Structural Similarity Based on Time-Span Tree

Time-span tree is a stable and consistent representation of musical structure since most experienced listeners deliver the same one, almost independently from context and subjectivity. In this paper, we pay attention to the reduction hypothesis of the tree structure, and introduce the notion of distance as a promising candidate of stable and consistent metric of similarity. First, we design a feature structure to represent a time-span tree. Next, we regard that when a branch is removed from the tree the information corresponding to its time-span is lost, and suggest that the sum of the length of those removed spans is the distance between two trees. We will show that the distance preserves uniqueness in multiple shortest paths, as well as the triangle inequality. Thereafter, we illustrate how the distance works as a metric of similarity, and then, we discuss the feasibility and the problem of our methodology.