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Dept. of Measurement and Information Systems, Budapest University of Technology and Economics

Digital Signal Processing Laboratory

 

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Signal Model Based Synthesis of the Sound of Organ Pipes

 

Introduction

 

It is well known for musicians and also sound engineers that today's exclusively used sound synthesis method in synthesizers and digital instruments is the so-called PCM method to reproduce/recreate the sound of acoustical instruments. The basis of this method is that the sound of the instrument is recorded, the record is compressed ("looped", taking into consideration the periodicity of the signal's stationary part) and stored. The method is even more efficient if it also takes into account that the neighboring pitches of the instrument are nearly the same, so using resampling techniques, even more memory space could be saved. The greatest disadvantage of this method is, however, that it cannot reproduce the stochastical behaviour of the instrument (i.e., noise, modulations, other random events).

 

To eliminate the problems of the sampling synthesis, a new synthesis method has been introduced in the 80's. The Physical Modeling (PM) tries to model not the sound, but the instrument itself. Using the instrument's parameters and its mathematical-physical relationships (based on the differential equations of the musical instrument), the sound of the instrument can be calculated. The problem of this approach is that large computational power is needed for high-quality modeling.

 

The signal model

 

Signal model based synthesis could be a well-balanced compromise between the computation efficiency and the sound quality. In this case first the deterministic and stochastic properties of the sound of an instrument are analyzed. Later, using the parameters come from the analysis, the reproduced sound become high-fidelity if the model is accurate enough.

 

As many of the musical instruments generate nearly periodic sound, the signal model is based on the discrete-time model of the periodic signals. From another point of view we have searched the answer to the following question: Is it possible to generate good-quality model using the classical, Fourier-expansion based (so-called additive) synthesis method, completed with some auxiliary signal processing (such as modulators, noise-generators, filters)?

 

The final organ-model has been set during the experiments (see also the next section). The model has three parts with three different functions (see Figure 1):

  • generator part (the periodic model and a noise generator)
  • transient part (responsible for the attack and decay transient behaviour of the sound, using independent IIR filters, as envelope-generators)
  • other effects part (includes the effect of the different position of the sound, the effect of the hall (reverberation), etc.)

 

 

Figure 1. The signal model used for modeling pipe-organs

 

 

 

Analysis

 

The parameters of the organpipe-models were derived off-line from original pipe-records. We have measured many pipes from three different organs in order to get the quantitative characteristics of each stops, and to set the significance of each parameter (e.g., the precision of modeling the transients).

 

Church of Császár

Church of Naszály

Church of Tata

 

Figure 2. The measured organs

 

Using a fully automatic analysis process, we could find both the determinisctic and stochastic numerical parameters. The whole process can be seen in Figure 3.

 

 

 

 Figure 3. The whole analysis process

 

 

 

Synthesis

 

The synthesis - based on the measured parameters - has been implemented real-time and also off-line. First we have used a Motorola 56001 Digital Signal Processor (DSP), later - to implement more feature - we have changed to an Analog Devices DSP. To make more polyphonic models, an off-line synthesis program under MATLAB has also been developed. The block-diagram of the synthesis can be seen in Figure 4.

 

Figure 4. Synthesis of organ sound

 

 

Results

 

The efficiency of the proposed model can be verified by listening to the sound examples (next section), and also by some quantitative measures. The following two pictures have been made using MATLAB. Figure 5 shows an original and model spectrum, while in Fig. 6 the attack transients of an original and model pipe can be seen.

 

Figure 5. Spectrum of original and model Bourdon pipe

 

 

Figure 6. Attack transients of the first 8 harmonics of an original and modeled Diapason pipe

 

 

Sound examples

 

The following links contain some demonstration records. One can compare original organ sound with its model, off-line simulation results of a larger organ and real-time implementation of one Bourdon register. The files are in mp3 format.

 

Related Publication:

 

János Márkus, Signal Model Based Synthesis of the Sound of Organ Pipes, Master's Thesis (in Hungarian), Budapest University of Technology and Economics, Dept. of Measurement and Information Systems, May 1999, p. 120. 

Detailed discussion of the method in Hungarian.

 

 

Useful Links:

 

Manufacturers of digital organs

 Further information: János Márkus