A Monte Carlo Study of Entropy from Sound Spectra

Percussion instruments are impulsively excited instruments which would work even if their behavior were strictly linear. They are classified as ``incidentally nonlinear" because, at small excitation amplitudes, their sound output is based entirely upon their natural mode frequencies, despite the fact that nonlinearity sometimes contributes a great deal to their sound. In this work, we studied Shannon entropy of suitably preprocessed Fourier spectra obtained from cuica 8 inches (a brazilian percussion instrument) by Monte Carlo method. First the sound is recorded using a professional microphone and decoded in WAV format through Audacity software. We implemented Fast Fourier transform aplaying MatLab\textregistered package to obtain indexed frequencies spectra. We found fundamental frequencies 661 Hz (E5) to sharp and 347 Hz (F) to bass sound. To each coarse-grain clustered in a subset of harmonics, the power spectrum was binned defining an array, corresponding to a suitable frequency. In this representation, adjacent bins differ by a frequency ratio of one cent. We mapped the correspondends intensities and computed Shanon entropy. We change randomly one of pitches and compute the entropy again. If entropy obtained is lower the change is accept, otherwise restore the previous value. The procedure is iterated until no further improvement restore previous value. This procedure furnish local minimum of the entropy and is inherently sensitive to all frequencies intervals.
The authors thank FAPEMIG by financial support.