An investigation of the second- and higher-order spectra of music
David R. Brillinger, Rafael A. Irizarry · 2011
For a variety of musical pieces the following questions are addressed: Are the power spectra of 1/.f form? Are the processes Gaussian? Are the higher-order spectra of 1/.fform? Are the processes linear? Is long-range dependence present? Both score and acoustical signal representations of music are discussed and considered. Parametric forms are fit to sample spectra. Approximate distributions of the quantities computed are basic to drawing inferences. In summary, 1/f seems to be a reasonable approximation to the overall spectra of a number of pieces selected to be representative of a broad population. The checks for Gaussianity, really for bispectrum 0, in each case reject that hypothesis. The checks for linearity, really for constant bicoherence, reject that hypothesis in the case of the instantaneous power of the acoustical signal but not for the zero crossings of the signal or the score representation. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.