Abstract
The time-span tree is a dependable representation of musical structure since most experienced listeners deliver the same one, almost independently of context and subjectivity. In this paper, we pay attention to the reduction hypothesis of the tree structure, and introduce a 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, that is, its corresponding pitch event is reduced, the amount of information comparable to its time-span is lost. Then, we suggest that the sum of the length of those removed spans is the distance between two trees. We will show mathematical properties of the distance, including that the distance becomes unique in multiple shortest paths. Thereafter, we illustrate how the distance works in a set of reductions. We consider a metric of similarity both from human cognition and from set operation, and discuss the relation of distance and similarity. Also, we discuss such other related issues as flexible tree matching and music rendering.
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Tojo, S., Hirata, K. (2013). Structural Similarity Based on Time-Span Tree. In: Aramaki, M., Barthet, M., Kronland-Martinet, R., Ystad, S. (eds) From Sounds to Music and Emotions. CMMR 2012. Lecture Notes in Computer Science, vol 7900. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-41248-6_23
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DOI: https://doi.org/10.1007/978-3-642-41248-6_23
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