Distance and Similarity of Time-span Tree
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- Tojo Satoshi
- Japan Advanced Institute of Science and Technology
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- Hirata Keiji
- Future University Hakodate
書誌事項
- タイトル別名
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- Distance and Similarity of Time-span Trees
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抄録
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.
収録刊行物
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- Information and Media Technologies
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Information and Media Technologies 8 (2), 347-354, 2013
Information and Media Technologies 編集運営会議
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詳細情報 詳細情報について
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- CRID
- 1390001205265549952
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- NII論文ID
- 130003369530
- 130003366951
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- NII書誌ID
- AA00700121
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- ISSN
- 03876101
- 18810896
- 18826652
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- HANDLE
- 10445/7802
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- 本文言語コード
- en
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- データソース種別
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- JaLC
- IRDB
- Crossref
- CiNii Articles
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- 使用不可