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https://hdl.handle.net/20.500.14094/90005009
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2024-04-20
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90005009 (fulltext)
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メタデータID
90005009
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open access
出版タイプ
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タイトル
Geometric-integration tools for the simulation of musical sounds
著者
Ishikawa, Ai ; Michels, Dominik L. ; Yaguchi, Takaharu
著者名
Ishikawa, Ai
著者名
Michels, Dominik L.
著者ID
A0292
研究者ID
1000010396822
KUID
https://kuid-rm-web.ofc.kobe-u.ac.jp/search/detail?systemId=4d25630092a491db520e17560c007669
著者名
Yaguchi, Takaharu
谷口, 隆晴
ヤグチ, タカハル
所属機関名
システム情報学研究科
収録物名
Japan Journal of Industrial and Applied Mathematics
巻(号)
35(2)
ページ
511-540
出版者
Springer Japan
刊行日
2018-07
公開日
2018-07-10
抄録
During the last decade, much attention has been given to sound rendering and the simulation of acoustic phenomena by solving appropriate models described by Hamiltonian partial differential equations. In this contribution, we introduce a procedure to develop appropriate tools inspired from geometric integration in order to simulate musical sounds. Geometric integrators are numerical integrators of excellent quality that are designed exclusively for Hamiltonian ordinary differential equations. The introduced procedure is a combination of two techniques in geometric integration: the semi-discretization method by Celledoni et al. (J Comput Phys 231:6770-6789, 2012) and symplectic partitioned Runge-Kutta methods. This combination turns out to be a right procedure that derives numerical schemes that are effective and suitable for computation of musical sounds. By using this procedure we derive a series of explicit integration algorithms for a simple model describing piano sounds as a representative example for virtual instruments. We demonstrate the advantage of the numerical methods by evaluating a variety of numerical test cases.
キーワード
Acoustic phenomena
Acoustic simulation
Geometric integration
Musical sounds
Partitioned Runge-Kutta methods
Separable Hamiltonian system
Sound rendering
Sound simulation
Symplectic integration
Virtual instruments
Virtual piano
カテゴリ
システム情報学研究科
学術雑誌論文
権利
© The Author(s) 2018.
This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
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資源タイプ
journal article
言語
English (英語)
ISSN
0916-7005
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eISSN
1868-937X
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関連情報
DOI
https://doi.org/10.1007/s13160-017-0292-6
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