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Please use this identifier to cite or link to this item: http://hdl.handle.net/10119/11579

Title: Distance and Similarity of Time-span Tree
Authors: Tojo, Satoshi
Hirata, Keiji
Keywords: GTTM
time-span tree
music structure
distance
similarity
Issue Date: 2013-04
Publisher: 情報処理学会
Magazine name: Journal of Information Processing
Volume: 21
Number: 2
Start page: 256
End page: 263
DOI: 10.2197/ipsjjip.21.256
Abstract: Time-span tree in Lerdahl and Jackendoff's theory [12] has been regarded as one of the most dependable representations of musical structure. We first show how to formalize the time-span tree in feature structure, introducing head and span features. Then, we introduce join and meet operations among them. The span feature represents the temporal length during which the head pitch event is most salient. Here, we regard this temporal length as the amount of information which the pitch event carries; i.e., when the pitch event is reduced, the information comparable to the length is lost. This allows us to define the notion of distance as the sum of lost time-spans. Then, we employ the distance as a promising candidate of stable and consistent metric of similarity. We show the distance possesses proper mathematical properties, including the uniqueness of the distance among the shortest paths. After we show examples with concrete music pieces, we discuss how our notion of distance is positioned among other notions of distance/similarity. Finally, we summarize our contributions and discuss open problems.
Rights: 社団法人 情報処理学会, Satoshi Tojo, Keiji Hirata, Journal of Information Processing, 21(2), 2013, 256-263. ここに掲載した著作物の利用に関する注意: 本著作物の著作権は(社)情報処理学会に帰属します。本著作物は著作権者である情報処理学会の許可のもとに掲載するものです。ご利用に当たっては「著作権法」ならびに「情報処理学会倫理綱領」に従うことをお願いいたします。 Notice for the use of this material: The copyright of this material is retained by the Information Processing Society of Japan (IPSJ). This material is published on this web site with the agreement of the author (s) and the IPSJ. Please be complied with Copyright Law of Japan and the Code of Ethics of the IPSJ if any users wish to reproduce, make derivative work, distribute or make available to the public any part or whole thereof. All Rights Reserved, Copyright (C) Information Processing Society of Japan.
URI: http://hdl.handle.net/10119/11579
Material Type: publisher
Appears in Collections:b10-1. 雑誌掲載論文 (Journal Articles)

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