A method for calculating the largest Lyapunov exponents analogs for the numerical series obtained from acoustic experimental data is proposed. It is based on the use of artificial neural networks for constructing special additional series which are necessary in the process of calculating the Lyapunov exponents. The musical compositions have been used as acoustic data. It turned out that the error of the largest Lyapunov exponent computations within a single musical composition is sufficiently small. On the other hand for the compositions with different acoustic content there were obtained various numerical values Lyapunov exponents. This enables to make conclusion that the proposed procedure for calculating the Lyapunov exponents is adequate. It also allows to use the obtained results as an additional macroscopic characteristics of acoustic data for comparative analysis.