Nonlinear Phenomena in Complex Systems, 2010, Vol.13, No.1, pp.70-78

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2010, Vol.13, No.1, pp.70-78

Cautionary Example of Nonlinear Time Series Analysis: From Tones to Sounds.
Said Bešlagić and Matjaž Perc

We study the route from basic tones towards sounds and chords in terms of dynamical complexity of the underlying time series of the sound recordings. Although this route offers increasingly complex waveforms for the analysis, we provide conclusive evidences that even the most complex of them is still periodic. The employed methods of nonlinear time series analysis leading to this conclusion are very instructive, showing how to avoid pitfalls and false claims when trying to distinguish experimentally obtained chaotic traces from those that merely incorporate a large number of harmonic and inharmonic frequencies yet are still periodic. We use methods of nonlinear time series analysis as well as waveforms outputted by a frequency generator and actual recordings of picked guitar strings for the analysis, thus employing resources that are readily available in the lab as well as classrooms.
Key words: quasiperiodicity, chaos, times series analysis, stringed instruments

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