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Software simulation of the tone-hole lattice in Clarinet-like systems

Schueller, Fritz and Poldy, Carl 

Arthur Benade introduced the notion of a tone-hole lattice in the early 1960s. He found that there exists a so-called “cutoff frequency” that is determined by the structural dimensions of the tube and its side-holes. Since then several other researchers have studied the properties of the tone-hole lattice, especially dealing with the row of open tone-holes. When simulating mechanical and acoustical systems it is convenient to use electromechanical and electro-acoustical analogies. Highly developed theories for electric networks can thus be directly used to simulate the behaviour of musical instruments. Special software applications, such as Micro-CAP by Spectrum Software of California, an electrical Circuit Analysis Program, can be used for this purpose. To build a bridge from the electrical to the mechanical and acoustical world there exist so called "macros" that were developed mainly by the second author, with mechanical input parameters, so the user need not necessarily think in electrical terms. Examples of such macros are two-ports representing lossy cylindrical and conical tubes, two-poles for short holes etc. all of which occur in wind instruments. Other useful two-ports are ideal transformers for coupling mechanical and acoustical parts of the model. The impedance-versus-frequency diagrams that are easily derived with the aid of Micro-CAP can help to detect influences of the several dimensions of the tone hole system. It is also possible to show pressure and flow profiles along the axis of the tube with opened and closed side-holes. Such work can lead to a further understanding of the properties of real woodwind instruments.