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Cognitive Similarity Grounded by Tree Distance from the Analysis of K.265/300e

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Sound, Music, and Motion (CMMR 2013)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 8905))

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Abstract

Lerdahl and Jackendoff’s theory employed a tree in a representation of internal structure of music. In order for us to claim that such a tree is a consistent and stable representation, we argue that the difference of trees should correctly reflect our cognitive distance of music. We report our experimental result concerning the comparison of similarity among variations on Ah vous dirai-je, maman, K. 265/300e by Mozart. First we measure the distance in trees between two variations by the sum of the lengths of time-spans, and then we compare the result with the human psychological similarity. We show a statistical analysis of the distance and discuss the adequacy of it as a criteria of similarity.

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Notes

  1. 1.

    In the case of Fig. 4, as all the edges have the length of \(2\), the lattice becomes equilateral.

  2. 2.

    For any member \(X\) of a set, there exists \(X^{c}\) and \(X \sqcup X^{c} = \top \) and \(X \sqcap X^{c} =\bot \).

  3. 3.

    Rendering was originally introduced in computer graphics, which means the operation of creating images from a model, such as a photorealistic image from a wireframe model.

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Acknowledgments

This work was supported by JSPS KAKENHI Grant Numbers 23500145 and 25330434. The authors would like to thank the anonymous reviewers of CMMR2013 for their constructive comments to improve the quality of the paper.

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Authors and Affiliations

  1. Future University Hakodate, 116-2 Kamedanakano-cho, Hakodate, Hokkaido, 041-8655, Japan

    Keiji Hirata

  2. Japan Advanced Institute of Science and Technology, 1-1 Asahidai, Nomi, Ishikawa, 923-1292, Japan

    Satoshi Tojo

  3. Kyoto University, 46-29 Yoshida-Shimoadachicho, Sakyo, Kyoto, 606-8501, Japan

    Masatoshi Hamanaka

Authors
  1. Keiji Hirata
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  2. Satoshi Tojo
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  3. Masatoshi Hamanaka
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Corresponding author

Correspondence to Keiji Hirata .

Editor information

Editors and Affiliations

  1. CNRS - LMA, Marseille, France

    Mitsuko Aramaki

  2. Toulon-Var University and CNRS - LMA, Marseille, France

    Olivier Derrien

  3. CNRS - LMA, Marseille, France

    Richard Kronland-Martinet

  4. CNRS - LMA, Marseille, France

    Sølvi Ystad

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Hirata, K., Tojo, S., Hamanaka, M. (2014). Cognitive Similarity Grounded by Tree Distance from the Analysis of K.265/300e. In: Aramaki, M., Derrien, O., Kronland-Martinet, R., Ystad, S. (eds) Sound, Music, and Motion. CMMR 2013. Lecture Notes in Computer Science(), vol 8905. Springer, Cham. https://doi.org/10.1007/978-3-319-12976-1_36

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  • DOI: https://doi.org/10.1007/978-3-319-12976-1_36

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12975-4

  • Online ISBN: 978-3-319-12976-1

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