Technique for the Analysis of Musical-Instrument Tones
M. David Freedman · The Journal of the Acoustical Society of America · 1965
A technique that can be used to analyze the transient part of a musical tone has been developed. The analysis can be carried out on a high-speed digital computer, the signals being presented to the computer through an analog-digital converter. The analysis procedure consists of four steps: (1) the determination of an adequate mathematical specification for an equation to represent the sound-pressure-wave generated by a musical instrument; (2) the determination of the constants in the equation for a given tone (No assumption is made regarding the frequencies of the partial tones. Inharmonic partials are detected and accounted for in the specification function.); (3) the verification of the results, both mathematically and by resynthesis of the tone (using a digital-analog converter), to check the adequacy of the representation (the former technique yields a more sensitive measure of the error.); (4) iterating, if necessary, to improve the results. At this stage, the original specification function may be altered, if necessary. Using this technique, reasonable success has been achieved in analyzing and resynthesizing tones.