The development of a modular paradigm for the physical modelling of musical instruments
Introduction
The in house research aims to investigate, develop and evaluate a modular and extensible paradigm for the software based construction of physical models of real musical instruments. Together with the ongoing experimental analysis of acoustic instruments and the interrelationship of their physical components such as excitation mechanisms, wave-guides, resonators; the project will use results to develop flexible, user-friendly software for the study and synthesis of musical instrument sounds. The software will model in detail the numerous physical processes involved in the generation of musical sound as individual modules of functionality that can be selected and interconnected by the user. Hence, the relative influence of the individual elements of sound generation and their inter-relationship will be investigated.
Background
Early sound synthesis techniques such as the addition of multiple harmonic oscillators or the filtering of harmonically rich single oscillators (Moog) have been complimented in recent years with frequency modulation (Chowning), granular (Roads) and wave-table synthesis techniques. All techniques have their own strengths and weaknesses when it comes to acoustic simulation and creative potential so many modern synthesisers offer the ability to mix and match. Modular sound synthesis is not new being originally based on interconnected analogue hardware it has found new popularity within recent software based synthesisers. However these modular synthesisers do not simulate the underlying mechanical processes of sound generation, so fail to recreate many of the subtitles of real musical instruments.
Physical modelling of musical instruments is where the elements of sound generation, propagation and auralisation are simulated by software in terms of energy convolution and transfer within and from the physical mechanisms of musical instruments. The real-time application of sophisticated physical modelling is relatively new having been facilitated by developments in ever more powerful digital hardware. Although algorithms for specific instrument types are being used commercially the scope for manipulation is limited. Typically physical modelling algorithms attempt to model the propagation of energy across one or more excited wave-guides (Karplus Strong) which is hence attenuated by bounding filters and tapped for further processing. Alternatively models may solve the wave equation (Hiller). Filters can also be used to simulate the formants of a resonating body before rendering the sound with appropriate reverberation (Schroeder). Many of the recent implementations of physical modelling have been proprietary and inflexible providing little scope for the researcher, student and sound designer to investigate and modify processes.
A modular paradigm for physical modelling would provide greater opportunities for the analysis, development and tweaking of physical models to accurately simulate real and imaginary musical instruments. Hence the user will be able virtually recreate the various physical elements that combine to create musical sound in a way that is both flexible and efficient. There will be no need to re-implement common elements for different instruments. Instead it will be the arrangement and relationship between constituent elements that define the sound.
Although there is a wide range of different physical mechanisms employed by different musical instruments most share striking similarities. Most instruments have mechanical excitation mechanisms, wave-guides bounded by impedances and resonating bodies that dynamically modify the resulting frequency spectrum. The resulting sounds generated are then propagated within a performance space and localised by the listener’s binaural hearing. The modular paradigm caters for both diversity and commonality of the sound creation process.
Programme Methodology
As well as drawing on existing literature the research project will have on going experiments and analysis together with software implementation and subjective evaluation stages. The table1 outlines necessary work.
Software development will be based on modern PCs with common soundcards using Visual C++ and Microsoft’s DirectX applications programming interface. The architecture will be extensible providing an easy means for future developers to add new and improved modules.
The user interface will allow the researcher, student or musician to select from menus lists of excitation mechanisms (plucks, hammers, bows, reeds, etc), wave-guides (strings, air columns, bars, membranes, etc) and resonators (boxes, sound boards, metal frames, etc) which can be place on a working area as icons. The icons can hence be linked directly or via other modules representing say bridges, nuts, dampers, etc.
Each icon when double clicked could provide the user with a series of adjustable parameters, for instance a string’s density, dimensions and constant of elasticity. The module paradigm can also be used laterally where each element is itself a collection of interconnected sub elements. For instance a bridge will have damping, stiffness and mass elements that determine impedance at the boundaries of oscillation. The different bridge elements define a complex behaviour where resonance or over damping may be exhibited. The relative strengths of stiffness and mass elements determine whether modes of vibration are harmonic or skewed so influencing the timbre of the instrument.
Individual physics elements effectively convolute energy transfer from input to output ports. Two port analysis techniques are a good example of how such processes can be modelled. A modular system would take account of the non-linear flow of energy and the importance of feedback loops.
The figure1 shows a very simplified version of how the user interface might look where icon representations of physical elements can be selected from a main menu and interconnected.
Experiments will involve the measurement of simplified and complex mechanical elements of musical sound generation with a view to understanding the energetic and temporal behaviour of processes and the importance inter linkage between elements. For instance the anechoic measurement of the time dependant nature of frequency spectrums for independent and inter linked wave-guides and resonators with respect to varying parameters and excitation mechanisms would provide important clues as to how best to simulate the interconnected elements. Of particular interest is the dynamic and temporal behaviour of a wave-guide’s boundary conditions, resonator formants and the influence of sound propagation within resonators. There will also be a need for some offsite measurement for larger musical instruments such as pianos, organs, etc.
Figure 1 : Example user interface
Further experiments will compare the constructed simulations of musical instruments with real equivalents. A degree of subjective testing will be required to evaluate the simulations and the usability of the software.
The modular paradigm allows a mixture between experiment, analysis and implementation in an on going and complimentary way.
Relevance to Beneficiaries
Research into the individual elements of musical sound generation would be greatly facilitated by the feedback that computer models provide. Modelling of individual interconnected elements gives both the researcher and the musical acoustics student an insight into the influence and interrelationship of physical elements. Thus putting them in a better position to improve the sound of real, recorded and simulated musical instruments.
Typically musicians require a large, rich canvas of authentic musical instrument simulations and the creative opportunities to develop new sounds. There is a wide range of different musical instruments from around the world that musicians would like to incorporate into their compositions without many of the artefacts and expressive limitations of conventional synthesis and sampling techniques. Physical modelling is clearly the way forward though the variety of instruments and creative requirements to find new sounds requires a flexible, adaptable and efficient paradigm.
References and Links
Chowning, J. (1977) "The Synthesis of Complex Audio Spectra by Means of Frequency Modulation," Journal of the Audio Engineering Society 21(7), 1973; reprinted in Computer Music Journal 1(2),.
Cook P. R.(1995) "A Hierarchical System for Controlling Synthesis by Physical Modeling," International Computer Music Conference, Banff
Hiller L. & Ruiz, P.(1971).
Synthesizing musical sounds by solving the wave equation for vibrating
objects: Part I. Journal of the
Audio Engineering Society, 19(6), 462-470.
Karplus, K. & Strong, A.(1983). Digital Synthesis of plucked-string and drum timbres. Computer Music Journal, 7(2), 43-55.
Moog, R. (1965) Voltage Controlled Electronic Music Modules, Journal of the Audio Engineering Society Vol. 13, Number 3 pp. 200
Morrison, J., Adrien, J.M., (1993) "MOSAIC: A Framework for Modal Synthesis", Computer Music Journal, Vol. 17, No. 1, pp. 45-56
Moore, R.F.(1990). Elements of
Computer Music. Englewood Cliffs, NJ: Prentice-Hall.
Porcaro N. , Scandalis P. , Smith J. O., Jaffe D. A., Stilson T. , (1995), “SynthBuilder--a graphical real-time synthesis, processing and performance system”, in Proceedings of the 1995 International Computer Music Conference, Banff, pp. 61-62, Computer Music Association,
Roads, C. Granular synthesis of sound. In Foundations of Computer Music. C. Roads and J. Strawn, eds. MIT Press, Cambridge, pp. 145—159, 1985.
Smith, J. O. (1992) Physical modeling using digital waveguides', Computer Music Journal, vol. 16, no. 4, pp. 74-91
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