Our research provides a thorough nonlinear analysis of the acoustics of the tarka, a musical instrument played during Carnival in the Andean region of Bolivia, Southern Peru, and Northwestern Argentina. While the musical properties of the tarka have been studied for many years, there is a little analysis on its physical properties, in particular, an explanation for the instruments characteristic rasping timbre. The tarka produces two different musical sounds with different digitizations, the roll and non-roll. These sounds are multiphonic, generated by a monophonic instrument in which two or more pitches can be heard simultaneously. Time series analysis using concepts such as power spectra, autocorrelation function, chaoticity tests, phase space reconstruction, Lyapunov exponents, and entropy-complexity measures have been used to characterize the tarka's sounds. This interplay of spectral techniques, nonlinear analysis, and the peculiarities of the tarka gives us a unique insight into the acoustics of artisanal instruments and furthermore an explanation relevant to other nonlinear generators.