Modeling of the kantele

The kantele is a traditional Finnish plucked string instrument with five metal strings in its basic form. The instrument is bridgeless, so the strings are terminated at one end by metal tuning pins, screwed directly into the soundboard. At the opposite end all strings are wound once around a horizontal metal bar called the varras and then knotted. Due to this special type of termination, the strings experience a strong beating effect. Also, nonlinearities, caused by tension modulation, have a strong effect on the sound.

The following table lists our kantele-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
N/A J. Pakarinen, V. Välimäki, and M. Karjalainen, ''Physics-Based Methods for Modeling Nonlinear Vibrating Strings.'' In Acta Acustica united with Acustica, No. 2, March/April, 2005. Two algorithms for simulating tension modulated strings (e.g. kantele strings) are presented: a spatially distributed waveguide model and a finite difference model. The waveguide model is essentially the same as below, whereas the finite difference model uses time-domain interpolation for modulating the wave velocities. Stability issues for both models are discussed.
J. Pakarinen, M. Karjalainen, and V. Välimäki. ''Modeling and real-time synthesis of the kantele using distributed tension modulation.'' In Proc. Stockholm Music Acoustics Conference, volume 1, pages 409-412, Stockholm, Sweden, August 6-9, 2003. Nonlinear kantele strings are modeled using a waveguide string with spatially distributed fractional delay filters. When the delay time of the fractional delay filters is varied, tension modulation nonlinearity can be simulated.

C. Erkut, M. Karjalainen, P. Huang, and V. Välimäki, "Acoustical Analysis and Model-Based Sound Synthesis of the Kantele," J. Acoust. Soc. Am., vol. 112, no. 4, Oct., 2002, pp. 1681-1691. © Acoustical Society of America, 2002. Reprinted by permission.
Two peculiar features of the kantele tones, i.e., the beating and nonlinear behavior of the harmonics, have been described by analysis, measurements, and synthesis. The effect of the tension modulation driving force (TMDF) is highlighted, and its analytical approximation is derived. TMDF is incorporated into the nonlinear string model in a physically sound fashion.

V. Välimäki, M. Karjalainen, T. Tolonen, and C. Erkut, "Nonlinear Modeling and Synthesis of the Kantele - a Traditional Finnish String Instrument," Proceedings of the International Computer Music Conference (ICMC'99), Beijing, China, Oct. 22-28, 1999, pp. 220-223.
A two-polarizational waveguide model with different delay line lengths is used to simulate the beating phenomenon. The pitch glide effect is modeled by inserting signal-dependent fractional delay filters at the termination of each delay line.

Välimäki, V., Huopaniemi, J., Karjalainen, M., and Jánosy, Z., ''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.
Various analysis and synthesis aspects of several plucked string instruments are discussed. A general physics-based string model for synthesis purposes is proposed. Time-varying fractional delay filters are suggested for modeling the time-varying pitch.

Karjalainen, M., Backman, J., and Pölkki, J., ''Analysis, Modeling, and Real-Time Sound Synthesis of the Kantele, a Traditional Finnish String Instrument,'' in Proceedings of the IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP'93), vol. 2, pp. 229-232, Minneapolis, Minnesota, USA, April 27-30, 1993.
This first scientific work on Kantele synthesis uses a four-delay line waveguide model in simulating the beating effect. The effect of the mode coupling caused by the tension modulation nonlinearity is implemented by integrating the squared delay line contents and summing the result into the output via an experimental filter.

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