This study examines the rhythmic and metric characteristics of the "perpetual motion" movements in Bach's music for unaccompanied violin. The patterns emerging from the steady streams of notes in these movements lie at the boundaries between rhythm and meter, wielding the power to both establish and undermine a listener's sense of time. In this paper I interpret these patterns as motions through rhythmic/metric space. In doing so I combine recent music-theoretic perspectives on transformation and spatial analysis with existing theories of rhythm and meter, both areas of which have rarely been applied to Baroque music.

            I begin by constructing a rhythmic/metric space which contains various "rhythmic strata" or periodic rhythmic patterns which can either conflict with or reinforce a particular metric hierarchy. After formalizing the relationships among elements in the space, I analyze selected passages from the solo violin sonatas and partitas according to their use of rhythmic strata. The analysis leads to the following observations: 1) Bach uses patterns which are, as Lester has claimed, "active" throughout the metric hierarchy; that is, strata span the vertical possibilities of the space. 2) Movements of the sonatas and partitas can be distinguished according to Krebs's "grouping" and "displacement" dissonances. 3) "Toggling" between strata is an important stylistic feature of the solo violin works. 4) Motion between strata can either occur directly or by means of a transitional rhythmic pivot. 5) While non-displaced strata are more common than displaced patterns, Bach sometimes engages all the permutational possibilities of a given cycle span.

Is syncopation displacement of the regular pulse, or suppression of it? These two common theoretical formulations focus on different sides of the syncopation coin. I mediate between them by theorizing syncopation as transformation of the regular pulse: displacement of a pulse transforms its quality as well as its location. Syncopation as transformation thus amalgamates displacement and beat identity, and reconciles significant conflicts between their conceptual, performative, and experiential implications.

To generalize this concept to a wide variety of metric frameworks, including asymmetrical and changing meters, I present the modular hierarchy, a generalization of common theories of metric structure, and define syncopation in relation to it, refined into two phenomena: syncopes and offbeats. My formalization departs from theoretical precedents by admitting certain metric structures hovering on the periphery of quantitative metric theory--non-isochronous meters, meters that are not maximally-even in their pulse distribution, etc.; by treating the displacement of individual pulses as well as of whole pulse layers; and by distinguishing between syncopes and offbeats. I demonstrate the utility of this framework by analyzing passages or pieces by Beethoven, Wagner, Schoenberg, and Herbie Hancock, and by setting my findings against the theories and analyses of Harald Krebs, David Lewin, Fred Lerdahl, Charles Morrison, and Keith Waters.The paper concludes by suggesting analogies to pitch-class structure.

The concept of meter inherently involves cultural bias. For some, music which doesn't easily fit within standard integer time signatures (e.g., 3/4 time) is either forced to fit or categorized as somehow deviant, or not well-formed a more recent scholarly term. Although the precise terminology differs, most descriptions of meter include the notion of a regularly recurring (isochronous) pulse which marks off equal units in the temporal continuum. Asymmetrical meters (e.g., 5/8 or 7/8) are non-isochronous at the beat level and are either not discussed or are reinterpreted in a way which does not reflect the reality of how, for example, a Balkan kopanitsa is heard, played or danced.

Despite its asymmetry, however, the kopanitsa still embodies the ancient Greek concept of a chronos protos. That is, at some fundamental level, there is a small, indivisible, isochronous unit of duration from which the beat(s) can be formed bottom-up through an additive process: a primary constraint for metric well-formedness according to some. What then do we make of the Norwegian springar or Transylvanian kett??s, in which not only each beat is a different length, but the subdivisions of one beat are incompatible with those of the next beat? This music is neither hypothetical nor experimental; these are characteristic dance forms with hundreds of years of tradition behind them which deserve to be included in the family of well-formed meters.

In some types of prolongations, the Stufe undergoes a gradual change to make a smooth voice-leading connection with what follows. In these cases, the chord is literally present at the beginning of its span, but not at the end. This is a very common gambit for initial tonic prolongations while never for the final ones. The type of open-ended prolongation under consideration presents serious cognitive challenges when applied to the dominant, in that it erodes the chord's characteristically urgent and insistent quality. Experimentation with these "disintegrating dominants" can be found throughout the tonal period, but they become more common in the music of the late 19^th century. This paper examines some contrapuntally and chromatically elaborate examples in the music of Johannes Brahms, with particular focus on the late sonatas for clarinet and piano, Op. 120. In order to frame the discussion, voice-leading graphs of works from a variety of composers and periods will be provided, including several complete movements. The paper raises important issues relating to the question of the auxiliary cadence. It also offers rehabilitation for a somewhat disparaged theoretical construct, the deceptive cadence. Finally it offers some speculation about the role that these techniques may have played in the erosion of tonality at the dawn of the 20^th century.

Recent writings on Sonata Theory by James Hepokoski and Warren Darcy differentiate between two types of sonata expositions in late-eighteenth-century instrumental works: the two-part exposition and the continuous exposition. Required of the two-part exposition is the medial caesura, which ends the transition zone and opens up the secondary-theme zone. The continuous exposition, by contrast, contains no medial caesura and therefore no secondary theme. In the first movements of Mozart's piano concertos, the two-part exposition is the norm for both the opening ritornello and the solo exposition. The F-major Concerto, K. 459, is unique in that both types of expositions can be found; thus, its form deserves further exploration from the perspective of Sonata Theory. The first section of this paper claims that the opening ritornello is continuous and the solo exposition two-part. As well, it addresses issues associated with the coexistence of both types of sonata expositions. The second section compares the Sonata-Theory interpretation to a reading derived from Caplinian formal functions. The two analytical approaches produce different analytical results, from which the paper concludes by proposing a hermeneutic interpretation of the movement's formal organization.

            Ever since its 1889 premiere, the Funeral March of Mahler's First Symphony has provided fertile ground for hermeneutic speculation. However, although various interpretations have been advanced, few have been grounded in anything resembling rigorous musical analysis. In fact, this movement has traditionally resisted close analytical treatment, perhaps because its canonic entrances and long stretches of static harmony seem almost too straightforward and self-evident to warrant intense analytical scrutiny. By contrast, this paper proceeds from the conviction that only through a close analysis of the work's form and thematic/tonal process can we arrive at a responsible interpretive reading of what Mahler was trying to say, both in this movement and in the symphony as a whole.

            We will first examine the tonal structure and narrative content of Mahler's Lieder eines fahrenden Gesellen, for not only does the concluding strophe of the final song furnish the musical substance of the movement's central Trio, but the cycle's large-scale harmonic relationships regulate the tonal progress of the Funeral March in ways that have not previously been recognized. After considering how the movement fits into the rotational structure and narrative plan of the symphony as a whole, we will examine the formal/tonal structure of the movement itself, utilizing the principles of rotational form, Schenkerian analysis, scalar collections, and transformational theory. These various analytic "lenses" will be employed to formulate a hermeneutic interpretation of the movement that is fully consonant with Mahler's own remarks about the piece, and that seeks to uncover exactly what it is that is being laid to rest and buried.

Ernst Kurth's distinction between "form" and "forming" highlighted the difference between product and process in the study of musical form. Similarly, this paper seeks to examine what a theory of "measuring" might entail, and how it might relate to meter. One could say that meter is some thing and measuring is something we do. But are meter and measuring truly separate concepts or is measuring just one aspect of that complex of features we have called meter? Certainly measuring plays a crucial role in processive theories of meter, and any successful description of a work's meter will be the result of careful measuring at some stage. Metrical structure could even be described as the "memory" of measuring.

Metric analyses are not normally dependent on any realization of a work. But when we measure, the performance and its expressive timings matter. We "place" the beats as we hear them. And we expect and appreciate certain temporal nuances in performance. Some expressive temporal effects such as the elongated downbeat--which creates what I call downbeat space--can be indicated by the composer. These temporal "deviations" affect our sense of meter in that they can alter the quality of the beats that we measure as well as our placement of them. Although by their nature such temporal nuances caneasily be "reduced out" (much like embellishing pitches in a harmonic analysis), their expressive quality and potential effect on the perception of meter is something that can effectively be made part of metric analysis.

Despite his large recorded output, Glenn Gould revisited few works in the studio. Certainly the most celebrated of his double recordings bookend his career, Bach's Goldberg Variations of 1955 and 1981. Gould discussed these two performances in the film made of the latter recording session and in a 1982 radio interview, during which he expounds a loose theory of a "constant rhythmic reference point", which he claims formed the organizing principle behind the time dimension of his 1981 recording. Gould did not theorize about his performances in any detail in his own writings, so these recorded comments combined with his studio recordings provide a rare opportunity to investigate the interaction of a theory and a performance that are explicitly connected.

            To discover whether Gould is successful in communicating his conceptions to the average listener, I conducted an empirical study collecting tapped responses to excerpts of both recordings, focusing on the transitions between adjacent variations in the set. I work from the standpoint of a referent level, a concept from music cognition analogous to the historical tactus and to Gould's constant rhythmic reference point. My results show individual and combined effects of composed metric structure and performance decisions, and indicate that Gould is able to control listeners' perceptions of referent level to a much greater degree with his 1981 Goldberg Variations.

Music students develop their early knowledge of tonal forms largely through two different types of assignments. The first is to take a musical example and label its constituent parts. Unfortunately, many students "escape" from this type of assignment with a surprising lack of involvement in the music, relying primarily on visual musical markers. The second type of assignment is to compose phrases or pieces based on a formal model. Composition assures an intense musical involvement, but can lead to wildly varied results. It is not surprising that students who have "escaped" musical involvement in the labeling exercises have difficulty mustering the imagination and control necessary to compose.

            I have invented another activity which I call music scrambles in order to bridge this common gap in labeling and composition expectations. Music scrambles present the complete set of two-bar groupings (bits) which make up a phrase or a larger form in a mixed-up order. William Caplin's descriptions of tight-knit themes (sentence, period, and hybrid) in his book Classical Forms are particularly well-suited for this exercise. The student's task is to rearrange the bits into a coherent whole based on one of the forms studied. Students become much more invested in both the music and the formal labels when they have an active role in making the music work.

As part of their study of tonal music, undergraduate music students almost invariably work through a rigorous set of harmonic dictation exercises. By contrast, most dictation curricula pay far less attention to the harmonic materials of the extended tonal and atonal repertoires. This paper helps to address this issue by laying out a series of harmonic dictation exercises designed to accompany an undergraduate music theory course in twentieth-century harmonic practice. Most of the exercises are several-voiced progressions approximately seven chords in length. Chord type and inversion identification drills play a secondary role. The curriculum explores extended tonal practice: triads, seventh chords, extended tertian chords, and quintal sonorities in various diatonic, modal, pentatonic, octatonic, hexatonic, and whole tone contexts. Other exercises engage atonal theory and are organized by trichordal set type, by larger familiar collections (hexatonic, octatonic, etc.), and by fb-class, Robert Morris's (1994) twelve-tone generalization of figured bass that lists pc intervals from a chord's bass note to each note above it. The paper provides an overview of the curriculum and addresses several parts in detail.

            Despite a recent abundance of literature and interest in "neo-Riemannian" analytical methods, the application of these methods remains in its nascent stages. Neo-Riemannian analysis is particularly well-suited for the analysis of passages lacking traditional tonal syntax, such as the "leitmotivs" in the music dramas of Richard Wagner. This paper uses two Wagnerian motives, the Servitude and Annihilation motives to illustrate the applicability of neo-Riemannian analysis. Using the approaches of Gauldin and Lewin as points of departure and using "neo-Riemannian" operations defined by Cohn, Douthett and Steinbach, Callender and others, this paper fuses a transformational analysis of the motives' tonally unrelated chords with a contextualization of the motives' interaction with their surrounding harmonic middleground. Particular emphasis is given to the motives' treatment in Alberich's Curse in Scene 4 of Das Rheingold and Hagen's watch from Act I, Scene 2 of Götterdämmerung. The fresh approach taken in this paper provides new insight into Wagner's technique of motivic manipulation and his negotiation of diatonicism and chromaticism. It provokes the possibility of further analyses of this kind, in which a fusion of transformational analysis and tonal analysis can be applied to music where the worlds of diatonicism and minimal voice-leading likewise coexist.

            As the rules of functional harmony became less strict in the Nineteenth Century, composers occasionally used seventh chords as non-functional color chords. There is currently no method of charting the interaction of triads with seventh chords. Analysts treat the seventh chord as a triad, omitting the added pitch. The analysis of seventh chords is impossible in a traditional Tonnetz due to the absence of the tritone division of the octave.

            This paper proposes a Tonnetz model that incorporates the tritone division of the octave, allowing the logical formation of seventh chords within it. This in turn allows for the mapping of harmonic direction between triads and seventh chords. The model incorporates the core components of neo-Riemannian theory: parsimonious voice leading and common tone maximization. It relies on the same PLR relationships found in neo-Riemannian Theory. Using compound PLR families, it can be used to analyze movement between triads and seventh chords through two dimensional pitch space.

            The properties of this Tonnetz are symmetrical in nature. A special formation of Mm and Half-diminished 7 chords results in a new transformation called the Cheshire Transformation. It is so named for the activity of the "appearance and disappearance" of tones as pitch space is traversed from triad to seventh chord and back to triad.

            This paper focuses on major-minor and half-diminished chords, using analytical examples from the compositions of Alan Hovhaness, Maurice Ravel, and Hugo Wolf.

Is there a way to conceive of a musical work's beginning and ending keys, even if there are exactly the same, as symbolized by two different places? If so, what is the kind of journey that unfolds in between, if it does not involve a homecoming? This analysis applies an innovative analytical technique published recently by Yale music professor Daniel Harrison ("Nonconformist Notions of Nineteenth-Century Enharmonicism", Music Analysis 21/2 (2002): 115-160.) to one of Michael Torke's most popular chamber works: Telephone Book (1985/95). Torke's Telephone Book with its many full-circle modulations is a musical depiction of the alphabetical ordering found in phone books. Application of Harrison's new theory now enables these modulations to be coherent with the idea of alphabetical order, with each move around the circle-of-fifths now seen as a move to a new entity like the alphabet cycling through letters and arriving at new ones (A???s to B???s etc.) There are eight such modulatory cycles in Telephone Book. A collection-by-collection analysis reveals pivot tones that are often at the forefront of melodic activity and ensemble interplay. Using Harrison's ideas of enharmonicism to reveal a unique tonal path for every modulatory cycle in Torke's Telephone Book shows a musical equivalency of alphabetical order. A telephone book arranged in alphabetical order, is a linear event, never returning but gradually moving to new letters. Torke's Telephone Book does this musically and Harrison's new analytical technique helps us to see how.

Every woman is distinctly enthralling and intriguing to Wolfgang Amadeus Mozart no matter her societal class. The female leads in Don Giovanni exemplify Mozart's treatment of class at the musical level. Mozart simultaneously maintains delineation between characters of noble blood and common folk on the surface, yet endows all characters with music rich in layers, narrative, and symbolism. This paper first investigates on all levels the musical complexity of Don Giovanni's noble ladies, Donna Anna and Donna Elvira. Carl Shachter's work on Donna Anna's first aria, "Don Ottavio, son morta!... Or sai chi l'onore," is discussed and used as a foundation for the presence of narrative and symbolism in Donna Anna's music. A look at Donna Elivira's first aria, "Ah! fuggi il traditor," reveals that melodic ideas and key centers play a part in layers of narration and symbolism. After having examined these two arias sung by the noble female leads in Don Giovanni, the focus of the paper moves to discussing the apparent simplicity of Don Giovanni's peasant girl principal, Zerlina. The paper then proceeds to show that although Zerlina's music is characteristically humble on the surface, it is just as full of layering, narrative, and symbolism as the music of the noble characters, Donna Anna and Donna Elvira. Conclusions are then drawn about how Mozart creates characterization for Zerlina in Don Giovanni and the implications of this characterization.

            Brahms's Intermezzo in E major, Op. 116, No. 6 features a placid surface, with fleeting disruptions to that placidity. These momentary disruptions, however, increase in significance and substance as the work progresses, and culminate with an emotional overflow that seems to have been driven by some deeper process. Using Schenkerian voice leading analysis as a foundation on which to construct my analyses, I invoke the literary theories of Roland Barthes to structure three levels of musical narrative at work in Brahms. In particular, I use three of Barthes's so-called narrative codes: the proairetic, the semic, and the hermeneutic (see Barthes, 1974, and McCreless, 1988). The hermeneutic code in particular functions in an important way in this Intermezzo, and serves as a musical foil to the otherwise placid proairetic code. The hermeneutic and proairetic codes are further complicated by the semic code. Through my analysis of this Intermezzo, I draw an analogy from Barthes's argument which asserts that music listeners as well may be seduced by the "plot" of a harmonic progression. Other processes, or musical narratives, may be overlooked.

The purpose of this paper is to examine alternative hearings of musical processes through Schenkerian analysis, as well as through Barthes's narrative codes. Brahms's Intermezzo Op. 116/6 provides particularly fertile analytical grounds through which complexities in hearing and analysis may be demonstrated.

Common models of multimedia, like Eisenstein's and Eisler's notions of synesthesia and counterpoint and Cook's metaphorical model, are based on the assumption that each medium is monolithic in character and that its content is unchangeable, due to an impermeable protective membrane between the different media. This theoretical presupposition does not reflect our perceptual process, but it merely reflects the independence of analytical modes in traditional analysis.

The movie "Kuhle Wampe" (Germany 1932) challenges traditional models of multimedia due to its experimental collective mode of production and Marxist didactic purpose. Instead of traditional single-character driven agency, energetic states from image and sound are combined to complex intermodal sets that signify even ideological messages. This process guided me to a new concept of medial interplay.

In contrast to traditional models of multimedia I make the radical proposal that in general the distinction between music and image in the analysis of film should be dropped completely. The effects of traditional cutting techniques in film can be described in terms of energetics. Since music as film can be interpreted as energetic embodiments of our most basic physical experience, the process of constructing agencies through gesture (Newcomb 1997) constantly crosses the borders of all media. The viewer/listener freely combines energetic states from all domains, regardless of whether they stem from sound or image (Hatten on intermodality 2004). By providing a level of alignment for all media, the concepts of gesture and consequently agency become the most important elements of a unifying theory of multimedia analysis.

The Sanskrit metrical formula yam?t?r?jabh?nasalagam is designed so that each grouping of three consecutive syllables encodes a unique pattern of long and short (the macrons and final syllable count as long for this purpose). And it does so in a continuous fashion, creating what the mathematician Sherman K. Stein has called a "memory wheel". One may see the cyclical pattern better by using binary numbers, with "1" as long and "0" as short, thus 01110100(01; the open parenthesis indicates that the final 01 loops around to the initial 01. The paper contains a set of short variations on the themes of combinatorial completeness and design suggested by the formula, featuring studies of scales and rhythmic patterns from Indian and Western music theories; in addition, it explores a number of compositional spaces of similar structure.

In contrast to pioneering studies by Lewin, Cohn, Hyer, and others that focus the application of Neo-Riemannian operations on the music of the nineteenth century, more recent studies apply the standard models to pop-rock progressions. In this study, I combine and extend selected existing models to produce an all-inclusive network for parsimonious operations and apply them to examples of the pop-rock repertoire.

Of the nine possible operations among triads, only three (P, L, and R) have been recognized, as the other six contain either an augmented or a diminished triad. In Part One of my paper I explore the voice leading of these operations and establish Gegenleittonwechsel, Halbrelativ, and Überleittonwechsel operations. Similarly, of the ten possible operations among seventh chords, only four are used in the Power Towers. In Part Two of my paper I alter the Power Towers to establish the remaining six, which involve major seventh and fully-diminished seventh chords.

            In Part Three, I explore split functions ??? operations in which the cardinality of notes changes from three to four. Two of the possible split functions, classified as Relative and Leittonwechsel splits, are recognized.

            In Part Four of my paper I reorganize the twenty-four major and minor triads into three octatonic systems and connect the triads to the Power Towers. Relative and Leittonwechsel splits are used as conduits, hooking major and minor triads from the Octatonic Propellers graph to major and minor seventh chords in the Power Towers.

The development of compositional systems capable of achieving a functional integration between the vertical and linear dimensions of musical structure in the absence of a unifying tonal center was perhaps the most significant compositional challenge encountered by the early serialists. A diverse array of compositional strategies emerged as the result of the quest for a "unified space." Stravinsky and Webern each developed unique and novel systems for generating harmonic structures and establishing reciprocal correspondences between them. These various systems of harmonic generation have been recognized by contemporary theory for some time now. Yet comparatively little research has been conducted that examines the explicit behavior of vertical and linear sets on the musical surface and how these sets interact to generate unified spaces.

This paper explores harmony and voice-leading in the canonic writing of Stravinsky and Webern. It adapts recent transformational theories including Klumpenhouwer Networks (K-nets) to illustrate some ways in which these composers were able to produce a functional integration between the vertical and linear dimensions of musical structure. K-nets are employed to generate network models of linear/vertical structure that characterize isographic relations expressed between sets on the musical surface and between graphs at higher levels of recursion. A set of categories is established to define the various forms of "diagonal" correspondence expressed between the linear and vertical networks. Analytical examples will be drawn from Stravinsky's Canticum Sacrum and Double Canon; and Webern's String Quartet, op. 28/2, Symphonie, op. 21/2, and Quartet, op. 22/1.

By arguing against conventional wisdom that Klangfarbenmelodie (herein abbreviated KFM) names the common twentieth-century practice "in which the timbres of successive tones gain melodic importance comparable to that of pitch," Alfred Cramer breathes life into Schoenberg's term through an imaginative play of metaphors (Spectrum 24/1: p. 1). As readers, he invites us to (re)consider the term as a synthesis of turn-of-the-century revelations concerning the "nature" (as opposed to artifice) of acoustics, phonetics, and various performance practices -- a suggestion that provides moment for pause. Shifting the term from some definite meaning into a stage on which theoretical understandings of music and acoustics fluidly converse, Cramer relieves us from having to consider whether, in fact, Schoenberg ever composed a KFM in order to reflect on what it could mean to hear his and other musics as KFMs.

Taking full advantage of the metaphorical window Cramer opens, this paper explores -- in music by Schoenberg, Arvo Pärt and Brian Eno -- the confluence between Schoenberg's term and acoustic properties of ringing bells. In much the way a bell's Schlagton [strike tone] initiates and unites series of scattered partials above, Schoenberg's own scattered writings on KFM, I'll argue, can be united by understanding his term to refer to complex resonances of bell-like Klänge: the often dissonant contrapuntal streams of pitched partials [Klangfarben?] emerging, reverberating, then dissipating through one anothers' melodies married by a fundamental pitch, audible both in ringing bells and many "non-tonal" compositions.

Many works that have been written since the 1960s explicitly incorporate disparate elements in a way that challenges traditional notions of unity. These pieces require new analytical approaches that will embrace, rather than deny, their postmodernist aesthetic of diversity. This paper discusses a group of pieces written in the 1960s that can best be understood as musical collages: the last movement of Bernd Alois Zimmermann's Musique pour les Soupers du Roi Ubu (1966), the first movement of George Rochberg's Music for the Magic Theater (1965), and the third movement of Luciano Berio's Sinfonia (1968). It demonstrates that in many cases, the diverse quotations these pieces contain are related by chromatic complementation. Furthermore, the structural basis of these pieces is related to the concept of chromatic saturation.

Through complementation, the disparate elements are brought into relationship with one another in a way that embraces the very elements that create the contrasts between them as a main constructive principle. By thus addressing the issue of unity in the postmodern musical work within the context of concrete analytical findings, the current study sheds new light on one of the most provocative issues of the postmodern debate. It also contributes significantly to the dispute regarding the prevalence of continuity or discontinuity between the modern and postmodern aesthetic, by demonstrating that the technique of chromatic saturation provides, at the very least, a concrete strand of continuity between them.

            The second half of the fifteenth century was a time of explosive experimentation during which Johannes Regis initiated a new compositional approach, whose features include five-voice scoring, predominance of sparse textures, varied vocal orchestration, textural delineation of the tenor by long note values, and placement of the tenor as an axial-voice between two upper and two lower voices. This axial-tenor model, which was further developed by the next generation of Franco-Flemish composers such as Josquin, Barbireau, Weerbeke, and Obrecht, had a profound impact on mainstream compositional practices that emerged over the course of the sixteenth century. Though consisting of over 150 motets and Masses by more than sixty composers, the axial-tenor repertory remains a relatively obscure niche in musical scholarship.

            Among the most innovative and influential works relevant to this repertory are the five-voice compositions of Jacob Obrecht, which include five motets and the Credo of his Missa Sub tuum presidium. In the process of examining these works, this presentation will uncover analytical evidence explaining Obrecht's approaches to formal articulation, text usage, and cantus-firmus placement in five-voice writing. Analyses will also describe polyphonic scaffolding and compositional process by including an overview of individual voice functions, ranges, and clef configurations.

Since the 1970s George Perle's compositional output has emanated from his theory of twelve-tone tonality, one that holds numerous difficulties for the analyst. This paper presents two transformational tools, sum squares and pentagrams, that are particularly useful in studies of Perle's music.

Perle's basic unit, the cyclic set,alternates members of inversionally related interval cycles. This formation produces a repeating pattern of sums, the tonic sums, between notes. Two cyclic sets align to form an array. To generate melodic and harmonic material Perle mostly uses axis-dyad chords,hexachordal segments of the arrays.

Any hexachordal segmentation may infer a number of potential arrays. Challenges emerge if segmentations comprise fewer pcs, since they cannot reveal all four tonic sums of the prevailing array. This is the case in Perle's "There Came a Wind Like a Bugle." This music suggests segmentation almost exclusively into tetrachords and pentachords.

Transformational networks provide a solution. The analyst arranged tetrachords into "sum squares," in which three pairs of pcs in adjacent and diagonal corners form sums. Eight different arrays may be generated from a single pair of sums. Segmentations of five pcs proved more refractory. The solution lies in the pentagram, which embeds five quadrilaterals, yielding five times more possibilities than the sum square.

Sum squares and pentagrams serve well as preliminary steps in determining which arrays can lead to a coherent, convincing interpretation of the piece. This paper demonstrates how these tools helped uncover Perle's sensitive, programmatic rendering of Emily Dickinson's poem, in surface events and array relationships.

        During Stravinsky's serial phase, he utilized rotational-transpositional (rT) arrays, in which each row is a cyclic permutation of the preceding one, transposed to begin on the same pitch-class (pc). In composing, he extracted pcs from these arrays in various ways. In this paper, I focus on the musical ramifications of one of Stravinsky's common tactics: In extracting pc segments, he often followed corresponding array pathways (i.e., matching rows with rows, diagonals with diagonals, etc.). He then incorporated these segments into the music in a way that invited further cross-comparison, due to formal corollaries or similarities in articulation, texture, orchestration, etc. I will refer to such related segments as Array-Pathway Analogues (APAs). Indeed, Stravinsky often employed various segments in a section, drawn from perhaps a mixture of array pathways; these would then be "answered" by a corresponding assortment of segments in another section. Thus I will often be considering not isolated APAs, but rather APA Groups (APAGs). The degree of surface relatedness of APA(G)s may vary, depending on their musical settings, but their intrinsic similarity lies in their similar interval-class (ic) and pc profiles, as will be explained in detail.

        Through analyzing a diverse sampling of passages, I elucidate how Stravinsky used APAs to create musical sections or movements that suggest varied restatements of other sections or movements. I argue that variations based on APAs are a subset of a more general Anasystemic Variation Procedure (AVP). Here "system" is used in the sense of an organized group of objects that are associated (and interpretively interdependent) so as to form a complex unity. The prefix "ana-" is used in the sense of "according to" (as in "analogue"). Thus, an AVP results in a variation based not on thematic correspondences per se, but rather on systemic correspondences. Construed in this fashion, we find precursors to Stravinsky's process within Western compositional practice, revealing his procedures to be both within a broader tradition as well as distinctive in material ways.

            In the early moments of Britten's Death in Venice, the protagonist, Aschenbach, walks through a garden in Munich and encounters a Foreign Traveler, who commands him to "see" exotic marvels. The Traveler's aria foreshadows a number of elements that arise from the moment of the hallucination: exotic images, dramatic personae, phonemic sounds, and musical ideas. Critics generally hold that once Aschenbach "awakens" from the hallucination, his trip to Venice and the ensuing events -- including his obsession with the boy, Tadzio -- comprise waking action (with the exception of the Scene 13 nightmare). Given the multivalent operatic processes that spring from the hallucination, though, we could speculate that Aschenbach never leaves Munich and merely imagines or dreams of the Traveler, Venice, and Tadzio. The music even replicates a state of diminishing awareness not unlike that of falling asleep right before the Traveler appears. From then on, we cross over into an exotic, at times surreal, sound world, leaving behind the consciously manipulated twelve-tone environment of Munich for good.

            Several possible readings of the hallucination and ensuing action drive the analysis in this paper. Is the vision a dream or daydream? Is it an erotic fantasy or merely the workings of an artist's imagination in preparation for putting pen to paper? The discussion engages psychoanalytic dream analysis to illuminate the way music reinforces and even guides the condensations and displacements of Aschenbach's imagination that disguise his hidden desires. Then it pans out to explore the conceptual commonalities that allow us to hear music simulate altered states of consciousness.

The second act of Parsfial contains two pivotal moments that drive the whole music-drama involving Kundry, the only woman, and Parsifal.  Each of these moments must be re-contextualized in an act of narration for the character telling the story to absorb the experience into their conscious state. Parsifal's narration of the kiss and Kundry's narration of the mocking of Christ redefine their subject-positions and subsequently their role within the opera.  These two narrative moments also have musical parallels, suggesting that they can be heard under a similar hermeneutic model, both articulating moments of pleasurable suffering.  For Adorno, the seductive enjoyment of pain is precisely what is unique to Wagner's music.  Both of the moments capturing the sweetness of suffering are part of Kundry and Parsifal's individuation through the psychological economy of Freud's Oedipal complex.  While musicologists and psychoanalysts have explored Parsifal's Oedipal relationship to Kundry as his surrogate mother, Kundry's own role in respect to Christ, as her father, has not been fully investigated.

While scholars such as Elisabeth Bronfen elegantly capture the impossibility of Kundry's own subject-formation, this paper will reevaluate the psychological framework of act two of Parsifal with Freud's late theories on the feminine Oedipal complex in respect to Kundry as daughter, lover, and mother.  This paper connects musical evidence of Kundry's inability to individuate while continuing to act as a fully formed individual, one whose subjectivity is trapped by her own neurosis and the traumatic hysteria of laughter bound by silence.