PAD AND SAD: TWO AWARENESS-WEIGHTED RHYTHMIC SIMILARITY DISTANCES Daniel Gomez-Mar´ ´ın Sergi Jorda` Perfecto Herrera Universitat Pompeu Fabra Universitat Pompeu Fabra Universitat Pompeu Fabra [email protected] [email protected] [email protected] ABSTRACT scales to determine similarity. In this paper we address the above-mentioned gap and propose two rhythm simi- Measuring rhythm similarity is relevant for the analysis larity distances that refine those currently available (and and generation of music. Existing similarity metrics tend probably rougher than desirable). The proposed distances to consider our perception of rhythms as homogeneous in have been derived from music cognition knowledge and time without discriminating the importance of some re- have been tuned using experiments involving human lis- gions from others. On a previously reported experiment teners. We additionally show that they can be adapted we observed that measures of similarity may differ given to work (at least) in a music-loop collection organization the presence or absence of a pulse inducing sound and the context, where music creators want to organize their build- importance of those measures is not constant along the pat- ing blocks in rhythm contrasting or rhythm flowing ways tern. These results are now reinterpreted by refining the where similarity would provide the criterion for such con- previously proposed metrics. We consider that the percep- catenation of elements. tual contribution of each beat to the measured similarity Previous work has used rhythmic descriptors, computed is non-homogeneous but might indeed depend on the tem- from audio signals, to analyze song databases. A common poral positions of the beat along the bar. We show that collection used for testing genre classification methodolo- with these improvements, the correlation between the pre- gies, The Ballroom dataset, has been sorted automatically viously evaluated experimental similarity and predictions using different rhythmic descriptors and methodologies [4] based on our metrics increases substantially. We conclude [30] [10] [25]. Out of the ballroom dataset very few au- by discussing a possible new methodology for evaluating thors have addressed rhythm in electronic music with rhyth- rhythmic similarity between audio loops. mic descriptors [11] [24] [2]. The logic behind most of these research is the assumption that if a corpus is clas- 1. INTRODUCTION sified according to annotated labels, the features used for that clustering are somehow related to the phenomena that Rhythm similarity is an important problem for both music generates the clustering. In other words, a correct classifi- cognition and music retrieval. Determining which aspects cation implies that the features used are perceptually rele- of the musical flow are used by musical brains to decide vant. if two musical excerpts share similarities with respect to rhythm, would make it possible to build algorithms that Using symbolic representations of music, other authors approximate human ratings about such relatedness. The propose metrics to evaluate rhythmic similarity that have applications of such algorithms in MIR contexts should shown to be useful in melody classification [34] or have be obvious and some have already been addressed [34] proven correlation with cognitive judgements in rhythmic [14] [6] [21]. Unfortunately, there is a gap between the similarity experiments [13] [26] [1]. knowledge provided by cognitive models and engineering However, neither the audio-based methodologies or the models with respect to similarity in general, and rhythm symbolic metrics for rhythm similarity ( [24] being an ex- similarity in particular. Rhythm similarity metrics used in ception) has been designed for exploring short audio seg- MIR are frequently based on superficial information such ments such as loops. Moreover, methodologies to evaluate as inter-onset intervals, overall tempo or beat rate, onset rhythmic similarity between two audio loops and retrieve density, and consider full-length songs to derive a single a value that can be analogous to a human rating are not similarity value. Contrastingly, rhythm similarity models yet available. Therefore we want to develop perceptually developed by cognitive scientists insist on the importance grounded rhythm similarity metrics to be used with short of syncopation, beat salience, periodicities and shorter time- audio loops. Our effort throughout this paper is to present two new rhythmic similarity metrics derived from revisiting the re- c Daniel Gomez-Mar´ ´ın, Sergi Jorda,` Perfecto Herrera. sults of our cognitive experiments on rhythm similarity Licensed under a Creative Commons Attribution 4.0 International Li- perception [9]. After revisiting our previous experiments, cense (CC BY 4.0). Attribution: Daniel Gomez-Mar´ ´ın, Sergi Jorda,` Perfecto Herrera. “PAD and SAD: Two Awareness-Weighted Rhythmic two metrics arise as useful in similarity prediction tasks. Similarity Distances”, 16th International Society for Music Information Based on those metrics we then introduce a new method- Retrieval Conference, 2015. ology to explore rhythmic similarity between audio loops. The metrics proposed are based on the requirement that rhythmic similarity must be rooted in current knowledge of rhythm perception, where the notions of beat entrain- ment, reinforcement and syncopation are fundamental. We hypothesize that a proper rhythmic similarity measure can be built upon those perceptual considerations, emphasiz- ing the idea that our attention when judging the similarity Figure 1. Lerdhal and Jackendorf0s [17] metrical weight between two rhythms is not evenly distributed in time. We profile (left) and the experimentally revised version of specifically propose that we are more aware of certain re- Palmer and Krumhansl [23] measured for musicians(right). gions of a rhythm than others, affecting the way in which we measure their similarity [7]. To test our hypothesis we use the results of perceptual experiments published previ- pected on the beat but were presented on a previous metri- ously [9], where subjects are asked to evaluate the simi- cal position [19]. larity between two monotimbral and monotonic rhythmic In order to represent the variability of expectancies along patterns, inducing a beat before the rhythms are presented. a rhythmic pattern, researchers use profiles that indicate Similarity ratings obtained from the experiment are com- the metrical weight of a note depending on its position. pared with predictions computed with our metrics for the Different profiles that highlight the importance of a beat same rhythmic patterns in order to analyze their correla- reinforcement or a syncopated event, depending on its oc- tion. currence within a full metrical period, have been proposed. High correlation values between the similarity ratings A main theoretical profile [17] and an updated version ex- of our previous experiment and the metrics presented here perimentally revised with musicians [23] are presented in are found, suggesting that blending awareness and synco- Figure 1. These profiles stress the existence of a percep- pation is important for accurately predicting rhythmic sim- tual hierarchy of sound events depending on their occur- ilarity. Although results are promising, there is still a need rence, suggesting that some reinforcements or syncopa- to expand the proposed metrics to include dynamics, dura- tions are perceptually more relevant than others. These tion and timbre, which also have a high impact on our per- ideas have led to algorithms that measure the syncopa- ceptual judgments. Finally we want to explore if the mea- tion of a monotimbral unaccented phrase [31]. Moreover, sures we propose, besides providing good fits and predic- these algorithms have been used to correlate syncopation tions of human judgements, can be used to organize loop with the difficulty to tap along rhythms [5], musical com- collections. The use of our metrics in audio analysis will plexity [32] [8] [28] and musical pleasure and desire to be discussed in the last sections of the paper, where we dance [36] stressing the idea that syncopation has a power- propose a methodology and evaluate it using audio loops ful effect on our perception of music. of drum break patterns. Our results for this pilot valida- tion present significant correlations between the similar- 2.2 Rhythmic Similarity ity judgements of the subjects and the predictions resulting from our methodology. Once we can extract a numerical value from a pattern of onsets such as its syncopation value, comparing patterns and establishing distances between them is mathematically 2. STATE OF THE ART possible. One main approach, proposed by Johnson-Laird [15], is to analyze the onsets present on every beat of a 2.1 Beat Induction rhythmic pattern and subscribe the beat to a category de- The fact that us humans induce a pulse sensation when lis- pending if it reinforces the beat, challenges the beat or tening to music is by no means trivial and it seems to be does nothing to the beat . This approach has been mod- an innate and involuntary process [35]. It is known that ified [29] and successfully tested in experimental condi- the mechanisms that favour our acquisition of a beat when tions [1]. These ideas will be further expanded throughout listening to music can also be triggered by any sequence this paper. of onsets [27]. This emergent beat entrainment is a cog- As most proposed similarity metrics are measured on nitive process