Rhythmic Grouping with the Mutual Nearest-Neighbor Graph and its Application to Predicting Perception of Rhythm Similarity
A formal model of rhythmic grouping is proposed for incorporating grouping information in measures of rhythm similarity, with the goal of improving prediction of perception of rhythm similarity. The grouping algorithm computes the mutual nearest neighbor graph (MNNG) of a rhythm’s onsets by connecting two onsets if both are nearest neighbors of each other. A group is a connected component in this graph. The classical edit distance between two rhythms expressed in box notation is the minimum number of insertions, deletions, and substitutions of pulses, required to transform one rhythm to another. A modification of the classical edit distance is proposed which equals the edit distance plus the weighted difference between the number of groups in each rhythm. Using a dataset of Middle Eastern rhythms, the distances were calculated between every pair of rhythms, yielding a distance matrix. The stimuli in the listening tests were acoustic idealized sounds of the rhythms. Pairwise comparison tests were performed with two groups of subjects that differed in terms of their familiarity with Middle-Eastern rhythms, yielding dissimilarity matrices which were subjected to the Mantel test to determine correlations. For the group familiar with the rhythms, the correlations with human subjects for edit distance alone, and edit + grouping information, were 0.689 and 0.716, respectively. For the group unfamiliar with the rhythms, the correlations with human subjects for edit distance alone, and edit + grouping information, were 0.686 and 0.804, respectively. The proposed MNNG model of rhythmic grouping outperformed other grouping models for both sets of listeners. The results suggest that listeners unfamiliar with rhythms of a culture make increased use of grouping information as a feature for rhythm similarity perception, compared to listeners familiar with the rhythms.