Modeling of the acoustic guitar

The acoustic guitar is a widely used musical instrument in various styles of classical and popular music. Some people think that digital synthesis of guitar music must be difficult, because the player can adjust the timbre in numerous ways: by changing the plucking style, the plucking position, or the force applied to the string, for example. Special playing techniques, such as legato and playing of harmonics, are also available. From the engineering viewpoint, all these are control problems, which are related to the playing of the instrument, but not on the sound production mechanism itself. In fact, we consider the acoustic guitar to be one of the easiest musical instruments for synthesis purposes. Still, it is far from being easy. We have improved our guitar synthesizer since early 1990s, and some of us think that it is still not perfect. For playing music with our guitar synthesizer, we need help from our colleagues at the Sibelius Academy (a university of music in Helsinki).

The physical modeling of the acoustic guitar is based on understanding the sound production chain, which we divide in three parts: (1) the plucking, (2) the string vibration, and (3) the soundbox. The soundbox is mainly an acoustic amplifier that is necessary for obtaining a sufficiently loud sound, but it also colors the string sound in an interesting way. Our physics-based guitar synthesizer is based on a simple algorithm, a so called waveguide model, that simulates the string vibration only. The plucking and the soundbox response are currently both included in the input signal of the synthesizer. This principle is called commuted waveguide synthesis. It allows the extraction of input signals for the synthesizer from recorded guitar tones. This process involves inverse comb filtering of the recorded tones so that the harmonics are suppressed.

The following table lists our acoustic guitar-related research in inverse chronological order. For some publications, the PDF-file and a companion web-page containing sound examples are provided. These can be found in the leftmost column.

Publication Short description

J. Pakarinen, ''Physical modeling of flageolet tones in string instruments.'' In the 13th European Signal Processing Conference (EUSIPCO 2005), Antalya, Turkey, September 4-8, 2005.
This paper introduces a physics-based method for synthesising flageolet tones, a.k.a. harmonics, produced by string instruments. The synthesis model is a waveguide string, connected to a wave digital damper. Also, a simplified model and a commuted version is presented.

J. Riionheimo and V. Välimäki, "Parameter estimation of a plucked string synthesis model using genetic algorithm with perceptual fitness calculation," EURASIP Journal on Applied Signal Processing, vol. 2003, no. 8, pp. 791-805, July 2003.
This paper describes a genetic-algorithm (GA) based calibration system on top of our earlier calibration routines for the acoustic guitar synthesizer. The GA-based method takes the waveguide string model parameter values from our previous routines and uses a GA to modify them and the excitation sequence in order to find a better fit to a given recorded guitar tone. It compares the original recorded tone and its own resynthesized tone in terms of an auditory error measure. Auditory masking is accounted for in a way similar to some audio codecs. The GA-based method is fully automatic and it slightly improves the sound quality, although synthesis is still based on our old waveguide string model.
N/A M. Laurson, V. Välimäki, and C. Erkut, "Production of virtual acoustic guitar music," in Proc. AES 22nd Int. Conf. on Virtual, Synthetic, and Entertainment Audio, pp. 249-255, Espoo, Finland, June 15-17, 2002.
In addition to discussing the state of the synthesis model and expressive notation package at that moment, the virtual 24-string acoustic "super guitar" is introduced.

P. Esquef, V. Välimäki, and M. Karjalainen, "Restoration and enhancement of solo guitar record­ings based on sound source modeling," Journal of the Audio Engineering Society, vol. 50, no. 4, pp. 227-236, April 2002.
New propositions to audio restoration and enhancement based on sound source modeling are presented. A case based on the commuted waveguide synthesis algorithm for plucked-string tones is described. The main motivation is to take advantage of prior information of generative models of sound sources when restoring or enhancing musical signals.

M. Laurson, C. Erkut, V. Välimäki, and M. Kuuskankare, "Methods for modeling realistic playing in acoustic guitar synthesis," Computer Music Journal, vol. 25, no. 3, pp. 38-49, Fall 2001.
This article summarizes the achievements on model-based sound synthesis of the acoustic guitar with improved realism. It discusses the calibration of the synthesizer and the implementation with the PWSynth in the ENP (Expressive Notation Package) environment.

M. Laurson, C. Erkut, and V. Välimäki, "Methods for modeling realistic playing in plucked-string synthesis: analysis, control and synthesis," in Proc. COST-G6 Conf. Digital Audio Effects (DAFx'00), pp. 183-188, Verona, Italy, Dec. 7-9, 2000.
Discusses developments in modeling realistic playing in plucked-string synthesis namely, transients between notes, pizzicato, and improved dynamics. Improved dynamics here means parameter estimation and modeling of piano, mezzo forte, and fortissimo plucks with the second-order filters. The implementation with the PWSynth is also discussed.

Penttinen, H., Härmä, A., and Karjalainen, M., ''Digital Guitar Body Mode Modulation with One Driving Parameter,'' in Proceedings of the COST-G6 Conference on Digital Audio Effects (DAFx00), pp. 31-36, Verona, Italy, December 7-9, 2000.
The resonant guitar body is modelled with a frequency warped filter structure. As a result the perceived size of the guitar body can be change by controlling only one parameter. Hence, creating a perceptually and physically inspired sound effect for the guitar. Can be used for acoustic and electric guitars.

T. Tolonen and H. Järveläinen, Perceptual study of decay parameters in plucked string synthesis, in AES 109th Convention, Preprint 5205, (Los Angeles, USA), Sept. 2000.
This paper reports the results of a listening experiment on perception of variation of decay parameters in plucked-string instruments. The results provide audibility thresholds for variation of the overall and frequency-dependent decay. The sounds used in the listening experiment were created with a digital commuted-waveguide-synthesis model.

T. Tolonen, V. Välimäki, and M. Karjalainen, "Modeling of tension modulation nonlinearity in plucked strings," IEEE Transactions on Speech and Audio Processing, vol. 8, no. 3, pp. 300-310, May 2000.
This paper presents a nonlinear discrete-time digital waveguide model simulating a vibrating string exhibiting tension modulation. Furthermore, a technique of obtaining the tension modulation parameter from the recorded plucked string instrument tones is presented. The paper extends the results reported in Välimäki99:ICASSP.

C. Erkut, V. Välimäki, M. Karjalainen and M. Laurson, "Extraction of Physical And Expressive Parameters for Model-based Sound Synthesis of The Classical Guitar," presented at the 108th AES Int. Convention 2000, preprint no. 5114, 52 p., Paris, France, Feb. 19-22, 2000.
This paper revises previous parameter extraction techniques for the classical guitar model and introduces an iterative optimization method. Furthermore, it develops techniques for extracting expressive performance characteristics, such as damping, repeated plucks, vibrato, different pluck styles, and dynamic variations. Some of the techniques developed in this paper are used in Laurson01:CMJ for calibrating the classical guitar model.
N/A Laurson, M., Hiipakka, J., Erkut, C., Karjalainen, M., Välimäki, V., and Kuuskankare, M., ''From Expressive Notation to Model-Based Sound Synthesis: A Case Study of the Acoustic Guitar,'' in Proceedings of the International Computer Music Conference (ICMC 1999), pp. 1-4, Beijing, China, October 22-28, 1999.
The article discusses the Expressive Notation Package (ENP). In addition, analysis and synthesis of vibrato in acoustic guitar is presented.

V. Välimäki, T. Tolonen, and M. Karjalainen, "Plucked-string synthesis algorithms with tension modulation nonlinearity," in Proc. IEEE Int. Conf. Acoustics, Speech, and Signal Processing (ICASSP'99), vol. 2, pp. 977-980, Phoenix, Arizona, March 15-19, 1999.
This paper describes a digital waveguide model of a nonlinear vibrating string when the nonlinearity is essentially caused by tension modulation. In addition, computationally efficient simplified algorithm presented in Karjalainen98:JMC is devised.

M. Karjalainen, V. Välimäki, and T. Tolonen, "Plucked-string models: from the Karplus-Strong algorithm to digital waveguides and beyond," Computer Music Journal, vol. 22, no. 3, 17-32, Fall 1998.
This paper describes how a waveguide model of a plucked string can be reduced to an extended form of Karplus-Strong model. Furthermore, the paper discusses further extensions to the derived model. The model introduced in this paper is widely used and extended in physical modeling of plucked-string instruments.
N/A V. Välimäki and T. Tolonen, "Development and calibration of a guitar synthesizer," Journal of the Audio Engineering Society, vol. 46, no. 9, pp. 766-778, Sept. 1998.
Discusses the development and the calibration routine used for the digital waveguide models amply applied by the Acoustics Lab @ TKK. Also, includes a separate and parametric model for the lowest guitar body modes, running at a slower sampling rate.

Tolonen, T., Välimäki, V., and Karjalainen, M., ''A New Sound Synthesis Structure for Modeling the Coupling of Guitar Strings,'' in Proceedings of the 3rd IEEE Nordic Signal Processing Symposium (NORSIG-98), pp. 205-208, Vigsø, Denmark, June 8-11, 1998.
This paper presents a new synthesis structure for physical modeling of the guitar. The model is capable of simulating the coupling of vibratory motion in guitar strings. The model extends the single-delay-loop model presented in Karjalainen98:CMJ.

Tolonen, T., and Välimäki, V., ''Automated Parameter Extraction for Plucked String Synthesis,'' in Proceedings of the International Symposium on Musical Acoustics (ISMA'97), vol. 1, pp. 245-250, Edinburgh, Scotland, August 19-22, 1997.
An improved parameter estimation algorithm is introduced for acoustic guitar synthesis: The sinusoidal modeling technique replaces the inverse filtering method in the extraction of the input signal. A few low-frequency resonances of the body are extracted and modeled using digital resonant filters.

Tolonen, T., and Välimäki, V., ''Analysis and Synthesis of Guitar Tones Using Digital Signal Processing Methods,'' in Proceedings of the 1997 Finnish Signal Processing Symposium (FINSIG'97), pp. 1-5, Pori, Finland, May 22, 1997. This paper received the Excellent Paper Award.
The second-generation commuted waveguide model is described in this paper that was presented at a national symposium. Improvements are introduced in the parameter estimation procedure and in the efficient implementation of the guitar synthesizer.
N/A Karjalainen, M., and Smith, J. O., ''Body Modeling Techniques for String Instrument Synthesis,'' in Proceedings of the International Computer Music Conference (ICMC96), pp. 232-239, Hong Kong, August 19-24, 1996.
This paper continues the theme of body modeling that was started five years earlier in the WASPAA'91 paper. The warped FIR filter is suggested for obtaining a perceptually good approximation of an impulse response.
N/A V. Välimäki, J. Huopaniemi, M. Karjalainen, and Z. Jánosy, "Physical modeling of plucked string instruments with application to real-time sound synthesis," Journal of the Audio Engineering Society, vol. 44, no. 5, pp. 331-353, May 1996.
Our first journal paper on physical modeling synthesis describes all aspects of the early commuted waveguide synthesizer. The main application is high-quality synthesis of acoustic guitar tones, but also several others string instruments are mentioned, such as the electric guitar and the kantele. Many methods explained here, for example the one-pole loop filter (see Eq. (6)) and the inverse filtering techniques, have been used for many years in almost the same form.
N/A Jánosy, Z., Karjalainen, M., and Välimäki, V., ''Intelligent Synthesis Control with Applications to a Physical Model of the Acoustic Guitar,'' in Proceedings of the International Computer Music Conference (ICMC'94), pp. 402-406, Aarhus, Denmark, September 12-17, 1994.
Rules-based methods to assist the player to control a physical modeling synthesizer are introduced. Related real-time demos included triggering of strumming using a single key on a MIDI keyboard, for example.

M. Karjalainen, V. Välimäki, and Z. Jánosy, "Towards high-quality synthesis of the guitar and string instruments," in Proc. Int. Computer Music Conf. (ICMC'93), pp. 56-63, Tokyo, Japan, Sept. 10-15, 1993.
This is our second paper on commuted waveguide synthesis. Parameter estimation methods using the short-time Fourier transform and others techniques are described. Julius O. Smith presented the commuted waveguide synthesis in the same conference.
N/A M. Karjalainen and V. Välimäki, "Model-based analysis/synthesis of the acoustic guitar," in Proc. Stockholm Music Acoustics Conf. (SMAC'93), pp. 443-447, Stockholm, Sweden, July 28-Aug. 1, 1993.
The commuted waveguide synthesis principle was first published in this paper. The sound quality of acoustic guitar synthesis was much improved by using a sampled body response as the input signal to a waveguide string model. Julius O. Smith at Stanford University independently invented the same idea.
N/A Karjalainen, M. and Välimäki, V. ''Implementation and Real-Time Synthesis of String and Wind Instruments on a Floating-Point Signal Processor,'' in Proceedings of the 6th European Signal Processing Conference (EUSIPCO'92), vol. 3, pp. 1717-1720, Brussels, Belgium, August 24-27, 1992.
The early real-time implementations of the TKK Acoustics Lab physical modeling synthesizers are described. Those days we used a Texas Instruments TMS320C30 signal processor.
N/A Karjalainen, M., Laine, U. K., Laakso, T. I.,and Välimäki, V., ''Transmission-Line Modeling and Real-Time Synthesis of String and Wind Instruments,'' in Proceedings of the International Computer Music Conference (ICMC'91), pp. 293-296, Montreal, Quebec, Canada, October 16-20, 1991.
Our early work on physical modeling of the guitar and the flute is summarized. The methodology used is currently called digital waveguide modeling.
N/A M. Karjalainen, U. K. Laine, and V. Välimäki, "Aspects in Modeling and Real-Time Synthesis of the Acoustic Guitar," in Proceedings of the IEEE Workshop on Applications of Signal Processing to Audio and Acoustics (WASPAA'91), New Paltz, NY, USA, October 20-23, 1991.
Synthesis of acoustic guitar tones using waveguide modeling techniques are described. Experiments on modeling the impulse response of the guitar body using high-order FIR and IIR filters are discussed.
N/A M. Karjalainen and U. K. Laine, "A Model for Real-Time Sound Synthesis of Guitar on a Floating-Point Signal Processor," in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'91), vol. 5, pp. 3653-3656, Toronto, Canada, May 14-17, 1991.
This was the first publication of the TKK Acoustics Lab on physical modeling synthesis. A waveguide model was used for simulating the string vibration. The Lagrange interpolation filter was proposed for implementing the fractional delay required for fine-tuning the pitch and for continuously changing the string length, such as in glissando playing.

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