Mathematical Modeling of Violin Vibrato Using Frequency Modulation Analysis of Annotated Audio Recordings

Violin vibrato is one of the most important expressive techniques in musical performance. However, mathematical modeling and acoustical analysis may be used to quantitatively analyze it. In this study, a simple sinusoidal model was used to approximate pitch modulation in violin vibrato. Publicly available annotated violin recordings from the Music Vibrato Dataset, including the Yangjian, Laurel, CMMSD, and Coler2011 subsets, were analyzed. 199 annotated vibrato segments were yielded from a total of 17 violin recordings. Among them, 191 met the predefined inclusion criteria for the primary analysis. Pitch values were converted from Hz to cents, while removing linear pitch drift and fitting a sinusoidal model to each vibrato segment to estimate vibrato rate and amplitude. The mean vibrato rate reported 6.541 Hz, and the mean vibrato amplitude reported 16.469 cents. A mean coefficient of determination (R2) was recorded as 0.718 by the sinusoidal model, with 90.1% of the analyzed segments producing R2 to be greater than 0.50. Manually annotated half-cycle measurements were used for validation, demonstrating a strong positive correlation between fitted and annotated vibrato rates (r = 0.810, p < 0.001). These findings indicate that a relatively simple quantitative model can provide a moderate representation of the largely periodic structure of violin vibrato while leaving a meaningful proportion of pitch variation unexplained. In addition, this study highlights the importance of interdisciplinary connection of mathematics, physics, and music through computational analysis of artistic performance, while demonstrating how publicly available dataset may support interdisciplinary research.