An Evaluation System for Metrical Models

In the young and rapidly expanding field of music artificial intelligence, one particularly active area of research has been metrical analysis (also known as meter-finding, beat tracking, beat induction, rhythm parsing, and rhythm transcription)—the problem of extracting metrical information from music. Indeed, it would probably be fair to say that no problem in the field has attracted as much attention and energy as this one. Table 1 shows a list of 25 studies that present computational models of metrical analysis. (The table includes all published studies—not master's and Ph.D. theses—that I have been able to identify and obtain. It includes only models that have been implemented or at least completely specified; well-known models in music theory such as Lerdahl and Jackendoff's (1983) are excluded for this reason. Also excluded are models that identify tempo only without identifying actual beat locations, such as Brown 1993. In cases where several studies present close variants of a single model, only one study is listed.)

The models in Table 1 reflect a variety of perspectives on the metrical analysis problem. They might be categorized along several different lines. One fundamental distinction concerns the nature of the input; until recently, almost all systems worked from symbolic ("note") input of some kind, but in the last few years several models have been proposed which operate directly from audio data. Some models assume a quantized input (for example, with durations represented by small integer values), whereas some allow the fluctuations in timing characteristic of human performance; some models generate just a single level of beats, whereas others generate several. Of course, the models might also be categorized in terms of their approach (rule-based, connectionist, oscillator-based, probabilistic, etc.), but this is a more complex matter, so I do not consider it in Table 1.

Perhaps the most basic question to address about a model—though it is not always addressed—is its goal. Some metrical analysis systems are clearly intended to model human cognition; others are simply designed to solve the practical problem of meter-finding in whatever way seems most effective. The importance of meter-finding as a cognitive process seems self-evident; meter is a basic part of musical experience and has been shown to influence other aspects of music cognition as well, such as melodic similarity (Gabrielsson 1973), expectation (Jones et al. 2002), harmony perception (Temperley 2001), performance expression (Sloboda 1983; Palmer 1997), and performance errors (Palmer and Pfordresher 2003). However, the practical problem is important as well. In particular, generating music notation for a piece requires identification of its meter. As argued in Temperley (2001), if we conceive of a metrical structure as a multi-leveled framework of beats (whole-note beats, half-note beats, and so on, down to the smallest rhythmic level in the piece), the metrical structure of a piece essentially provides the information required to rhythmically notate it. And, precisely because of the central role of metrical structure in music cognition (as argued above), it will inevitably come into play in other problems of musical engineering. For example, tasks such as matching queries to a musical database, categorizing pieces by style or mood, or generating an accompaniment for a melody will surely require the consideration of metrical information.

Whatever the goals and assumptions of a metrical model, an important and obvious question to ask is, "How good is it?" That is, what percentage of the time does it actually produce the correct result? (The "correct result" can be defined as the metrical structure inferred by competent listeners. There might, of course, be some subjective differences among listeners; one might also take the music notation for the piece to represent its meter. But in most cases, I would argue, there will be agreement among these sources.) If a model is intended as a practical tool for meter-finding, the importance of this question hardly needs defending. If the model is intended as a hypothesis about cognition, the relevance of its level of performance is less clear. A model could perform perfectly, producing exactly the correct structure (i.e., the one...