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

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.

[1]  Stefan Bilbao,et al.  The Changing Picture of Nonlinearity in Musical Instruments: Modeling and Simulation , 2014 .

[2]  V. Braun,et al.  Using thematic analysis in psychology , 2006 .

[3]  Shanmuganathan Rajasekar,et al.  Nonlinear dynamics : integrability, chaos, and patterns , 2003 .

[4]  Christine Anderson Dynamic Networks of Sonic Interactions: An Interview with Agostino Di Scipio , 2005, Computer Music Journal.

[5]  Paul Mulholland,et al.  Investigating the effects of introducing nonlinear dynamical processes into digital musical interfaces , 2015 .

[6]  Insook Choi,et al.  Sound synthesis and composition applying time scaling to observing chaotic systems , 1994 .

[7]  R. T. Schumacher,et al.  ON THE OSCILLATIONS OF MUSICAL-INSTRUMENTS , 1983 .

[8]  Todd Winkler,et al.  Making Motion Musical: Gesture Mapping Strategies for Interactive Computer Music , 1995, ICMC.

[9]  John Bowers,et al.  Simple interfaces to complex sound in improvised music , 2000, CHI Extended Abstracts.

[10]  C. Sparrow The Lorenz Equations: Bifurcations, Chaos, and Strange Attractors , 1982 .

[11]  Sanjaye Ramgoolam,et al.  A remark on T-duality and quantum volumes of zero-brane moduli spaces , 2000, hep-th/0006159.

[12]  Simon Dixon,et al.  A Zoomable Mapping of a Musical Parameter Space Using Hilbert Curves , 2014, Computer Music Journal.

[13]  Matthew Wright,et al.  Problems and Prospects for Intimate Musical Control of Computers , 2002, Computer Music Journal.

[14]  Edwin Prévost,et al.  Free Improvisation in Music and Capitalism: Resisting Authority and the Cults of Scientism and Celebrity , 2009 .

[15]  Derek Bailey Improvisation: Its nature and practice in music , 1980 .

[16]  Yoshisuke Ueda,et al.  Steady Motions Exhibited by Duffing's Equation : A Picture Book of Regular and Chaotic Motions (Functional Differential Equations) , 1980 .

[17]  Holger H. Hoos,et al.  Editors' Notes , 1979, Computer Music Journal.

[18]  Nicola Orio,et al.  Evaluation of Input Devices for Musical Expression: Borrowing Tools from HCI , 2001, Computer Music Journal.

[19]  Grebogi,et al.  Critical exponents for crisis-induced intermittency. , 1987, Physical review. A, General physics.

[20]  Juliana Küster Filipe Bowles Decomposing Interactions , 2006, AMAST.

[21]  Miroslav Spasov,et al.  Using Strange Attractors to Control Sound Processing in Live Electroacoustic Composition , 2015, Computer Music Journal.

[22]  Paul Mulholland,et al.  Dynamical Interactions with Electronic Instruments , 2014, NIME.

[23]  Jeff Pressing,et al.  Nonlinear Maps as Generators of Musical Design , 1988 .

[24]  Chris Kiefer,et al.  Musical Instrument Mapping Design with Echo State Networks , 2014, NIME.

[25]  Simon Waters Performance Ecosystems: Ecological approaches to musical interaction , 2006 .

[26]  D. Francis Review of Basics of Qualitative Research Techniques and Procedures for Developing Grounded Theory (2nd edition) , 1999 .

[27]  B. Kendall Nonlinear Dynamics and Chaos , 2001 .

[28]  George E. Lewis Improvised Music after 1950: Afrological and Eurological Perspectives , 1996 .

[29]  Stefan Bilbao,et al.  Modelling collisions of nonlinear strings against rigid barriers: Conservative finite difference schemes with application to sound synthesis , 2016 .

[30]  A Keep Instrumentalizing: approaches to improvising with sounding objects in experimental music , 2009 .

[31]  N. Fletcher,et al.  The nonlinear physics of musical instruments , 1999 .

[32]  Tom Mudd,et al.  Nonlinear Dynamics In Musical Interactions , 2017 .

[33]  Andrea Valle,et al.  Feedback Systems: An Analytical Framework , 2013, Computer Music Journal.

[34]  Edward Kleinhammer,et al.  The Art of Trombone Playing , 1999 .

[35]  Stefan Bilbao,et al.  Numerical Experiments with Non-linear Double Membrane Drums , 2013 .

[36]  Stefania Serafin,et al.  From Idea to Realization - Understanding the Compositional Processes of Electronic Musicians , 2009 .

[37]  A. Strauss,et al.  The discovery of grounded theory: strategies for qualitative research aldine de gruyter , 1968 .

[38]  Nikolaos Stefanakis,et al.  Sound Synthesis Based on Ordinary Differential Equations , 2015, Computer Music Journal.

[39]  S. Wiggins Introduction to Applied Nonlinear Dynamical Systems and Chaos , 1989 .

[40]  Dan Slater Chaotic Sound Synthesis , 1998 .

[41]  John R. Lindsay Smith,et al.  Clarinet parameter cartography: automatic mapping of the sound produced as a function of blowing pressure and reed force , 2010 .

[42]  Stefan Bilbao,et al.  Finite difference schemes in musical acoustics: A tutorial , 2018 .

[43]  Makis Solomos,et al.  Audible Ecosystems and emergent sound structures in Di Scipio's music. Music philosophy helps musical analysis , 2009 .

[44]  Cyril Touzé,et al.  Modal approach for nonlinear vibrations of damped impacted plates: Application to sound synthesis of gongs and cymbals , 2015 .

[45]  Christopher Haworth,et al.  Ecosystem or Technical System? Technologically-Mediated Performance and the Music of The Hub , 2014 .

[46]  Marcelo M. Wanderley,et al.  Instrumental Gestural Mapping Strategies as Expressivity Determinants in Computer Music Performance , 1997 .

[47]  Y. Pomeau,et al.  Intermittent transition to turbulence in dissipative dynamical systems , 1980 .

[48]  Tina Krekels,et al.  Loosening the saxophone: entanglements of bodies in the politics of free improvisation , 2019 .

[49]  Marcelo M. Wanderley,et al.  Mapping performer parameters to synthesis engines , 2002, Organised Sound.

[50]  Ross Kirk,et al.  Mapping Strategies for Musical Performance , 2000 .

[51]  Richard Glover Minimalism, Technology and Electronic Music , 2013 .

[52]  Stefan Bilbao,et al.  Improved frequency-dependent damping for time domain modelling of linear string vibration , 2016 .

[53]  Anselm L. Strauss,et al.  Basics of qualitative research : techniques and procedures for developing grounded theory , 1998 .

[54]  Ron Kuivila,et al.  Open Sources: Words, Circuits and the Notation-Realization Relation in the Music of David Tudor , 2004, Leonardo Music Journal.

[55]  Dylan Menzies Composing instrument control dynamics , 2002 .

[56]  Pauline Oliveros Acoustic and Virtual Space as a Dynamic Element of Music , 1995 .

[57]  Keith Potter,et al.  The Ashgate Research Companion to Minimalist and Postminimalist Music , 2013 .