If you're familiar with Danuta Mirka's Metric Manipulations in Haydn and Mozart (New York: Oxford University Press, 2009), you might well be asking yourself what is meant by the term ‘hypermetric’ in the title of this recently published sequel. You wouldn't be alone. Although the concept of hypermetre has a considerable historical legacy, discussion about it has until recently been restricted to a small subfield of music theory. Additionally, there is much scholarly disagreement over the idea of hypermetre, the term itself and its implications. Put simply: to hear hypermetre is to hear a metrical order that supersedes the bar line, counting a bar or other lengthy interval as a single beat in a higher order of metric regularity. But how high – that is, up to what extended duration – is this regularity relevant? What is ‘hyper’ about hypermetre, and isn't all of this regularity essentially just more metre? What did eighteenth-century thinkers have to say about it?

These are some of the questions Mirka tackles head-on in her superb and highly musical second volume. Along the way to answering them, she also develops one of the most comprehensive studies of classical phrase theory in recent memory. What makes the book so compelling is how Mirka synthesizes four decades of music-theoretical research on rhythm and metre and deftly weaves in insights from topic theory, schema theory, historical music theory and music cognition. The result is an impressive set of new theoretical tools for eighteenth-century music that pertain not only to hypermetre but also to the analysis of melody, rhythm and small-scale forms.

Mirka carries forward the dynamic model of metre from her earlier book; the theory combines the preference-rule approach of Fred Lerdahl and Ray Jackendoff's A Generative Theory of Tonal Music (Cambridge, MA: MIT Press, 1983) with the notion of projection from Christopher Hasty's Meter as Rhythm (New York: Oxford University Press, 1997). These two seemingly opposed views laid the groundwork for the theory of metre set forth in Metric Manipulations, which relies on cognitive entrainment and the projection of regular durations. In Hypermetric Manipulations, Mirka expands on this theory to explain hypermetre. On the one hand, metre for Mirka is equivalent to entrainment: a mode of attending to or expecting events at regular time intervals. On the other, hypermetre is based on counting, which builds compound projections on top of simple projections: that is to say, hypermetre is a process of consciously predicting the longer, composite spans made up of metric time intervals. With this theoretical move, Mirka answers the fundamental question of what is meant by the ‘hyper’ in hypermetre. Instead of referring to the notation of the barline and its inscribed durations, hypermetre refers to the metre that we hear when actively counting compound projections rather than simply entraining. For this theoretical and analytical insight alone, the book represents a significant step forward in studies of hypermetre.

Mirka plays fast and loose with theories borrowed from music cognition, generative grammar and process philosophy, ignoring their explicit contradictions and conflicts with each other. Unfortunately, she does not imagine the historical theorists in her archive to be as inventive as she is. In chapter one, Mirka reads several texts of eighteenth- and early nineteenth-century music theory in order to provide a historical perspective on the concept of hypermetre. The task is admittedly difficult, because the theorists in question did not use the same terms or work with the same definitions. But in the eighteenth century, theorists and composers began to realize that sometimes single written bars actually contained two small bars inside them (the theory of the ‘compound measure’). And sometimes single bars actually passed by so quickly that each bar could be felt as a single beat (as in the famous Scherzo from Beethoven's Ninth Symphony). Scholars generally point to these phenomena in historical accounts of hypermetre, and there has been some consensus on the topic. William Rothstein has suggested that in developing a theory of ‘higher rhythm’, Gottfried Weber probably drew on late eighteenth-century theories of the ‘compound measure’ penned by Kirnberger, Türk and Vogler (Rothstein, ‘National Metrical Types in Music of the Eighteenth and Early Nineteenth Centuries’, in Communication in Eighteenth-Century Music, ed. Danuta Mirka and Kofi Agawu (Cambridge: Cambridge University Press, 2008), 112–159).

Mirka, by contrast, is surprisingly stiff in her account of this history and strongly rejects Rothstein's genealogy of hypermetre. Citing a few conflicting remarks about accentuation patterns among the theories of Kirnberger, Türk and Vogler, she ultimately concludes that these small differences indicate that there can be no link found between them. She takes a hard-line view of these inconsistencies, asserting in strong terms that ‘Kirnberger's concept of compound meter found no followers except his pupil, Schulz, and generated no line of tradition leading to Gottfried Weber . . . [Kirnberger] would not have endorsed the modern concept of hypermeter’ (8). And, further, ‘Kirnberger's compound meters are unrelated to the modern concept of hypermeter’ (8). No matter what these theorists might have written specifically about accentuation in ‘compound measures’, it is nevertheless clear to me that they understood the notated bar to act, sometimes, as a beat. Mirka herself recognizes this later in the book, within the context of chapter 7's discussion of dissonance treatment. There, she notes that Kirnberger and his pupil Schulz occasionally thought of a single bar as the second half of a larger metric unit, analogous to the second half of a bar. Referring to this insight of Kirnberger and Schulz, Mirka writes: ‘all these examples bear witness to the recognition of higher metrical levels by eighteenth-century music theorists’ (265). The book's internal contradiction on the historical record may reflect an evolution of Mirka's thinking over the time of her writing. For my own part, I would imagine that our eighteenth-century predecessors were just as creative and imprecise as we are, and I would suggest that the strict letters of their definitions do not delimit the breadth and richness of their ideas. I would also add that the history of hypermetre is one that is deeply interwoven with the history of musical notation and of print – a narrative that, unfortunately, is yet to be written in full.

After formulating her own theory of hypermetre in chapter 1, Mirka moves into phrase theory for chapter 2. More precisely, she focuses here on the interaction between hypermetre and phrase structure, a notoriously tricky domain that Rothstein names ‘phrase rhythm’. This is perhaps the best and most useful chapter in Mirka's book. In it, she recovers a long-forgotten taxonomy of hypermetre/phrase alignment from Theodor Wiehmayer's Musikalische Rhythmik und Metrik (Magdeburg: Heinrichshofen, 1917) and updates it using insights borrowed from Eric McKee. Although the different perspectives on phrase rhythm in this chapter are not necessarily new, Mirka's clear and concise synopsis of the theoretical field is powerful, useful and refreshing. I know I will return to this chapter in future analytical work.

Standard classical phrases of four bars generate higher orders of metric regularity. But what happens when those phrases are expanded, contracted, elided and otherwise altered? Mirka takes up these challenges in chapters 3 to 6, which form the heart of the work. In order to grasp properly the complexities of phrase structure, Mirka often moves quite far from hypermetre; she attends in detail to nearly every possible scenario of eighteenth-century phrase manipulation, even when there are no consequences for the hypermetric pattern. There are some very valuable insights in this core part of the book. For instance: phrase elisions can be either ‘left’ (the start of a new phrase elides with the tail of the preceding phrase) or ‘right’ (with the tail of the first phrase eliding with the start of the next). Left elisions are surprising and thrilling, and they create a big, dazzling effect; they are therefore better suited to the symphony and other public genres. Right elisions and overlaps are sneakier, more subtle and intriguing, and are thus best suited to the insider genre of the string quartet (134). There are countless similar gems, in which Mirka brings a distinct perspective on hypermetre together with broad observations on style. Scholarship like this is music theory at its finest.

Not all hypermetric irregularities have their origins in phrase manipulations. Some are the result of sequences, continued figuration, fugato, extended cadences or special rhetorical figures in the composition, and these are the subjects Mirka takes up in chapters 7 and 8. In one of the most exciting discoveries of the book, Mirka reveals the possibility of different metrical profiles for cadential schemata (281–298). Once we hear a cadential pattern initiated and can predict the emphasis given to its most important elements, we might be forced to reorient ourselves within the hypermetric grid. Here, Mirka begins to thematize a favourite cadential trope in Haydn's chamber music, in which the first violinist mounts an ascent into the upper tessitura before dropping to set up an important cadence. Her observations on this phenomenon culminate in the final section of the last chapter.

In lieu of a conclusion, Mirka ends the book with two extended analyses, both drawn from Haydn (String Quartet Op. 50 No. 3, first movement, and String Quartet Op. 64 No. 1, first movement). Counting along with Mirka, I'm convinced by much of what she writes about the hypermetre in these works. But there are plenty of other, different hypermetres I can hear in these pieces also, and I tend to think that the multiplicity of the possible hearings is the point. It's for this reason that I was puzzled to see an old joke recycled in Hypermetric Manipulations, which Mirka borrows from Rothstein, who in turn took it from Carl Schachter: ‘Perhaps’, the joke goes, ‘the government might one day appoint a Commissar of Metrics who will decide such matters for us. Before that day arrives, however, we shall have to live with these disagreements as best we can’ (91). Whatever frisson an oblique reference to a communist official might have had in the 1980s – when Schachter introduced this quip – I get much more of a thrill from the rest of Mirka's compelling book. Her insights suggest that it's ultimately more fun to let the Commissar off duty, count as you like and get lost in the play of confusions. The world of Haydn and Mozart is thankfully full of them.