery relationship. and we explain the formal or the results. Next I illustrate these relationships "in context'' with musical examples ranging from Middle Ages to the present. In the end. I postulate that the presence of these relationships in the history of Western music allows to assign them the category of fundamental components of rhythmic thought.