Archive
IJMSTA - Vol. 7 - Issue 2 - July 2025
ISSN 2612-2146
Pages: 9
Characterization of idiophonic timbre excerpts by DFA/DCCA auto and cross-correlations methods
Authors: P.J. Gomez Jaime, F.M. Oliveira Filho, G.F. Zebende
Categories: Journal
Abstract - Investigating the relationships within and between time-series, particularly in the context of seasonal variability in meteorological, social, market, and political issues, is common practice. However, discussions and projects focusing on the statistical behavior of sound samples during emissions are relatively less frequent. This paper aims to characterize the time-series memory of two idiophone instruments, the Aerophone and the Cyclophone, by examining their levels of auto-correlation and cross-correlation. To achieve this objective, we applied aspects of timbral segmentation, as outlined by Hajda and Riera, to explore the connection between their fundamental levels and their cross-correlation, thereby deepening our understanding of these sonorities. We designed an exploratory and descriptive methodology with a quantitative approach, utilizing the DFA method to quantify the auto-correlation and the ?DCCA cross-correlation coefficient. Our analysis of the samples revealed a significant change in behavior concerning the auto-correlation function, applicable to the entire time-series or to four specific sub-stretches. This enabled us to calculate two auto-correlation exponents: α1 for small time scales and α2 for large time scales. Subsequently, using the same time-series pieces from both the Aerophone and Cyclophone, we measured the cross-correlation between the left and right channels. In this case, we observed that each instrument has its own unique characteristic pattern.
Keywords: Timbre, Musical Persistence, DFA auto-correlation, DCCA cross-correlation, ?DCCA coefficient
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