At moments of cadential expectation in 'Noctuelles', Ravel suddenly introduces motifs of short, irregularly grouped rhythmic values that suspend the basic pulse, dissipate the rhythmic energy, fragment the prevailing 3/4 meter, and disrupt hypermetric regularity. In this way, Ravel delays the clear establishment of 3/4 meter in order to manipulate the listener's expectations of metric stability. I characterise these moments as "metrically unmeasured units of (musical) time" because their intrusion suspends the basic pulse which in turn prevents the perception of 3/4 meter and disrupts hypermetric regularity. In studying the effects of these units upon hypermetric patterns, I investigate complex dissonant relationships between hierarchic levels. I refer to the work of Justin London, Jonathan Kramer and Richard Cohn to show how Ravel establishes unstable metric hierarchies by resolving dissonances on one, but not between interrelated levels. The function of these units to create dissonance is enhanced through Ravel's manipulation of form which gives rise to a disorienting musical experience. However, such an experience is not pervasive since two transformations of dissonant motifs hint at the eventual reinstatement of meter. In examining Ravel's manipulation of metric and formal expectations, I show how this neglected perspective provides an insight into many perplexing yet characteristic aspects of his music.

        Harald Krebs, among others, has mapped the term "dissonance" from the pitch domain to the metrical domain, describing conflicts between metrical layers as "metrical dissonance." The analysis of Schoenberg's "Valse de Chopin" presented here investigates how metrical dissonance can contribute to energetic processes in a manner analogous to pitch dissonance. Musical "energetics" are defined for the purposes of this paper as musical processes and forms that can be described using Ernst Kurth's metaphors of kinetic and potential energy, intensification and de-intensification, and wave dynamics.?       

The metaphors of energetic theory also form the basis for some new perspectives on text-music relations. The analysis shows how metrical conflicts dramatize psychological conflicts - conflicts which themselves are of an "energetic" nature. The central conflict in the "Valse de Chopin" is between manic (energetically overcharged) and depressive (energetically deficient) interpretations of the waltz.?        François-Joseph Fétis, Ernst Kurth and others have shown that energetic processes are an important aspect of tonal repertoires. By identifying energetic tendencies (associated with metrical processes) in Schoenberg's atonal music, I demonstrate one of the ways in which his break with the past represents at the same time a continuation of tradition.

        Rhythm and meter in nontonal music propose specific challenges, as the new resources of pitch language are associated with a change of rhythmic language. Elliott Carter's music offers compelling strategies for dealing with the new rhythmic resources. The paper examines ways in which Carter's rhythmic organization is connected to the overall formal layout of the music, specifically in his Second String Quartet. The paper seeks to understand the degree to which the notated meter reflects the heard surface, and the ways in which the notated meter recedes and acts at constantly varying distances from the surface, according to the structure of the work. Of particular interest is how the work's rhythmic organization interacts with its pitch language.?        The paper proposes that although Carter's music defies constant regular meter, the notion of meter offers a fruitful way to understand the rhythmic realm of the quartet. The paper concludes by suggesting ways in which Carter's rhythmic practice may be connected to earlier rhythmic practices, with examples of Brahms's works.

        Binary beat divisions at multiple levels of the metric hierarchy are standard characteristics of popular music since 1950, and especially that of the 1960's and 1970's pop/rock charts. Overriding metric consonance was challenged and even abandoned by various strands of the progressive rock movement during those years, but was never displaced as a pop paradigm. This paper explores ways in which rock songwriters began to create metric dissonance in their music via non-binary groupings, while remaining within the pale of current pop conventions. Within their historical context, Led Zeppelin is not generally considered a progressive band, but one regularly finds in their music (especially after 1972) provocative rhythmic procedures and metric dissonance which act as structuring principles. Drawing on studies by Richard Cohn and Jeff Pressing, I will consider the basic repeated units of rock music as pulse cycles, and investigate common riffs and rhythms as generated subsets of these cycles. In particular, I will examine "The Ocean" (1973) as a case study. In the final portion of the paper I will explore the formal effects of non-binary groupings found in these songs, and suggest a conceptual model which integrates the resolution tendencies of both the rhythmic and harmonic domains.

Olivier Messiaen's passionate belief in the profound symbology represented by the cryptic mysteries of the Roman Catholic faith inspired him to weave these very symbols into the fabric of his compositions, which is evident in the programmatic titles given to most of his works. Equally apparent is the composer's proliferate use of the word "language" to emphasize the communicable nature of his compositional method. When combined, these two concepts become the foundation for an interpretive framework that transforms Messiaen's works into the aural equivalent of a religious icon.?       

Two compositions from different periods in Messiaen's life, "Le Banquet céleste" and "Couleurs de la cité céleste," elegantly illustrate the iconic properties of this repertoire. The former is a reflection of the physical and metaphysical actions that take place during transubstantiation while the latter features tonal constructions steeped in the mystical significance of Revelation's numerology. Messiaen further highlights these tonal constructions by associating them with specific colors drawn from Revelation's text. As with Skryabin and Kandinsky, Messiaen taps into the power of music and color to create a medium for the expression of his profound belief in the supernatural.

A theme in John Tavener's compositions is the musicalikon, inspired by Greek Orthodox religious artworks. To produce this reflective state, Tavener turned to the palindrome, creating musical structures by mapping pitches onto a "magic square" of twenty-five letters. Tavener used the palindrome extensively in his 1987 composition for cello and strings,The Protecting Veil?.        

The eight movements of theVeil depict scenes in the life and death of the Mother of God, linked by a palindromic statement ("veil theme"). Eachikon expresses different subject matter through a unique "tableau theme." The accompanying strings sound recurring rhythmic gestures ("bell clusters") over which the soloist plays a "paradise palindrome" derived from the magic square, altering pitch, rhythm, and tempo and interpolating extra pitches into the core notes.The Protecting Veil includes palindromes at every structural level -- from the ternary form of several movements, to simultaneous palindromic statements in different rhythmic values in canon. A massive palindrome marks the emotional crux of the piece in movement V ("Lament of the Mother of God at the Cross"). Through his use of palindromes, the composer evokes the stillness of theikon -- rather than propelling the listener toward a goal, Tavener asks him to remain stationary, gazing into the fathomless depth of mirrors.

        Francis Poulenc has received less than a fair share of the sophisticated analytical attention lavished on early twentieth-century composers. Too often his music has fallen prey to analysis where surface details are highlighted, but no attempt is made to uncover deep structural features or question critically what his music might mean. This paper will thus suggest that the Concerto for Two Pianos (1932), his most popular and endearing "self-portrait," ironically contains musical and biographical testaments of his melancholic persona, for the Concerto was composed shortly after a period of personal anguish stemming from his anxiety over his homosexuality (Orledge, 1998). In addition, it will be shown that the Concerto is pivotal in understanding other works by Poulenc: namely, Aubade (1929), a programmatic concerto for piano and solo dancer based on the myth of Diana, and Les Mamelles de Tirésias (1943), an opera based on the surreal text of Apollinaire (1917). This paper will ultimately claim that a homosexual narrative, stemming from the composer's relationship with the dogmatic views of the Church, is imperative to understanding Poulenc and his music.

        Sometime in the late 1920s, Ruth Crawford was "born again." Diary entries from this period betray a new interior life heavily influenced by the Theosophy of the day, and felt with an intensity and fervor to rival that confessed by any of the noted luminaries in the world's pantheon of converts. And as any missionary will tell you, it is precisely this intensity and fervor which drive the person "born again" into a new faith life to directly or indirectly spread the adopted gospel, to proselytize according to their personal gifts.?       

While Crawford scholars tend to marginalize the musical significance of Crawford's spiritual/religious transformation (no doubt encouraged by Crawford's tendency to do the same), my presentation places it front and center. I will argue that a knowledge and music-analytical reading of concepts and energies implicit and explicit in Crawford's unique spiritual palette demonstrate that she too acted on the (de-) convert's classic desire to make public statements of faith, to evangelize. I will show how a specific element from Crawford's new pan-Theosophistic world view served as a compositional catalyst, a template even, for her Piano Prelude IX. I argue that musical form, content, and process in the prelude are Crawford's sonic expressions of the concepts of time, space, and cosmic dynamics outlined in the famous Hindu creation myth, "The Waters of Non-Existence."

Factors including trends toward multiculturalism, pressure from accrediting agencies, personal preferences of a new generation of teachers, and time's passing challenge us to do more in less time in our curricula. Yet tonal music remains a key focus in our curricula. How can we find time to cover more material? Though we will finally have to rethink the content and structure of our curricula, we can, right now, raise our expectations of what our students know when they arrive on campus.

We devote substantial resources to teaching terminology, concepts, and skills that students should have mastered before beginning college. The situation would be improved if college-bound music students had improved means and motivation to master fundamentals while in high school. We propose a three-fold approach. We should (1) develop and promote minimum standards for core music theory courses; (2) promote the teaching of theory in high-school music programs; (3) support the development of and promote the use of web-based resources for music fundamentals training. One such project, called Music Fundamentals Online, will be demonstrated. We will never cover all we want or ought to in our programs. But by raising the bar, we can buy ourselves a little time.

In brief, the idea behind contract grading is simple: a student completes a certain number of tasks at a certain level of competence in order to earn a grade. At the beginning of a course, the instructor specifies the criteria for grading; each student then contracts for a grade. If at the end of the semester a student satisfactorily completes all of the required tasks for this grade, he or she receives the corresponding grade--with no mystery, fanfare, pleading, or guilt.

My aims here are to explore the pedagogical implications and applications of contract grading, to stimulate thought about the nature of evaluation, and to argue that it is not only possible but profitable to teach a course that has no exams, tests, or quizzes. Using model syllabi as points of departure, I shall share my observations and experiences with contract grading in upper-division music theory courses in form and analysis, and twentieth-century music.

Many schools now offer a course devoted to building bridges between the analysis of a piece and its effective performance. Such courses often treat these two musical activities as interdependent: anaytical points can help the musician to make wiser performance decisions; on the other hand, intuitive performance decisions can later be qualified (and justified) through an analytical exploration of the passage in question. For my presentation I will demonstrate several ways in which concepts from the musical approach of Pablo Casals (documented in David Blum's book Casals and the Art of Interpretation, 1977) may be utilized in teaching a course in Analysis for Performance, drawing upon my own experiences with this course in the classroom.

In the first portion of my talk I will present several musical examples from Blum's volume, discussing Casal's handling of dynamics and time relationships (rhythmic patterns, rubato, and proper tempo) in relation to harmonic language, voice leading, and motivic process. Blum's particular method of transcribing Casal's instructions to performers, showing expansion and contraction of note values as well as a discrete approach to tempo rubato and ritardando, will also be explained. In the second portion of my talk I will offer a model assignment where students are asked to add personal performance markings to themes by Mozart and Schumann, explaining their choices in reference to an analysis of each excerpt. Actual student responses will be included as a part of this discussion.

Cross-disciplinary study can be very appealing as we seek to impart greater awareness of music theory's cultural contexts. Comparing different disciplines' ideas during a particular zeitgeist can help not only to elucidate their original theories, but also to understand potential for further adaptations and permutations. Here, we explore such links between psychologist Frederick Bartlett's 1932 theory of conceptual schema and Heinrich Schenker's theory of fundamental structure in tonal music.

The poster focuses primarily on Bartlett's recall experiment incorporating the Native American story "The War of the Ghosts". It outlines how Bartlett's young British subjects "normalized" the unknowns of the story by means of omissions, changing order of events, transformation, and rationalization; and suggests parallels in some of the principles of Schenkerian theory. The experiment will then be re-presented through the eyes of a contemporary American student who was familiar with the Native American culture of Northern California (the apparent origin of the story) through a study of _ISHI, Last of His Tribe_ (whose existence was first known in 1911). Studying how Bartlett's original schema are differently influenced when cross-cultural awareness has been developed, it concludes by suggesting a parallel with current applications of Schenker's ideas in American classical jazz.

        It seems likely that we determine key in part through matching newly presented melodic patterns with those already stored in long-term memory. In an attempt to unravel the human process of inducing key, I have developed a computer algorithm, Keyfinder, which assigns key based on the identification of ordered melodic patterns in music. Since a computer will be substituted here for long-term memory, two different systems of pattern ratings-one from psychology by Carol Krumhansl and one from music theory by Fred Lerdahl-were used to represent the brain's pattern matching. In both sets of ratings, patterns with higher ratings are analogous to frequently-heard pairs of notes which easily induce a key. Likewise, patterns with lower ratings can be compared to pairs of notes which are unlikely to occur and may cause tonal confusion. Keyfinder was created to yield the best statistical fit between the particular melodic patterns of a piece of tonal music and either the psychology-based or the music-theoretical-based ratings. It outputs a correlation for all 24 keys, with the highest correlation predicting the actual key of the piece.

        This paper examines the very different comic effects of Shostakovich's opera *The Nose* and the Nikolai Gogol short story on which it's based. Shostakovich's self-commentary indicates that he vowed to serve Gogol's text faithfully and that he understood Gogol's style of humor (in which comic events are related in a "serious tone" and the absurd is treated as something ordinary). Despite all this, however, the score of *The Nose* is not serious in tone but in fact wildly parodistic and comic. Focusing on the textual and musical manifestations of one scene, I show that Gogol's and Shostakovich's comic devices are in fact inverses of one another. Both involve what philosopher John Moreall calls an "incongruity" between what we expect and what we actually experience; yet, to borrow from comic theorist James Feibleman, Gogol's incongruous humor involves "understatement," Shostakovich's "exaggeration." The paper concludes by proposing some explanations for this difference, considering how well a faithfully understated adaptation might have worked and whether the opera's exaggerated style of comedy might have been influenced by director Vsevolod Meyerhold, under whose encouraging eye the young Shostakovich wrote much of his opera.

        The degree to which Benjamin Britten's opera, The Turn of the Screw, reproduces the ambiguities of Henry James's original novella has been a point of contention since the opera's premiere. A century of literary criticism has generated two popular but mutually exclusive readings of James's story: the ghosts the governess believes to be haunting Miles and Flora, her two young charges, may be real, or they may be hallucinations - unconscious expressions of her repressed desire for the children's guardian. Although most critics now agree that the novel's subjective narrative point of view allows for both readings, critics of Britten's opera have long argued whether the opera can sustain both readings. In spite of this dispute, no analysis of the opera has attempted to resolve the issue.

        One aspect of the opera that largely determines its possible readings, but which has never been the primary focus of an analysis, is the opera's "narrative" point of view. Unlike the novella, which is written exclusively from the governess's point of view, the opera's point of view is problematic - the governess is undeniably the main character, but there are scenes from which she is absent. This paper shows that the opera has a shifting point of view that is ultimately determined by the music. It elaborates the musical processes that create this shift, giving special analytical attention to a musical process that mimics the governess's cognitive process, and to three scenes in Act II that musically embody Miles's point of view. The opera's fluid point of view invites a reading that makes use of both the audience's initial identification with the governess and the subsequent musical and dramatic elements that compromise that identification.

        Edvard Grieg's song cycle, *Haugtussa*, (The Mountain Maid) opus 67, a relatively late composition in Grieg's oeuvre (composed in 1895), exemplifies Grieg's synthesis of folk elements and art music within his own unique voice. It is considered by many scholars to contain some of Grieg's best vocal compositions. Arne Garborg, the author of the poem cycle from which Grieg took his texts, makes effective use of parallelism throughout his poem cycle, using metaphor, poetic meter, and stylistic borrowing from traditional Norwegian folksong rhythms to make connections between poems. Grieg set several of these interconnected poems in his song cycle, complementing the literary parallels with musical ones. The interrelationship of two of the songs from the cycle, "Møte" (Meeting) and "Vond Dag" (Hurtful Day) is the focus of this paper. The two poems frame the short love affair between the heroine, Veslemøy, and the young man, Jon. I will discuss the connections between these pieces with regard to poetic and musical structural elements, as well as poetic and musical metaphor. Of particular importance is Grieg's use of two predominant motives-an arpeggiated tonic triad (the "Veslemøy" motive) and a falling, three-note gesture-in the musical interpretation of these poems.

       The paper examines the recitative portions of each of the three Hymns to Venus from Wagner's opera Tannhauser (Act I, scene 2), in which expressionistic, apparently anomalous chord progressions are featured. In each case, the questionable voice leading involves an apparent prolongation of the dominant function at the end of each recitative via a startling variety of diminished- seventh and dominant-seventh chords, whose resolutions seem arbitrary at best. A better explanation of these passages requires the subjugation of the more obvious dominant arrivals to their subsequent deceptive resolutions. A sub- surface tetrachordal bass descent is thus revealed at the heart of each Hymn; in each case, a predominant expansion engulfs incidental dominant harmonies that are initially heard as structural.

       The analyses raise a larger issue: even if an initial dominant arrival is accented prominently, it may not be appropriate to connect it analytically to a subsequent dominant function. A detailed Schenkerian analysis of the Introduction to the first movement of Schubert's Fourth Symphony uncovers a deep-level structure exactly parallel to the structure observed in the Hymns. In the context of these examples, the deceptive resolution of any dominant is considered to be its functional negation. Concluding observations on the first movement of Beethoven's "Moonlight" Sonata and the Prelude to Bach's Fourth Suite for Solo Cello in Eb Major, however, suggest that other readings may sometimes be more appropriate.

       When Wozzeck describes his hallucinations to the Doctor in Berg's opera, he conjures up mysterious images of some secret geometric code. "Lines and circles," he mutters, "strange figures . . . if only one could read them!" Analytic interpretations have focused upon the circle as a symbol of Wozzeck's state of mind and Berg's own view of life, but with ambiguous results. Some see it as a pessimistic image of fatalistic doom, others as an optimistic metaphor for hopeful rejuvenation. A dialectical conception of the opera, however, suggests their unresolved juxtaposition-simultaneously asserting affirmative and negative conceptions of life.

       But it is Wozzeck's "lines" rather than his "circles" that unlock the geometry of ambivalence encoded in the "strange figures" of the open field. A "dialectical ramp" of two intersecting lines in oblique motion embodies this vacillation between dynamic affirmation and static negation. Tracking this "strange figure" as a musical metaphor reveals a profound ambivalence at the heart of Berg's masterpiece. Half soldier, half seer, wandering across the open field of life, Wozzeck catches a fleeting glimpse of this ambiguous geometry, of hope and despair tugging against one other, juxtaposed without victor, each sharing Berg's stage to weave a delicate synthesis of unresolved antinomies.

       David Raksin's score to the 1944 film Laura generated one of the most popular ballads of its time. Most of the primary melodic tones in the well-known melody (of the chorus) are undermined rather curiously by Raksin's strikingly unusual accompaniment, which harmonizes them with a fundamental bass a ninth lower. This talk will attempt to grapple with the perplexing question: are these ninth chords stable, in the sense of Kirnberger's essential dissonances, or are these seemingly strong melodic tones actually unresolved dissonances, displacing the "true" melodic tones that never appear?

       After outlining a brief history of the ninth chord as both real (essential) and supposed (non-essential), I will propose two very different Schenkerian readings: one that (somewhat liberally) recognizes such dissonant Stufen, and one that does not. Both of these readings will be explained in some detail and the second, in particular, will inform a hermeneutic interpretation of the work both as a popular song (with Johnny Mercer's lyrics) and in its cinematic context.

       György Ligeti discussed his "micropolyphonic" music of the mid-1960s at length, in an attempt to explain why its composed structure seems to bear no relation to its actual sound. On the surface his comments support those of the philosopher Roger Scruton and the theorist Fred Lehrdahl, both of who maintain that effective listening strategies rely on the perception of hierarchy in musical structure.

       The real question posed by Scruton and Lehrdahl is whether a modernist music of consequence is possible. Without discounting cognitive research, I question that an "order that can be heard" must serve as a paradigm for listening to music. Using the example of Ligeti's micropolyphonic music and recent research on cognitive metaphor, I will argue that to "hear the sounds as music" is never restricted to parsing a work's concrete, self-referential details, but relies on the necessary mediation of metaphor. Ligeti's music and its accompanying commentary suggest that modernist music itself might serve as a metaphoric solution to the problem of "listening to modernism." To quote Jean-Claude Risset, his music is "about composing the sound itself, not merely composing with sounds," a sophisticated critique of modernism, and of the presumptions-both cognitive and historical-that would limit our musical perception.

       One of the most important developments in compositional technique in the last forty years is the use of formal designs based on gradual musical transformations operating over long passages of time, a technique employed in works by György Ligeti, Tristan Murail, Kaija Saariaho, John Adams, and Arvo Pärt among others. An attempt to provide a perceptual account of repertoires in which gradual transformations feature prominently poses two basic questions. First, since the ability to parse music into small perceptual units, or groups, is central to most work in the perception of form, how does one establish groups without clear boundaries for segmentation? Second, how might one represent groups of a duration which exceed that of working memory? Drawing on Irène Deliège's work in cue abstraction, as well as recent work in categorization and dynamic mental models, this paper proposes that mental representations of gradual transformations consist of one or more basic musical categories referring to regions of music, which may or may not exhibit clear demarcations, and procedural knowledge concerning the manipulation of these categories over time. Analytical insights informed by this approach are drawn from the opening section of John Adams' Shaker Loops, as well as excerpts from other contemporary repertoires.

       Order, duration, and time are important elements in Olivier Messiaen's music, particularly in his highly organized works from the 1950s. During this period, Messiaen experimented with constructing rhythms by means of a systematized permutation of a small number of note values, with recursive rhythmic ostinati, with formal designs involving repetition and reordering of segments and--by means of these techniques--with different conceptions of musical time.

       Even in serial works such as the Livre d'orgue (1951), Messiaen rarely employs inversion, and still less transposition. Instead, in the domains of both pitch-class and duration, he is more concerned with permutational techniques that are independent of interval content, favoring retrograde and various forms of interversion. This paper focuses in particular on Messiaen's concept of interversion: the composer often uses the term for a type of chiasmic retrograde, in which a series of, say, twelve elements would be reordered to 11, 0, 10, 1, 9 . . . But he uses the same term more generally for any sort of systematic permutation, such as when he systematically cycles through the n! possible orderings of a set of cardinality n. In all of his uses of interversion, Messiaen can be seen to be concerned about maintaining invariant relations and, more generally, with maintaining the identity of his collections even under different sorts of permutation.        Many of the same processes that govern the reordering of notes or durations at the local level also operate over the span of entire sections or entire Messiaen compositions. Here, too, a systematic interversion of repeated elements can be shown to generate the forms of pieces during this period.

       Messiaen's preoccupation with time operates on two levels within his music. On the one hand, his emphasis on manipulating durations, permuting their order, and creating rhythmic ostinati out of them shows a composer's traditional concern with developing material and building a musical structure forward in time from an initial motive. On the other hand, from a listener's perspective the music often seems more static and meditative than forward-moving and developmental. Messiaen's music challenges the listener and the analyst to think of rhythm and musical time in a new way, as a dimension that can be cyclical and recursive rather than merely unidirectional.

        Hugo Riemann's theory of rests, though not widely known, offers provocative insights for theorists and performers. This theory essentially states that notated rests within musical motives do not represent zero values but rather negative values. As a theoretical result, dynamic energy may continue to intensify during such rests (contrary, perhaps, to the acoustic facts).

        Riemann's analysis of the opening theme of Beethoven's Piano Sonata in E-flat Major, Op. 7 indicates motivic groupings that encompass long rests. To realize this theme's full expressive potential, says Riemann, "we must not allow the Pegasus of our imagination to shrink back from every rest." (Within German Romanticism, the winged-horse Pegasus symbolizes the spirit of poetry.) Riemann underscores these rests with crescendo wedges. Calling for an interpretation outside the realm of physical possibility, these wedges summon performer and listener to a transcendent, ideal musical world.

        This paper will examine Riemann's analysis of Beethoven's Op. 7 against the backdrop of Hegelian phenomenology that informs his analytical perspective. Its potential musical rewards will be weighed against the feats of imagination we as listeners are asked to perform.

       Friedrich Nietzsche's carefully worded Beyond Good and Evil is renowned for its artistic and aesthetic vision. That this vision often appeals to specific musical terminology at the crux of its arguments as a way of accentuating its thesis has been somewhat overlooked within music scholarship. Perhaps most striking is this essay's consistent employment of tempo as a method of differentiating the German artistic venture from that of the rest of contemporary Europe. The first half of my paper examines this development through close (and critical) readings of excerpts from Nietzsche's 1882 essay, and takes into account that such allegations are intimately connected with nationalistic or ideological claims-claims which are often distasteful to modern sensibilities, despite their necessary recognition by today's most prominent Nietzsche scholars. The second half of the paper explores the possible resonance of these claims within the music of Nietzsche's sometime friend, Richard Wagner. Act two scene two of Tristan und Isolde serves as a model for the tracing of these philosophical constellations, and aims to provide an alternative method of approaching Wagnerian opera.

       Melody in sacred vocal music of the Renaissance has long been noted for its arch-like contours and overall beauty of shape. Reese characterizes the "Palestrina curve" as "a gradual rise in the melodic line followed by a fall that balances it with almost mathematical exactness." This description and others have been of a very general nature; in this paper I use modern analytical tools based on recent developments in contour theory, especially as presented by Morris, Laprade, and Marvin, in order to explore deeper structural aspects that can further explain the essence of Renaissance melody. Tools include Marvin and Laprade's CSIM function, to measure contour similarity, and Morris's contour-reduction algorithm, to facilitate structural reduction of melodies. Morris' algorithm usually requires several stages before the prime contour is attained. Like a Schenkerian middleground reduction, these middle stages can illuminate much about the music. In the cases under study, an overall tonal structure comes to light that emphasizes tonic and dominant functions as our modern view would term these relationships, even superseding the Renaissance system of final and reciting tone. Examples by Palestrina, Josquin, and Lassus are examined with these approaches to reveal other structural aspects of Renaissance melody.

       There is much to learn about meter and dissonance control in the Spanish Baroque from Reglas generales, the thoroughbass treatise of José de Torres (1670-1738), and from the two previous Spanish treatises from which he draws most extensively: Fragmentos músicos, by Pablo Nassarre (1664-1724) and El porqué de la música, by Andrés Lorente (1624-1703). Music of this transitional period shows, on one hand, certain features of Spain's prima-prattica tradition, such as identification by modal rubrics, cadential organization according to psalm-tone differentiae, and limited use of paraphrased plainchant canti firmi, and on the other, a more cosmopolitan, Baroque conception of harmony and dissonance control, an exploitation of homophonic textures, and a preference for characteristically Baroque accompanimental idioms, most importantly, thoroughbass.

       Although Lorente and Nassarre do not specifically deal with the concept of thoroughbass in their treatises, their discussions of meter and dissonance control are used to great advantage by Torres in Reglas generales (Madrid, 1702, 1736) the first Spanish treatise to present thoroughbass accompaniment at the keyboard according cosmopolitan European practice. For this reason Torres can be viewed as the beneficiary of much of the information presented in Lorente's El porqué de la música (Alcalá de Henares, 1672, 1699) and Nassarre's Fragmentos músicos (Zaragoza, 1683; Madrid, 1700).

        This presentation describes an evolving personal transformation regarding rock music. Several years ago my students pointed out that my displeasure with rock was exactly the same as their initial discomfort with contemporary art music--simply the result of unfamiliarity. Rock wasn't "my" music, any more than Schoenberg was theirs. So, to demonstrate the open-mindedness that I wanted from my students, I undertook an intensive listening/analysis of rock recordings. And after a while, I began to like the music, so that I now attend rock concerts by and with my students, and frequently include rock in my teaching curriculum (particularly as aural skills dictation materials).?       

Among the benefits of this experience has been its validation of basic teaching methods--many in-depth listenings, analyses, and discussions of a particular kind of music do in fact lead to a greatly enriched experience with that music. Another, personal, benefit has been experiencing a new source of musical enjoyment. And a third benefit is the increased credibility and sense of connection I have with my students. For me these benefits easily justify the inclusion of rock within the core curriculum.

        Like many musicians who now teach and "do" theory in university music departments, I came to theory by way of composition, and I continue to think of myself both as a composer and as a theorist. However, more and more I think of these as separate activities that perhaps even require opposite and contradictory perspectives. ?       

It is a cliche of undergraduate teaching to explain analysis, and perhaps theory as a whole, as being "composition in reverse." The composer* puts together* her or his materials into a piece, it is said, and the analyst *breaks apart* the sections and motives to reveal the structure and content of the work. The trouble with this model, as much for pedagogy as for analysis, is that it can imply that the *one* best analysis is the one that most exactly retraces the compositional process, leading students into the intentional fallacy and leading even more sophisticated musicians into a too-narrow explanation of a work. With only a few exceptions, the least interesting analyses or discussions of pieces are by their composers, who often do little more than retrace the technical steps they took in composing the work; these discussions can be the among the most narrow and pedantic. ?       

As a composer, I feel that my aim is to be *exclusive*--to find the single best solution to a compositional problem and to choose it over the others. Composers must move quickly from the general to the specific, putting a vague idea into concrete form. The best analysis and the best theory are *inclusive*: they acknowledge that any explanation is provisional at best, excludes other equally valid interpretations, and cannot do more than provide one view from one singular perspective. Theory at its best is a powerful generalization from many different analyses, an idea that reveals an unexpected principle common to many different contexts and treatments. I believe it is this belief in the power and utility of generalization and inclusiveness that theorists share and that differentiates us not only from composers, but also from performers, historical musicologists, and others of our fellow musicians.

        Altering the core curriculum invariably provokes stimulating discussion, but the issues raised are becoming predictable. Theorists are by now accustomed to deciding what portion of our precious four or five semesters we can spend on twentieth-century music, and we are starting to ask ourselves with increased frequency whether we are adequately representing women and minorities, popular music, and music of other cultures. However, we have yet to inquire in any serious way how research in music cognition should impact our pedagogical perspective (for instance, facilitating musical memory or accommodating different learning strategies). This is especially surprising in relation to aural skills classes, given the wealth of relevant information available. ?       

I do not mean to imply that theory teachers are failing. On the contrary, I think that we are educating students reasonably well, given that so many of our curricular choices seem to be determined by a combination of what has worked in the past and pedagogical instinct. Music cognition research could inform our curricular decisions and serve as a catalyst for further improvement, leading us to develop teaching techniques that will be more helpful to a broader range of students.

        Analyses dating from 18th- or 19th-centuries present a challenge to modern-day theorists, who cannot ignore recent methods of analysis. Engagement with historical analysis requires a deft negotiation between past and present to ensure that each receives its due. One of the most significant of the few examples from the eighteenth century is the complete fundamental bass analysis of J.S. Bach's Fugue in B minor from Book I of the Well-tempered Clavier, published in 1773 under the name of J. P. Kirnberger, though it probably represents the work of his student J.A.P. Schulz. It seems ironic that two major scholars of the history of 18th-c. theory, David Beach and Joel Lester, have dismissed this rare analysis of a complex work as of little value in understanding Bach's music.?       

I propose to reevaluate this analysis using the model recently proposed by Thomas Christensen for the interpretation of the historical texts of music theory: a hermeneutic dialogue, as set out by Hans-Georg Gadamer, which speaks to the past on its own terms, but which recognizes our inescapable immersion in the present. I will actualize this dialogue by showing how the historic analysis can be incorporated in a substantive way into my own Schenkerian analysis; the voice-leading analysis can than serve to reinterpret the fundamental-bass reading, thus continuing the hermeneutic circle. This could serve as a model for the practice of modern-day theory that meaningfully interacts with and listens to the past without sacrificing itself to it.

        Insight into Brahms's sonata forms has been aided by attention to the relationship between his expository strategies and Schubert's practice of organizing his expositions around three keys. Emphasis on the three-key idea, however, has also had the effect of concealing a number of qualitatively different exposition types. The present study suggests the possibility for a more differentiated categorization of Brahms's expositions. Three-part expositions that arise via a mode shift in the secondary area are as common as expositions based on three distinct keys. These mode-shift patterns derive from late eighteenth-century alternatives to bi-polar organization, rather than from Schubertian innovations. A concern to demonstrate variety within the mode-shift category accounts for the choice of the fourth movement of the C-minor Piano Quartet and first movement of the First Symphony for detailed examination. The quartet and symphony demonstrate that different mode-shift strategies can relate to differences in approach to tragic expression. The paper highlights the role played by stereotypical musical topics in realizing these different approaches and concludes with a comparison of Brahms's incorporation of religious topics in the two works.

        Since the nineteenth century, when musical analysis became an established part of the practice of music theory, musical notation in the form of the score has been an essential component of the discipline. As contemporary theorists begin to look beyond the central canon of Western art music, however, they encounter many musical traditions that do not use notation. While relatively fixed works do occur in some of these oral traditions, in others, improvisation is prevalent. A particular piece might vary widely from one performance to another, even though it is always known by the same name. How might theorists approach such repertoires? In particular, how might the traditional textual practices of music theory affect the study of improvised music??       

These are some of the questions I will address in my paper. I will begin with a consideration of the role of notation in contemporary music theory; then, drawing from ethnomusicological sources, I will discuss some of the issues that theorists might consider when using notation to study non-notated music. In the second part of my paper, I will focus specifically on improvisation, considering several arguments about the nature of improvisation and their implications for the theoretical study of improvised music.

        This paper will explore the harmonic field in which simultaneously improvising jazz musicians play, and will propose a generative theory of jazz harmony; that is, a theory that describes the process of harmonic negotiation that takes place between players in a small-group jazz performance. The linguistic concepts of deep, shallow, and surface structures are used in this theory to reconcile the many possible variations or realizations of a specific harmonic progression. The paper will present two analyses in support of this theory. The first analysis will compare three common variants of the 12-bar blues progression, showing that each of the three progressions can be seen as a different surface manifestations of a common underlying harmonic deep structure. The second analysis will examine a recorded performance by the Thelonious Monk Quartet of Monk's composition "Rhythm-A-Ning." The analysis of "Rhythm-A-Ning" will show that, in a sense, jazz musicians literally "make the changes" in performance; the specific harmonic progressions they choose to play may be flexibly realized, often changing from simple to complex within the course of a single performance.