An Oscillator Model of Categorical Rhythm Perception

An Oscillator Model of Categorical Rhythm Perception Rasmus B˚a a ˚ th (rasmus.baath@lucs.lu.se) Erik Lagerstedt (drattans@gmail.com) Peter G¨ardenfors (peter.gardenfors@lucs.lu.se) Lund University Cognitive Science Lund University, Kungshuset, Lundag˚ard, 222 22 Lund, Sweden Abstract Categorical perception is a well studied phenomenon in, for example, colour perception, phonetics and music. In this ar- ticle we implement a dynamical systems model of categorical rhythm perception based on the resonance theory of rhythm perception developed by Large (2010). This model is used to simulate the categorical choices of participants in two experi- ments of Desain and Honing (2003). The model is able to ac- curately replicate the experimental data. Our results supports that resonance theory is a viable model of rhythm perception and they show that by viewing rhythm perception as a dynami- cal system it is possible to model properties of categorical per- ception. Keywords: Categorical perception; rhythm perception; dy- namical systems; resonance theory Introduction Categorical perception occurs when categorization is ampli- fied by the perceptual systems so that distances within a cat- egory are perceived as being smaller and distances between categories are perceived as larger than they are according to the values of some physical measurement. It is a common phenomenon that is well studied in, for example, colour per- ception, phonetics and music (Harnad, 1990). A central ques- tion for understanding categorical perception is: What is the underlying mechanism? There have been attempts to model categorical perception in terms of neural networks (Damper & Harnad, 2000). In this article, we will focus on mod- elling categorical rhythm perception and present a model that is based on oscillators. In the field of music perception rhythm refers to a tempo- ral pattern of sound onsets. A rhythm in this sense does not have to be periodic or recurrent. This is in contrast with how that word is used in other fields (cf. circadian rhythm or delta rhythm). A related concept that does involve periodicity is beat. When listening to a piece of music a common response is to move one’s body with a perceived periodic pulse (Snyder & Krumhansl, 2001), that pulse is the beat of the correspond- ing piece of music. It is not common that all beats in a piece of music are perceived as being equally accented and a peri- odically recurring pattern of strong and weak beats is called a meter. For example, a duple meter would imply that every second beat is perceived as having a stronger accent while ev- ery third beat is perceived as having a stronger accent in the case of a triple meter. Rhythm perception and the ability to entrain to a musical beat was long thought to be uniquely hu- man and, while it has recently been shown that some vocal mimicking species are, to some degree, able to move in syn- chrony with a beat (Schachner, Brady, Pepperberg, & Hauser, 2009), humans are still unique in their aptitude for rhyth- mic processing. Already infants have been shown to have a sense of rhythm (Honing, Ladinig, H´aden, & Winkler, 2009) and there exists only one documented case of ”beat deafness” (Phillips-Silver et al., 2011), that is, the inability to reliably synchronize to a musical beat. Desain and Honing (2003) showed in two experiments that listeners reliably experienced rhythms as belonging to rhyth- mic categories and that categorizations were strongly influ- enced when the listeners were primed with a metric beat be- fore hearing a rhythm. Furthermore, participants agreed to a large degree on which rhythms belonged to what category and, similar to categorization of other kinds of stimuli (c.f. J¨ager (2010) on colour categories), the categories were found to be roughly convex with respect to a temporal performance space (G¨ardenfors, 2000). Honing (2013) concludes that: ”It is puzzling, however, that although meter was shown to exert a strong influence on the recognition of rhythm [. ] existing computational models of meter can explain this phenomenon only to a small extent”. In this article we show that an os- cillation based, resonance theory model of rhythm percep- tion (Large, 1996, 2010) can replicate many of the findings of Desain and Honing (2003). Our results support the notion that resonance theory is a viable model of rhythm perception and show that by viewing rhythm perception as a dynamical system it is indeed possible to model the properties of cate- gorical rhythm perception. Resonance Theory and Categorical Rhythm Perception Modelling of human timing and rhythm perception has a long history. One influential model is the one described by Wing and Kristofferson (1973), which is based on an information theoretic perspective. Like many such models (cf. Repp, 2005), it models a participant’s behaviour when attempting to elicit isochronous timing responses. An alternative to this information theoretic perspective is to take a dynamical sys- tems perspective and model time and rhythm perception as an emergent, dynamic phenomenon. A number of models of this kind have been proposed (e.g., Large, 1996; Noorden and Moelants, 1999). Here, the term resonance theory (cf. Large, 2010) will be used to refer to this type of models. Res- onance theory does not dictate a specific model but rather in- corporates a number of related models. All can be consid- ered as dynamical system models and they consist of one or more resonating oscillatory units. Resonance theory provides a compelling framework since it is biologically plausible, has