HUT Acoustics Lab

Extraction of Physical And Expressive Parameters for Model-based Sound Synthesis of The Classical Guitar


This URL is a companion to the paper "Extraction of Physical And Expressive Parameters for Model-based Sound Synthesis of the Classical Guitar" by Cumhur Erkut, Vesa Välimäki, Matti Karjalainen and Mikael Laurson, presented in AES108th Convention, Paris in February 2000. Preprints are available under request. The actual sound examples used in the presentation are marked with unfilled circular bullets, which require a gigantic bandwidth. For the ease of downloading, the same examples are mixed to a single channel, downsampled and denoted with the filled square bullets.

0. Introduction

Model-based sound synthesis (a.k.a physical modeling) is one of the active research areas at the HUT Acoustics Lab within the last decade. Model-based sound synthesis is crucial in developing sound source models, which is later used for creating a complete virtual acoustic environment. Three major steps in model-based sound synthesis are:

  1. Developing a generic model for a particular family of sound sources.
  2. Handling the control of the model.
  3. Developing algorithms for calibration of the model parameters

A detailed model for simulating plucked-string instrument family has been described in [1], which allows very realistic synthesis of string instruments. The control problem is usually tackled with general or specially designed real-time controllers. Within the scope of the sound source modeling, an alternative method, which uses traditional common music notation with expressive add-ons for particular instruments to control the real-time synthesizer, has been purposed in [2]. The present paper deals with the third step, i.e., the calibration of the model parameters. The individual character of a specific musical instrument is reproduced only when the model parameters have been carefully calibrated. An example of such a calibration process is described in [2, 3]. A short example, prepared by Mikael Laurson, demonstrates the synthesizer and the calibration procedure prior to the present work described here.

As the following sound example shows, despite the fact that the individual tones sound quite natural in Sound Example 1, the absence of the transients between the plucks degrade the overall naturality of the whole fragment:

This paper describes the add-ons to the calibration process for obtaining efficiency and robustness, and discusses the methods to capture expressive information, mainly to overcome the problems such as in Sound Example 2.

1. The Synthesis Model

The basic string model of Fig. 1 is the core of any guitar model, but when its parameters are calibrated accurately, high quality sounds capturing the characteristics of the classical guitar can still obtained. The basic model is used in the present study for (backwards-) compatibility with earlier papers [3, 4, 5].

2. Extraction of Physical Parameters

The core calibration scheme shown in Fig. 2 is used earlier to extract the parameters of the basic model in Fig. 1. The model parameter outputs are the integer and fractional parts of the delay line length (obtained from the fundamental frequency estimate f0), the gain g and the coefficient a for the loop filter in Eq. 3, and the excitation signal. The following sound example demonstrates the core calibrator outputs: The first tone is the analyzed tone, the second tone is the extracted excitation signal (a plucked-body signal), and the third tone is the resynthesized tone using the extracted parameters.

Although this calibration scheme gives parameters for realistic resynthesis of individual tones, the following problems arose with particular samples:

  1. The analysis points exhibit large fluctuations.
  2. Different SNR values do not allow a fixed thresholding value for termination of several algorithms.
  3. For some tones, very large complex spectral data should be stored.
  4. Sometimes the extracted model parameters gives a different synthetic tone, compared to the original. Then, manual parameter tweaking turns out to be the only solution for naturalness.

Therefore, we propose the extended the calibration scheme shown in Fig. 3. As a preprocessing step, the low-level attributes are extracted, then the STFT-based core calibration scheme of Fig. 2 to extracts the model parameters. The low-level attributes are used to prune the time-domain waveform or the complex STFT matrix. The final iteration block is an optimization routine for fine tuning of the model parameters.

2.2 Optimization

An important phenomenon for string instruments is the two-stage decay, which results from different damping characteristics for different polarizations of the string vibration (for a detailed discussion of the phenomenon and methods to simulate it, see [6] ). Note that the basic string model used in this work is a single polarization model, hence it cannot simulate the two-stage decay. Therefore, the analyzed tones which exhibit this phenomena are the worst-case input signals for the core calibrator. However, the use of the optimization routine helps to deal with this problem, as the following sound example shows. The synthetic tone without the optimization has a very slow decay, but the optimization helps to synthesize a closer tone to the original.

3. Extraction of Expressive Parameters

The strategies for extracting the expressive information from the recorded tones discussed in the paper can grouped as follows:

  1. Expressive information contained in tone-to-tone transitions (such as in the case of damping or repeated plucks): A micro-excitation signal is extracted, and the initial and final values of the loop filter parameters are obtained.
  2. Expressive information contained in variations within a single tone (such as in the case of vibrato): The fundamental frequency trajectories are obtained, a nonlinear LS sine fit to this trajectory gave the desired vibrato depth.
  3. Operations on the excitation signal (such as in the case of different pluck styles and dynamic variations).

3.1 Damping

In classical guitar playing, the strings are damped by the use of the flesh of a right-hand finger. The extended calibration routine of Fig. 3 is executed for the undamped part and the damping part separately, the hop-size for STFT is set to 1/100th of the window length for the damping part. The optimization routine is constrained to change only the loop gain g. The following sound example demonstrates analyzed and resynthesized damped tones, and a short musical fragment of damped tones synthesized by the method discussed in the paper.

3.2 Repeated Plucks

When an already vibrating string is replucked, a phenomenon similar to damping is observed; the flesh of the alternating right-hand finger damps the string for a brief instance. This regime is very short (between 20 and 60 ms), however the removal of this short segment effects the naturalness of the sound. For the resynthesis of the replucked tones, natural sounding tones are obtained, when the damping excitation signals, described in Section 3.1, are used between the repeated plucks. The following sound example demonstrates tones synthesized without and with replucking transient signals, and a short musical fragment of replucked tones synthesized by the method discussed in the paper.

The following sound example demonstrates the use of the method in another musical context, namely tremolo playing:

3.3 Vibrato

The vibrato is produced by repeatedly stretching of the string to fluctuate the fundamental frequency. We analyzed typical slow and fast vibrato regimes on various strings and fret positions by extracting the time-varying fundamental frequency
of each tone using the autocorrelation method and obtained typical vibrato depths by a nonlinear LS sine fit. The following sound examples are composed using the obtained vibrato depths:

3.4 Different Pluck Styles

The extracted piano and forte excitation signals can be derived from the fortissimo excitation signals by proper scaling and low-pass filtering. The coefficients of the pluck-shaping are determined by deconvolution the fortissimo excitation signals with forte and piano excitation signals and performing a weighted fit. The following sound example demonstrates the analyzed and resynthesized dynamics for classical guitar:

4. Conclusions

The following sound examples demonstrate various methods (damping, replucking and pluck-shaping) discussed in the paper. The first example is created with csound using this (zipped) orchestra, score and the sample files.

Some remarks about the demonstration and source files:

  1. The demonstration is created using the simple string model discussed in the paper together with 5 different optimized excitation signals and 4 damping excitations.
  2. The loop-filter parameters are the optimized parameters.
  3. The pluck-shaping filter parameters given in the paper are average filter coefficients, given the fortissimo excitation signals. Since the excitation signals used in the demonstration are forte signals, the pluck-shaping filter parameters are properly scaled.
  4. To obtain a crescendo effect, the pluck-shaping filter parameters are interpolated.
  5. For the sake of demonstration, the damping regimes are overemphasized.

A more natural sounding sound example with the damping excitations is prepared by Mika Kuuskankare, using the full-scale guitar model and the "Expressive Notation Package (ENP)" described in [2].

References

[1] M. Karjalainen, V. Välimäki, and T. Tolonen, "Plucked-string models: from the Karplus-Strong algorithm to digital waveguides and beyond," Computer Music J., vol. 22, no. 3, pp. 17-32, Fall 1998.

[2] M. Laurson, J. Hiipakka, C. Erkut, M. Karjalainen, V. Välimäki, and M. Kuuskankare, "From expressive notation to model-based sound synthesis: a case study of the acoustic guitar," in Proc. Int. Computer Music Conf. (ICMC'99), pp. 1-4, Beijing, China, Oct. 22-28, 1999.

[3] V. Välimäki, J. Huopaniemi, M. Karjalainen, and Z. Jánosy, "Physical modeling of plucked string instruments with application to real-time sound synthesis," J. Audio Eng. Soc., vol. 44, no. 5, pp. 331-353, May 1996.

[4] V. Välimäki and T. Tolonen, "Development and calibration of a guitar synthesizer," J. Audio Eng. Soc., vol. 46, no. 9, pp. 766-778, Sept. 1998.

[5] T. Tolonen and V. Välimäki, "Automated parameter extraction for plucked string synthesis," in Proc. Int. Symp. Musical Acoustics (ISMA'97), vol. 1, pp. 245-250, Edinburgh, UK.

[6] Tolonen, Tero. Model-Based Analysis and Resynthesis of Acoustic Guitar Tones. Master's thesis. Report no. 46 / Helsinki University of Technology, Department of Electrical and Communications Engineering, Laboratory of Acoustics and Audio Signal Processing. TKK, Otaniemi, 1998.


This URL: http://www.acoustics.hut.fi/~cerkut/calib
Last modified: February 29, 2000
Author: Cumhur Erkut