Finite-Difference Schemes in Musical Acoustics: A Tutorial

Bilbao, Stefan; Hamilton, Brian; Harrison, Reginald; Torin, Alberto

doi:10.1007/978-3-662-55004-5_19

Cited by 17 publications

(54 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Various schemes have been devised to approximate equation ( 2) [6]. These methods demand meticulous handling to address potential issues stemming primarily from numerical errors.…”

Section: Methodsmentioning

confidence: 99%

“…Notably, I (l)→(t) and I (t)→(l) correspond to the p-th order upsampling interpolant of the spatial grid and its corresponding downsampling operation, respectively. For more exploration of the intricacies of this scheme, we encourage interested readers to refer to Bilbao [6].…”

Section: Methodsmentioning

confidence: 99%

“…Diverse perspectives within the sound synthesis domain, some possessing a physical interpretation and others diverging from such constraints, have enriched the field. However, this paper is firmly centered on physical modeling, particularly focusing on the finite difference method [6,7].…”

Section: Introductionmentioning

confidence: 99%

“…Kirchhoff [16] and Carrier [17] introduced a generalization of a wave equation to a nonlinear string model, where the longitudinal motion is averaged over the length of the string and only transverse motion is explicitly modeled [6]. While this approximation is valid under certain conditions [24], perceptually important effects such as phantom partials arise from the coupling between longitudinal and transverse motion [23].…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

A Study on Research Trend of Thesis and Dissertation in the Department Korean Traditional music at Seoul National University

Lee¹

2019

Tongyang Ŭmak

View full text Add to dashboard Cite

For the right-angled Artin group action on the extension graph, it is known that the minimal asymptotic translation length is bounded above by 2 provided that the defining graph has diameter at least 3. In this paper, we show that the same result holds without any assumption. This is done by exploring some graph theoretic properties of biconnected graphs, i.e. connected graphs whose complement is also connected.

show abstract

“…Various schemes have been devised to approximate equation ( 2) [6]. These methods demand meticulous handling to address potential issues stemming primarily from numerical errors.…”

Section: Methodsmentioning

confidence: 99%

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

A Study on Research Trend of Thesis and Dissertation in the Department Korean Traditional music at Seoul National University

Lee¹

2019

Tongyang Ŭmak

View full text Add to dashboard Cite

show abstract

“…Playing an instrument is therefore the navigation of the phase space of this system, the governance of the forces affecting the behavior of a specific trajectory through the possible states of the instrument. This comparison is not presented merely as an analogy: Many current digital models of musical instruments are based on nonlinear differential equations that precisely describe systems of this kind (Bilbao et al 2018). The elaboration of the complexity of these systems is presented here as a way into discussions on the inherent complexity and nuance often found in interactions with acoustic musical instruments.…”

Section: Interactions With Nonlinear Dynamic Processesmentioning

confidence: 99%

The Role of Nonlinear Dynamics in Musicians' Interactions with Digital and Acoustic Musical Instruments

Mudd

Holland

Mulholland

2019

Computer Music Journal

View full text Add to dashboard Cite

Nonlinear dynamic processes are fundamental to the behavior of acoustic musical instruments, as is well explored in the case of sound production. Such processes may have profound and under-explored implications for how musicians interact with instruments, however. Although nonlinear dynamic processes are ubiquitous in acoustic instruments, they are present in digital musical tools only if explicitly implemented. Thus, an important resource with potentially major effects on how musicians interact with acoustic instruments is typically absent in the way musicians interact with digital instruments. Twenty-four interviews with free-improvising musicians were conducted to explore the role that nonlinear dynamics play in the participants' musical practices and to understand how such processes can afford distinctive methods of creative exploration. Thematic analysis of the interview data is used to demonstrate the potential for nonlinear dynamic processes to provide repeatable, learnable, controllable, and explorable interactions, and to establish a vocabulary for exploring nonlinear dynamic interactions. Two related approaches to engaging with nonlinear dynamic behaviors are elaborated: edge-like interaction, which involves the creative use of critical thresholds; and deep exploration, which involves exploring the virtually unlimited subtleties of a small control region. The elaboration of these approaches provides an important bridge that connects the concrete descriptions of interaction in musical practices, on the one hand, to the more-abstract mathematical formulation of nonlinear dynamic systems, on the other.

show abstract

Simulation of the geometrically exact nonlinear string via energy quadratisation

Ducceschi

Bilbao

2022

Journal of Sound and Vibration

View full text Add to dashboard Cite

Finite-Difference Schemes in Musical Acoustics: A Tutorial

Cited by 17 publications

References 53 publications

A Study on Research Trend of Thesis and Dissertation in the Department Korean Traditional music at Seoul National University

A Study on Research Trend of Thesis and Dissertation in the Department Korean Traditional music at Seoul National University

The Role of Nonlinear Dynamics in Musicians' Interactions with Digital and Acoustic Musical Instruments

Simulation of the geometrically exact nonlinear string via energy quadratisation

Contact Info

Product

Resources

About