More advanced physical models can be designed,
based on the principles explained in the previous sections.
Resonant Bodies & Coupling
The simple lowpass filter in the example can be replaced by more sophisticated models.
For instruments with multiple strings, coupling between strings can be implemented.
Scattering Junctions
Scattering junctions appear when the acoustic impedance changes,
for example by a change in diameter in a wind instrument.
They can be modeled with allpass filters.
The figure below shows a model of a wind instrument with several waveguides,
connected with scattering junctions (de Bruin, 1995):
@article{bilbao2019physical,
author = "Bilbao, Stefan and Desvages, Charlotte and Ducceschi, Michele and Hamilton, Brian and Harrison-Harsley, Reginald and Torin, Alberto and Webb, Craig",
title = "Physical modeling, algorithms, and sound synthesis: The NESS project",
journal = "Computer Music Journal",
year = "2019",
volume = "43",
number = "2-3",
pages = "15--30",
publisher = "MIT Press One Rogers Street, Cambridge, MA 02142-1209, USA journals-info\textasciitilde …"
}
@inproceedings{chafe2004case,
author = "Chafe, Chris",
title = "{Case studies of physical models in music composition}",
booktitle = "{Proceedings of the 18th International Congress on Acoustics}",
year = "2004"
}
1995
Vesa Välimäki.
Discrete-time modeling of acoustic tubes using fractional delay filters.
Helsinki University of Technology, 1995. [details]
[BibTeX▼]
@book{valimaki1995discrete,
author = "Välimäki, Vesa",
publisher = "Helsinki University of Technology",
title = "{Discrete-time modeling of acoustic tubes using fractional delay filters}",
year = "1995"
}
@article{de1995physical,
author = "de Bruin, Gijs and van Walstijn, Maarten",
journal = "Journal of New Music Research",
number = "2",
pages = "148–163",
publisher = "Taylor \\& Francis",
title = "{Physical models of wind instruments: A generalized excitation coupled with a modular tube simulation platform*}",
volume = "24",
year = "1995"
}
@inproceedings{Karjalainen1993towards,
author = "Karjalainen, Matti and Välimäki, Vesa and Jánosy, Zoltán",
booktitle = "{Computer Music Association}",
pages = "56–63",
title = "{Towards High-Quality Sound Synthesis of the Guitar and String Instruments}",
year = "1993"
}
@article{smith1992physical,
author = "Smith, Julius O",
journal = "Computer music journal",
number = "4",
pages = "74–91",
publisher = "JSTOR",
title = "{Physical modeling using digital waveguides}",
volume = "16",
year = "1992"
}
@article{hiller1971synthesizing,
author = "Hiller, Lejaren and Ruiz, Pierre",
title = "Synthesizing musical sounds by solving the wave equation for vibrating objects: Part 1",
journal = "Journal of the Audio Engineering Society",
year = "1971",
volume = "19",
number = "6",
pages = "462--470",
publisher = "Audio Engineering Society"
}
@article{hiller1971synthesizing2,
author = "Hiller, Lejaren and Ruiz, Pierre",
title = "Synthesizing musical sounds by solving the wave equation for vibrating objects: Part 2",
journal = "Journal of the Audio Engineering Society",
year = "1971",
volume = "19",
number = "7",
pages = "542--551",
publisher = "Audio Engineering Society"
}