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Methodology

In both their 1995 and 1996 papers, Adachi and Sato test lip frequencies over a range from 60 to 700 Hz in increments of 20 Hz in order to excite the first six resonance modes of the trumpet. They use different blowing pressure values for each partial, based on measurements summarized in Elliot and Bowsher (1982). For this project, flip values are tested over the same range, though increments of 50 Hz are used instead of 20 Hz for the sake of efficiency. Values of flip equal to the peaks in the measured impedance were also tested, with the p0 values used in Adachi and Sato (1996), to try to excite the specific resonance modes. For both tests, some lip frequencies were tested using multiple blowing pressures when the flip values fell between two impedance peaks.

Adachi and Sato indicate appropriate values for all predetermined parameter values except for ξequily, the y-coordinate of the equilibrium lip position. They state that this value can be determined as a function of flip and p0 and must be changed to satisfy two conditions: that the maximum amplitude of oscillation is achieved, and that the lips do not come in contact with one another or only have a contact time much shorter than the oscillation period. As they do not provide a methodology for determining ξequily, and as Fréour uses a fixed parameter with no indication of its derivation, for this implementation, a range of ξequily values were tested for each combination of of flip and p0, and the oscillation with the maximum amplitude was chosen when oscillation was achieved. For each combination, eight values of ξequily were tested, ranging from -0.0001 to 0.002m.