The production of phantom partials due to nonlinearities in the structural components of the piano

Rokni, Eric; Neldner, Lauren; Adkison, Camille; Moore, Thomas R.

doi:10.1121/1.5006351

Cited by 4 publications

(1 citation statement)

References 14 publications

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“…It has been proposed [73] that the nonlinear coupling between longitudinal and transverse motion of the string is the origin of so-called phantom partials in piano tones. Though the model ( 29) does indeed produce additional inharmonic partials due to nonlinear mixing, it has been suggested recently that this effect may not be the major contributor to observed phantom partials in the piano, which may be due to interaction between the strings and structural components [74].…”

Section: Full Geometrically Nonlinear Modelmentioning

confidence: 94%

Models of musical string vibration

Bilbao

Ducceschi

2023

Acoust. Sci. & Tech.

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Musical string vibration has been the subject of scientific study for centuries. Recent increases in computational power have allowed the exploration of increasingly detailed features of perceptual significance through simulation approaches. The starting point for any simulation is a welldefined model, usually framed as a system of differential equations, with parameters determined by measurement and experiment. This review article is intended to take the reader through models of string vibration progressively, beginning with well-known and well-studied linear models, and then introducing new features that form the basis for the modern study of realistic musical string vibration. These include, first, nonlinear excitation mechanisms, such as the hammer-string and bow-string interaction, and then the collision mechanism, both for pointwise obstructions and over a distributed region. Finally, the linear model of string vibration is generalized to include geometric nonlinear effects, leading to typical nonlinear behaviour such as pitch glides and the appearance of so-called phantom partials due to nonlinear mixing of modes. The article concludes with a general overview of numerical simulation techniques for string vibration.

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Section: Full Geometrically Nonlinear Modelmentioning

confidence: 94%

Models of musical string vibration

Bilbao

Ducceschi

2023

Acoust. Sci. & Tech.

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Structural contributions to phantom partial generation in the piano

Moore

Neldner

Rokni

2018

The Journal of the Acoustical Society of America

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The results of experiments designed to determine the origin of the anomalous frequency components in the sound of the piano commonly referred to as phantom partials are reported. It is shown that these overtones, which occur at the sum and difference frequencies associated with the transverse string motion, are produced by nonlinearities in both the string and the wooden components of the piano. However, the contribution from the string is significantly smaller than the contributions from other components.

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A finite element model of the Japanese koto constructed from computed tomography scans

Coaldrake

2020

The Journal of the Acoustical Society of America

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This paper presents a method for using computed tomography (CT) scan images of a Japanese koto as the basis of a mesh of a finite element model. The CT images gave access to previously inaccessible internal geometry. Images of grain structure and orientation in all three dimensions of the koto's Paulownia wood was important to the model's development. Obtaining the wood's physical properties for the Voigt notation and using curvilinear coordinates to rotate it to account for the grain was also a critical step. Following the model construction, studies were conducted to investigate the koto's fundamental vibrational behavior. First, the model predicted the koto's mode shapes and frequencies. Simulations in the frequency and time domains also identified unreported aspects of the koto's acoustics. Second, five physical experiments were conducted including transducer studies, Chladni patterns, an acoustic camera tests, and the response of the koto when played. The acoustic camera in particular gave insights into the koto's sound radiation. The combined results advance the limited knowledge of the koto including identifying 100 Hz as the first eigenmode and 85 Hz as a major air mode.

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The production of phantom partials due to nonlinearities in the structural components of the piano

Cited by 4 publications

References 14 publications

Models of musical string vibration

Models of musical string vibration

Structural contributions to phantom partial generation in the piano

A finite element model of the Japanese koto constructed from computed tomography scans

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