research-article

No longer 'somewhat arbitrary': calculating salience in GTTM-style reduction

Authors:

Keiji HirataAuthors Info & Claims

DLfM '18: Proceedings of the 5th International Conference on Digital Libraries for Musicology

Pages 26 - 33

https://doi.org/10.1145/3273024.3273037

Published: 28 September 2018 Publication History

Abstract

Following earlier work on the formalisation of Lerdahl and Jack-endoff's Generative Theory of Tonal Music (GTTM), we present a measure of the salience of events in a reduction tree, based on calculations relating the duration of time-spans to the structure of the tree. This allows for the proper graphical rendition of a tree on the basis of its time-spans and topology alone. It also has the potential to contribute to the development of sophisticated digital library systems able to operate on music in a musically intelligent manner. We present results of an empirical study of branch heights in the figures in GTTM which shows that salience calculated according to our proposals correlates better with branch height than alternatives. We also discuss the possible musical significance of this measure of salience. Finally we compare some results using salience in the calculation of melodic similarity on the basis of reduction trees to earlier results using time-span. While the correlation between these measures and human ratings of the similarity of the melodies is poor, using salience shows a definite improvement. Overall, the results suggest that the proposed definition of salience gives a potentially useful measure of an event's importance in a musical structure.

References

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Nicola Dibben. 1994. The Cognitive Reality of Hierarchic Structure in Tonal and Atonal Music. Music Perception 12, 1 (1994), 1--25.

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B. Efron and C. Stein. 1981. The Jackknife Estimate of Variance. The Annals of Statistics 9, 3 (1981), 586--596.

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Mark Gotham. 2017. Hierarchy and position usage in 'mixed' metrical structures. Journal of New Music Research 46, 2 (2017), 103--117.

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Masatoshi Hamanaka, Keiji Hirata, and Satoshi Tojo. 2015. Structural Similarity Based on Time-Span Sub-Trees. In Mathematics and Computation in Music, Tom Collins, David Meredith, and Anja Volk (Eds.). Springer International Publishing, Cham, 187--192.

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Niels Chr. Hansen. 2011. The Legacy of Lerdahl & JackendoffâĂ&Zacute;s A Generative Theory of Tonal Music: Bridging a significant event in the history of music theory and recent developments in cognitive music research. Danish Yearbook of Musicology 38 (2011), 33--55.

[6]

Keiji Hirata, Satoshi Tojo, and Masatoshi Hamanaka. 2014. Cognitive Similarity Grounded by Tree Distance from the Analysis of K.265/300e. In Sound, Music, and Motion: 10th International Symposium, CMMR 2013, Marseille, France, October 15--18, 2013. Revised Selected Papers, Richard Kronland-Martinet Mitsuko Aramaki, Olivier Derrien and Sølvi Ystad (Eds.). Springer, Cham, Switzerland, 589--605.

[7]

Keiji Hirata, Satoshi Tojo, and Masatoshi Hamanaka. 2016. An Algebraic Approach to Time-Span Reduction. In Computational Music Analysis, David Meredith (Ed.). Springer, Cham, Switzerland, 251--270.

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Michel Imberty. 2000. The Question of Innate Competencies in Musical Communication. In The Origins of Music, Björn Merker Nils L. Wallin and Steven Brown (Eds.). MIT Press, Cambridge, MA, USA, 449--462.

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Fred Lerdahl and Ray Jackendoff. 1983. A Generative Theory of Tonal Music. MIT Press, Cambridge, Mass.

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Fred Lerdhal. 2001. Tonal Pitch Space. Oxford University Press, New York.

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Alan Marsden. 2005. Generative structural representation of tonal music. Journal of New Music Research 34, 4 (2005), 409--428.

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Alan Marsden. 2010. Recognition of Variations Using Automatic Schenkerian Reduction. In Proceedings of the 11th International Society for Music Information Retrieval Conference (ISMIR 2010). International Society for Information Retrieval, 501--506.

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David Rizo and Alan Marsden. 2016. A Standard Format Proposal for Hierarchical Analyses and Representations. In Proceedings of the 3rd International Workshop on Digital Libraries for Musicology (DLfM 2016). ACM, New York, NY, USA, 25--32.

Digital Library

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Heinrich Schenker. 1979/1935. Free Composition (Der Freie Satz). Longman, New York.

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John A. Sloboda and David H. H. Parker. 1985. Immediate Recall of Melodies. In Music Structure and Cognition, Ian Cross Peter Howell and Robert West (Eds.). Academic Press, London, UK, 143--167.

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Satoshi Tojo and Keiji Hirata. 2013. Structural Similarity Based on Time-Span Tree. In From Sounds to Music and Emotions: 9th International Symposium CMMR, London, UK, June 19--22, 2012, Revised Selected Papers, Richard Kronland-Martinet Mitsuko Aramaki, Mathieu Barthet and Sølvi Ystad (Eds.). Springer Verlag, Berlin, Heidelberg, 400--421.

Digital Library

[19]

Satoshi Tojo, Alan Marsden, and Keiji Hirata. 2017. On Linear Algebraic Representation of Time-span and Prolongational Trees. In Proceedings of the 13th International Symposium on Computer Music Multidisciplinary Research (CMMR). Matosinhos, Portugal.

Cited By

Luke SCarnovalini F(2024)A Hierarchical, Modular Music SequencerProceedings of the 19th International Audio Mostly Conference: Explorations in Sonic Cultures10.1145/3678299.3678343(429-438)Online publication date: 18-Sep-2024
https://dl.acm.org/doi/10.1145/3678299.3678343
Hamanaka MHirata KTojo S(2023)Implementation of melodic morphing based on generative theory of tonal musicJournal of New Music Research10.1080/09298215.2023.216971351:1(86-102)Online publication date: 2-Feb-2023
https://doi.org/10.1080/09298215.2023.2169713
Hamanaka MHirata KTojo S(2023)Time-Span Tree Leveled by Duration of Time-SpanMusic in the AI Era10.1007/978-3-031-35382-6_5(47-58)Online publication date: 22-Jun-2023
https://doi.org/10.1007/978-3-031-35382-6_5
Show More Cited By

Index Terms

No longer 'somewhat arbitrary': calculating salience in GTTM-style reduction
1. Applied computing
  1. Arts and humanities
    1. Sound and music computing

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cover image ACM Other conferences

DLfM '18: Proceedings of the 5th International Conference on Digital Libraries for Musicology

September 2018

101 pages

ISBN:9781450365222

DOI:10.1145/3273024

Program Chair:
Kevin Page
University of Oxford

Copyright © 2018 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected].

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Association for Computing Machinery

New York, NY, United States

Publication History

Published: 28 September 2018

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Japan Society for the Promotion of Science

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DLfM '18

DLfM '18: 5th International Conference on Digital Libraries for Musicology

September 28, 2018

Paris, France

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DLfM '18 Paper Acceptance Rate 14 of 27 submissions, 52%;

Overall Acceptance Rate 27 of 48 submissions, 56%

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Cited By

Luke SCarnovalini F(2024)A Hierarchical, Modular Music SequencerProceedings of the 19th International Audio Mostly Conference: Explorations in Sonic Cultures10.1145/3678299.3678343(429-438)Online publication date: 18-Sep-2024
https://dl.acm.org/doi/10.1145/3678299.3678343
Hamanaka MHirata KTojo S(2023)Implementation of melodic morphing based on generative theory of tonal musicJournal of New Music Research10.1080/09298215.2023.216971351:1(86-102)Online publication date: 2-Feb-2023
https://doi.org/10.1080/09298215.2023.2169713
Hamanaka MHirata KTojo S(2023)Time-Span Tree Leveled by Duration of Time-SpanMusic in the AI Era10.1007/978-3-031-35382-6_5(47-58)Online publication date: 22-Jun-2023
https://doi.org/10.1007/978-3-031-35382-6_5
Hirata KTojo SHamanaka MHirata KTojo SHamanaka M(2022)Application of GTTMMusic, Mathematics and Language10.1007/978-981-19-5166-4_9(211-228)Online publication date: 6-Dec-2022
https://doi.org/10.1007/978-981-19-5166-4_9
Foscarin FJacquemard FRigaux PSakai M(2019)A Parse-Based Framework for Coupled Rhythm Quantization and Score StructuringMathematics and Computation in Music10.1007/978-3-030-21392-3_20(248-260)Online publication date: 31-May-2019
https://doi.org/10.1007/978-3-030-21392-3_20

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