Inner metric analysis as a measure of rhythmic syncopation

Inner Metric Analysis (IMA) is a method for symbolic music analysis that identifies strong and weak metrical positions according to coinciding periodicities within note onsets. These periodicities are visualized with bar graphs known as metric weight and spectral weight profiles. Analyzing these profiles for the presence of syncopation has thus far required manual inspection. In this paper, we propose a simple measure using chi-squared distance for quantifying the level of syncopation found in IMA weight profiles by considering each as a distribution to be compared against (1) a uniform distribution 'nominal' weight profile, and (2) a non-uniform distribution based on beat strength. We apply this measure to the task of predicting perceptual ratings of syncopation using the Song (2014) dataset of 111 single-bar rhythmic patterns and compare its performance to seven existing models of syncopation/complexity. Our results indicate that the proposed measure based on (1) achieves a moderately high Spearman rank correlation (r_s=0.80) to all ratings and is the only single measure that reportedly works across all categories. For so-called polyrhythms in 4/4, the measure based on (2) surpasses all other models and further outperforms five models for monorhythms in 6/8 and three models for monorhythms in 4/4.