Perception of longitudinal components in piano string vibrations

Bank, Balázs; Lehtonen, Heidi-Maria

doi:10.1121/1.3453420

Cited by 11 publications

(10 citation statements)

References 5 publications

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“…[2][3][4][5] In addition to the recent focus on these complications, research within the past two decades has shown that piano strings vibrate in the longitudinal direction, which produces significant audible effects. 3,6 The origin of these longitudinal vibrations and their relationship to the transverse motion are the subject of the work reported here.…”

Section: Introductionmentioning

confidence: 93%

“…However, questions regarding the origins of longitudinal waves in piano strings remain unanswered. Recent studies indicate that longitudinal waves significantly contribute to the piano sound, 6 but the excitation mechanisms that initiate these waves are still not completely understood. 7 Theoretical work on the longitudinal vibrations in strings dates back to the middle of the last century, 8 and there has been significant progress within the last 20 years.…”

Section: Introductionmentioning

confidence: 99%

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Coupling of transverse and longitudinal waves in piano strings

Etchenique

Collin

Moore

2015

The Journal of the Acoustical Society of America

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The existence of longitudinal waves in vibrating piano strings has been previously established, as has their importance in producing the characteristic sound of the piano. Modeling of the coupling between the transverse and longitudinal motion of strings indicates that the amplitude of the longitudinal waves are quadratically related to the transverse displacement of the string, however, experimental verification of this relationship is lacking. In the work reported here this relationship is tested by driving the transverse motion of a piano string at only two frequencies, which simplifies the task of unambiguously identifying the constituent signals. The results indicate that the generally accepted relationship between the transverse motion and the longitudinal motion is valid. It is further shown that this dependence on transverse displacement is a good approximation when a string is excited by the impact of the hammer during normal play.

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Section: Introductionmentioning

confidence: 93%

Section: Introductionmentioning

confidence: 99%

Coupling of transverse and longitudinal waves in piano strings

Etchenique

Collin

Moore

2015

The Journal of the Acoustical Society of America

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“…While digital waveguides are capable of the highly efficient modeling of linear string behavior, they are not very well suited to model nonlinear string vibration. On the other hand, the nonlinear longitudinal vibrations of the low and middle range of piano strings are very important for realistic bass piano sounds [41]. Because of this need, and by the help of increased computational resources, modal-based academic [17,35,42] and commercial 1 piano models have been developed around year 2005-2006.…”

Section: Modal Synthesis Of String Vibrationsmentioning

confidence: 99%

Model-Based Digital Pianos: From Physics to Sound Synthesis

Bank

Chabassier

2019

IEEE Signal Process. Mag.

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Piano is arguably one of the most important instruments in Western music due to its complexity and versatility. The size, weight, and price of grand pianos, and the relatively simple control surface (keyboard) have lead to the development of digital counterparts aiming to mimic the sound of the acoustic piano as closely as possible. While most commercial digital pianos are based on sample playback, it is also possible to reproduce the sound of the piano by modeling the physics of the instrument. The process of physical modeling starts with first understanding the physical principles, then creating accurate numerical models, and finally finding numerically optimized signal processing models that allow sound synthesis in real time by neglecting inaudible phenomena, and adding some perceptually important features by signal processing tricks. Accurate numerical models can be used by physicists and engineers to understand the functioning of the instrument, or to help piano makers in instrument development. On the other hand, efficient real-time models are aimed at composers and musicians performing at home or at stage. This paper will overview physics-based piano synthesis starting from the computationally heavy, physically accurate approaches and then discusses the ones that are aimed at best possible sound quality in real-time synthesis.

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“…They are, however, not considered of perceptual significance in the three highest octaves (above C5), 3 which is the range where duplex stringing generally is considered most important. Longitudinal modes gain much of their energy from transversal string modes.…”

Section: Introductionmentioning

confidence: 98%

Acoustical and perceptual influence of duplex stringing in grand pianos

Öberg

Askenfelt

2012

The Journal of the Acoustical Society of America

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This study investigates the acoustical and perceptual influence of the string parts outside the speaking length in grand pianos (front and rear duplex strings). Acoustical measurements on a grand piano in concert condition were conducted, measuring the fundamental frequencies of all main and duplex strings in the four octaves D4-C8. Considerable deviations from the nominal harmonic relations between the rear duplex and main string frequencies, as described by the manufacturer in a patent, were observed. Generally the rear duplex strings were tuned higher than the nominal harmonic relations with average and median deviations approaching +50 cent. Single keys reached +190 and -100 cent. The spread in deviation from harmonic relations within trichords was also substantial with average and median values around 25 cent, occasionally reaching 60 cent. Contributions from both front and rear duplex strings were observed in the bridge motion and sound. The audibility of the duplex strings was studied in an ABX listening test. Complete dampening of the front duplex was clearly perceptible both for an experiment group consisting of musicians and a control group with naive subjects. The contribution from the rear duplex could also be perceived, but less pronounced.

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Perception of longitudinal components in piano string vibrations

Cited by 11 publications

References 5 publications

Coupling of transverse and longitudinal waves in piano strings

Coupling of transverse and longitudinal waves in piano strings

Model-Based Digital Pianos: From Physics to Sound Synthesis

Acoustical and perceptual influence of duplex stringing in grand pianos

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