This article is in five sections, each of which deals with a problem basic to the theory of musical meter. The first sets up a conceptual framework in which meter, group structure, and accent are related to one another. The second explores the practical and aesthetic functions of metric perception. In the next section, grouping and accent, as the determinants of meter, are thoroughly investigated. A penultimate section discusses several operations of metric distortion, and the final section considers the bases for, and significance of, deeper levels of meter. In a general sense, the article attempts to make sense out of the tangle of conflicting views that constitutes the recent literature on this subject. Each of its sections departs from a survey of prevalent views and proceeds to mediate among these by integrating them in a general framework in which they are more or less easily accommodated without mutual contradiction.

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In this study I examine some relations between pieces and the models we make to represent pieces. I use the terms "piece" and "model" with reference to someone's experience of a musical work. The piece is that level of such an experience at which eventfulness is of such density and particularity as is sufficient to establish the identity of the work in question. In contemporary music theory, models are usually spoken of as ordered hierarchies of levels. I accept this characterization of our musical experiences as multi-levelled, but I will speak here of a model as an expression of one level in such a hierarchy, one of those at which eventfulness is determined by one or more of several considerations, such as the need to memorize a work, the desire to relate it to other works, or the simple impulse to understand it better. This is because my present concern is not with the logic which relates the stages in a hierarchy of experience, but with comparisons between things which are basically of the same type. Only single levels extracted from the totality of an experience of a work share with the piece its basic attribute of comprising certain events and no others. In other words, only single levels can be listened to as if they were pieces of music. Eventfulness in a model need not be of lower density than eventfulness in the corresponding piece, and there are many examples in music theory of models containing more events than the piece-segments they represent. 1 This would not be appropriate, however, in the case of a model of underlying structure. Such a model attempts to capture a level of experience at which a work is grasped as a single pattern or unitary structure rather than as a concatenation of patterns or composite of parts. It is inconceivable that a set of events larger than that comprising a piece would be grasped in this way. For this reason, I will say that the relation "being a model of the underlying structure of" implies "being in a one-to-many correspondence with," where l As an illustration, consider one of the standard explanations of the prohibition of direct octaves: the piece contains direct octaves, the model, as a result of added events, "hidden" parallel octaves. Frequent instances of models with added events are found in the works of Kirnberger, Sechter, and other fundamental-bass theorists; for example, the progressions IV-V and VI-V, occurring in some piece, may be understood to express the fundamental-bass succession II-V, a notion which leads to the addition of an implied root-that of the II-in the model.

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It seems as if we've finally begun to figure out how to get into those mysterious houses built just after the turn of the century by Schoenberg and Webern. To say that we've found the keys does not, however, represent an apt way of narrowing the metaphor, since, for better or for worse, they built these houses without doors. At best they may be said to have painted door-like signs on their exteriors, or, in some cases, to have graced their facades with doors grouped in threes and fours, leading not to the inside but instead to one another and back out.The use of keys is not recommended in connection with attempts to penetrate doorless, lockless houses, even if these be the well-worn master keys with which much success has been had in the past. Entry is gained only by dismantling part of the structure, for which task keys are not the implement of choice. New tools are needed to do this kind of work: powerful precision tools which can be modified to meet the demands of particular jobs.The tools developed in recent years by people who care deeply about motivic or, as it is often called, atonal music do appear to be tools of the required sort. With respect to power, precision, and flexibility, the set-theoretic concepts developed by Babbitt, Lewin, Perle, Martino, Howe, and, most notably, by Forte constitute an avenue of approach to this music which is impressive in its potential. At the same time, the nascent overview of what this music is all about, one emerging as a result of initial attempts to apply these concepts, is not an encouraging one and tends to undermine the positions of those who regard this repertoire as a musical legacy of the first rank.The problem as I see it resides not in the tools but in the manner of their application. Precision equipment for penetrating facades it not designed to be hurled like a demolition ball at the objects it is meant to transform. One is better off, on the whole, with crude tools employed with subtlety than with a refined technology for which one lacks the appropriate strategies.In my view, misuse of the new technology for dealing with motivic music has taken the form of attempts to apply all of the relations defined in the theory of unordered pitch-class sets to each an every analytical context. Instead of regarding the theory as a universe of possible relations and trying to determine criteria for deciding which relations are actually germane to