[1.2] After a decade of suspenseful silence, the anticipated book has indeed appeared. Its processive perspective is familiar from the earlier articles, but its topic, the music it discusses, and its grounding in philosophy, psychology, and music theory are fresh. For the importance of its subject, for the quality, consistency, and depth of its theoretical insight, and for the wisdom and clarity of its exposition, Meter as Rhythm should be read and appreciated. It requires a willingness to engage with seemingly small musical details, with diverse musics, and with a speculative, philosophical mode of exposition, but the reader’s persistent efforts will be well rewarded.

[2.2] Hasty problematizes this opposition on both perceptual and logical grounds. As an alternative, he defines meter simply, without reference to accent or pulse, as the potential of a duration to be immediately reproduced. This potential arises in connection with sensations that we gather about events as they "become," or unfold in time. To describe meter from the perspective of an active listener, Hasty appropriates concepts and terminology from Alfred North Whitehead’s Process and Reality. From this perspective, he says, meter is "a process in which the determinacy of the past is molded to the demands of the emerging novelty of the present." (168). It is thus "rhythmic" in the sense that it, too, is emerging, active, creative and perpetually novel.

[2.3] The essence of meter, in Hasty’s theory, is the process of "projection." Specifically, as an event becomes, its duration accumulates "projective potential," or the potential to condition our expectations about the duration of future events. In the simplest case, the duration’s projective potential is "realized" when "there is a new beginning whose durational potential is determined by the now past first event." We perceive this realization when we project that the second event will replicate the duration that it makes past. The second event’s duration may or may not actually realize this projection, and the parity or disparity that is manifest at its end (at the beginning of a third event) corresponds to musical perceptions of "too short" or "too long" that may be expressively and analytically significant.

[3.2] Chapter 9 reworks some traditional conceptions of meter in terms of projection. Metrical accent is defined as "the accent of beginning"; this resembles Jonathan Kramer’s definition (The Time of Music, Schirmer, 1988, p. 86), but has substantive differences. "Beginning" itself is a function that is determined processively—that is, the function of beginning is only perceived as a duration that is begun becomes. The significance of a beginning depends on whether the duration of interest is that of a single event, or of a harmony, or of a series of associated successive durations. In the last case, the later durations in the series contribute to the continuation of the duration of the whole group.

[3.3] Accordingly the distinction between strong and weak (metrical) accent is replaced with a functional distinction between beginning and continuation, as shown in Example 2 (Hasty’s 9.2).

Each small vertical stroke above a note head symbolizes not a beat but to the "becoming" of the entire mensurally determinate duration that is begun by the attack of the note. The larger vertical stroke over the first notehead refers to the becoming of entire duration of two quarter notes; because the half note duration is continued through a series of briefer durations, its onset is called a "dominant beginning." The slanted stroke over the second notehead indicates that, even while its duration begins, the earlier beginning (of the two-note group) is still actively becoming, so the second event’s becoming is a "continuation" of that duration.

[3.4] The functions of beginning and continuation are not immutable. They may be reassessed as later events modify the listener’s sense of what has begun. For instance, anacrusis is understood in this context as a continuation that becomes "detached" from a beginning.

[3.5] Hasty first employs the concepts of projection, beginning and continuation to analyze the meter of common brief durational patterns. The analyses show how patterns with the same meter signature are actually quite different in projective action. They also permit some original and interesting distinctions, such as between acceleration and increased activity of division. Other effects, such as "silent beginning," are also explained as results of projection.

[3.6] Since meter entails the projected reproduction of a duration, duple meter is privileged in the theory. (Indeed the duple bias is reflected frankly in the two-column layout of the book’s text.) Triple meter can nevertheless be explained, however, in the manner shown in Example 3 (Hasty’s 9.18f).

This shows a half-note projection Q, corresponding to a potential duple meter, that is denied by events starting at the asterisk that favor (say, by motivic repetition) a dotted-half projection R. The third quarter note in this situation is then regarded as a "deferral"–it functions to delay the next dominant beginning. More complex meters are also analyzed in similar terms.

[4.2] Analyzing the meter of a musical passage in these terms entails identifying its projections, and distinguishing beginnings, continuations, and anacruses at the beat and measure level. The theory allows one to explain how, in many cases, the basic projection-functions are modified subtly and richly by denials, overlappings, and contractions. A complete analysis thus explains the continuity or discontinuity in a passage, locates certain common types of projections that execute such formal functions as closure, and identifies certain common metrical processes such as the "contraction of projective focus."

[4.3] The emphasis on beat and measure does not preclude a consideration of longer excerpts. A whole chapter is devoted to examining how projection—which is perceived only in relatively brief time spans up to a few seconds—may be "simulated" over larger time spans by means of grouping parallelisms and mutually reinforcing briefer projections. Indeed, in the analyses of common-practice tonal music, the focus is not so much the smaller patterns (which generally accord with the notated meter signature) but on the varieties of larger-scale "hypermetrical" contractions and elisions, and their effect onmus ical continuity. To further clarify how he regards this "simulated" meter, Hasty compares his readings to Schenkerian-oriented analyses by Schachter and Rothstein.

[4.4] One of the most impressive aspects of the book is the variety of music that is analyzed. The tonal works analyzed in depth include the first movement of Beethoven’s First Symphony and the Trio of Mozart’s Symphony No. 35. But there are also quite convincing accounts of meter in non-tonal modernist music by Wolpe and Carter, showing what thwarts larger-scale projections, and explaining how various denials and deferrals of dominant beginnings facilitate continuity and the sustaining of energy. With reference to the Webern Saxophone Quartet Hasty explains how hiatus contributes to the creation of a "phrase" built of successive projective "consituents," each of which possesses varying degrees of openness or closure. He also provides detailed and exciting readings of vocal polyphony by Monteverdi and Sch�tz, readings that convincingly connect the observed metrical effects to the syntax and semantics of the poetry. No one has succeeded better in expressing verbally the rhythmic nature of these musics.

[5.2] It is also remarkable that this carefully elaborated theory—in sharp contrast to some contemporary theories of pitch—emphasizes sensation over structure and feeling over logic. The analyses treat not quantities but qualities of (to cite a few examples) "breadth and spaciousness," "suspense and elasticity," "urgency," "mobility," "relaxation," "focus," and getting "lost in a moment of ending." Style, in this view, "is above all an environmentally (culturally and personally) specific manner of feeling duration." Such statements may appear foreign to some theorists, but Hasty makes them meaningful through a carefully reasoned and clearly expressed theory of how such feelings arise from a single, intuitively plausible principle.

[5.3] Although the content of his projective theory is primarily speculative, Hasty grounds it by telling references to a variety of psychological studies. Further important precedents for his ideas are revealed in the original glosses and interpretations he provides of earlier music theory. Heinrich Koch, for example, is cited to describe meter "as a creative act of attention, not bound by law, but arising from the exercise of our cognitive or imaginative powers. Mattheson’s conception of Bewegung–movement through time–is also cited as an early recognition of the essentially processes aspects of rhythm. The 19^th-century theorist who most anticipates Hasty’s theory is Hauptmann, who clearly discusses meter as a process whereby duration is created, a process grounded in an innate perceptual disposition for measure.

[5.4] Hasty also gives due consideration to recent rhythmic theories—Cooper and Meyer, Lerdahl andJackendoff, as well as Schachter and Rothstein—finding a basis for dialogue even with those that maintain an opposition of meter and rhythm. Other supporting references range widely through twentieth-century philosophy, science, German music theory, and musicology.

[5.6] Some other minor negligences also bother me. The book suffers from a few production problems: a smattering of typographical mistakes in the text, and, more seriously, some rhythmic errors in the musical examples (Ex. 15.2, an excerpt from le marteau, is an especially egregious and by no means solitary instance). More substantively, many analytical decisions about interpreting the onset of an event as a dominant beginning or a continuation hinge on questions of segmentation that are not addressed directly by the theory. Hasty gives the impression that these questions are impossible to address systematically, but a more explicit discussion of segmentation would help justify some of his analytical decisions.

[5.7] This book is not an easy read. The concepts are original and their author is thorough, so their exposition is long, detailed, and philosophical.. Since the theory does not assume any of the common ways of thinking about meter and rhythm, it may not fall into most reader’s comfort zones. Indeed it demands sustained concentration—and a good memory, since the brief index provides little help. But I found it absolutely compelling. It is a vital contribution that has broad potential to affect how we listen, value, and teach music of all styles—potential that will be realized to the extent that we attend to the insights it contains.

2. I gratefully acknowledge Tom Roeder for realizing my design of this example in the Java programming language.
Return to text...