Time-Integrated Curvature of Fundamental Frequency as a Novel Approach to Pitch Complexity: Insights From...

Commonly used methods for computing the fundamental frequency (F0) variability either fail to capture time-dependent variations (such as the range, standard deviation, and coefficient of variation) or are abstract in terms of interpretations (such as polynomial regressions fitted over an annotated region). A novel approach based on time-integrated curvature was proposed to capture temporal variations in the F0 across an utterance. A corpus comprising one group of adults and three age groups of children was used to perform a preliminary test of this method in comparison with the range and coefficient of variation.

The time-integrated curvature of F0 was computed based on the second derivative of F0, which indicates its bending direction and the degree at each instant. The second derivative was squared, integrated, and normalized to the utterance length to obtain an estimation of the total time-dependent variations in F0. Linear mixed-effects models were used to evaluate the effect of age group on the new method, as well as the F0 range and coefficient of variation.

Both the coefficient of variation and the time-integrated curvature of F0 showed a significant effect on age groups. While the coefficient of variation showed a significant difference between adults and children in general, the time-integrated curvature also demonstrated similarities in neighboring age groups. These results are in line with previous research showing that children do not produce adultlike complexities in pitch contours.

This study demonstrated that the novel approach provided valuable insights into first-language pitch development and indicated further applicability in areas where time-dependent F0 variations are relevant, such as speech pathology and forensic voice comparison.