Finding the beat in music is a basic, at times unconscious, activity that is often our initial response to a series of musical events. While models of the psychological processes by which we accomplish this task abound, less has been said about how music itself might influence these processes. Psychologically-grounded metric theories such as that of Lerdahl and Jackendoff (1983) have for many years provided valuable frames for understanding music, but have limited utility when investigating real-time listening situations. As an example from work in meter perception, the Dynamic Attending Theory of Mari Reiss Jones posits an initial beat, but the difficult question of what musical factors might be involved in choosing this initial beat has only tentatively been broached. I investigate three beat-finding factors suggested in recent literature with an experimental protocol using both isochronous pulses and musical excerpts as stimuli: first, the perceptual salience of pulses as function of tempo; second, the temporal regularity of a pulse (pulse(s) at or approaching isochrony); third, the presence of faster and slower integrally-related pulses. While a pulse’s isochrony and its position within an excerpt’s metric hierarchy were found to be more important factors in beat-finding than tempo, all three factors operate in differing proportion based on personal characteristics of study participants, such as musical training and performance experience. These findings suggest that any theory of meter or meter perception claiming to describe a listener’s likely hearing of a metric structure must consider the whole of that structure before positing an initial beat, must take into account a performed realization of it, and must provide a richer description of “the listener.”

A child using crayon and paper could create a vivid image of a musical performance by drawing in time to the music, thereby capturing a great deal of information about tempo, dynamics, articulation, rhythm, and relative pitch. Unfortunately, the information contained in such an image would be recorded far too capriciously and haphazardly to be of analytic use. The problem is to generate an image from performance that would contain a wealth of musical information, be isotropic to the performance, and be of potential analytic use. To what analytic use an image might be put is the question at the heart of assessing the value of the image, and that question is largely contingent upon the desiderata for undertaking to generate such an image in the first place, which might include multi-resolution perspective (the image should show both general aspects of the form of an entire work and also show aspects of minute detail),

potential for comparative analysis (images of a performance of the same music should be subject to comparison with one another, and any moment of a performance should be subject to comparison with any other moment of that performance), real-time representation (durations represented in the image should be measurable in real time), richness of parameters (the image should represent pitch, duration, timbre, articulation in a comprehensive fashion), and flexibility (the image could be realized in more than one way, for instance, in terms of pitch or pitch-class).

The images on this first attempt were block-angle matrices generated within a Matlab environment from various musical performances. The paper reports on how the matrix is read and, the information these matrices contain, and their susceptibility to analysis. A variety of music illustrations will be used including nursery songs, pop music, Bach, Schoenberg, and Debussy.

Making meaningful ties to students’ performance experience is key to maintaining their interest in undergraduate core curriculum courses. By encouraging students to make connections to literature they are studying, the course content becomes an influence on their daily life as a practicing musician. Using a combination of technology in the classroom and web-based materials allows users to take repertoire study to a higher level of application that goes beyond the traditional mode of communication between professor and students. Students can explore pieces by manipulating and reconstructing elements to gain an understanding of both local and structural events. This paper will not only provide a guided tour of classroom and web-based listening projects, but will also illustrate how web-based technology is changing the pedagogy of music theory and aural skills.

Projects range from literature audio palettes where students manipulate and reconstruct elements to gain an understanding of both local and structural events, to projects that encourage students to discover and discuss performance issues such as intonation and balance of a given part to the full score.

In a recent atonal analysis seminar, my students found Schoenberg’s Herzgewächse (Op. 20, 1911) and Webern’s Opus 18 Lieder (1925) to be especially unpleasant listening. This impression was based on commercially released recordings. Recording a musical work tends to reify a particular performance, and therefore the performer. However, several recordings of atonal works that we encountered contained numerous errors of vocal intonation. At best, such performances misrepresent the composers’ intentions; at worst, they contribute to perceptions that this repertoire is inherently “ugly,” “neurotic,” etc.

The issue of performer errors leads to an interesting question: Do these errors nevertheless support the prevailing set-type language of the musical work? My presentation focuses on two recordings of Schoenberg’s Herzgewächse, Op. 20. This work is one of Schoenberg’s most difficult, both for the performer and for the analyst. For the performer it is particularly demanding in its range and control; it is consequently well suited for such “error analysis.”

After briefly discussing aspects of the Herzgewächse’s set structure, I turn to how recordings represent (or misrepresent) the “idealized performance” symbolized by the score. Recorded passages are compared to the score, and “checked” using a piano. Transcriptions of performer deviations are then analyzed for their set content and compared to the set structure of the “correct” work. The pedagogical implications of this exercise are twofold: first, it reinforces the importance of atonal aural skills pedagogy in comprehension and performance of this repertoire; second, it reminds us all not to trust everything we hear.

Since theories of Renaissance music typically focus on cadences, modes, imitation and dissonance treatment, there has been less attention given to issues of form. William Caplin has shown that in late eighteenth-century style, each phrase member has a particular formal function within a composition (signifying initiation, continuation or conclusion). In this paper, I explore to what extent such formal distinctions are present in Renaissance music, using examples from William Byrd’s Cantiones Sacrae (1575, 1589 and 1591) to illustrate.

I also invoke Peter N. Schubert, whose presentation types resemble Caplin’s “basic idea”: these types are the imitative duo (id), the non-imitative module (nim) and the canon. I identify new models in Byrd where features of the nim and id blend to form a hybrid presentation type (e.g., two imitative voices plus homophonic support is semi-imitative presentation). I assert that the choice of presentation type is tied to formal location (nims and ids predominate at a composition’s beginning, whereas canons and hybrids tend to initiate formal units in the middle of a composition).

The developmental procedures found in hybrid presentation types (such as transposition and invertible counterpoint) become useful devices for creating formal and modal loosening as a section unfolds. Caplin’s theory shows how musical content and formal function are inseparable in Classical style. This paper posits that presentation types, middle passages and concluding gestures in Renaissance style can similarly be differentiated, primarily on the basis of the contrapuntal techniques they contain.

The tenor motets of Johannes Regis, which are traditionally representative of the earliest sustained efforts to compose for five voices, initiated a new type of composition whose features include predominance of sparse textures, 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 “Regis-type” motet, or axial-tenor motet, was further developed by Franco-Flemish composers of Josquin’s generation. Despite the invaluable studies that have identified essential features of and established a historical context for the axial-tenor motet, current scholarship is virtually silent regarding the prevalence of axial-tenor writing in the fifteenth century.

The five-voice motets of Costanzo Festa demonstrate that axial-tenor composition 1) continued to develop twenty to thirty years later than conventionally believed and 2) was not cultivated solely by the Franco-Flemish but by composers from all over Europe active in the generation after Josquin. Historical facts, such as Festa’s activity at the Papal Chapel and the prevalence of axial-tenor works in Vatican sources from the 1480s to the 1500s, and theoretical treatises widely known in sixteenth-century Italy, which cite and discuss an axial-tenor motet by Regis, will support the hypothesis that Festa was familiar with and influenced by the axial-tenor repertory. A formal analysis of his Deus venerunt gentes (1527) will reveal unequivocal consistencies with the tenor motets of Regis and Franco-Flemish composers of the late fifteenth century.

This paper explores the coordination between diatonic and chromatic partitionings of the octave. It proposes a framework of six different spaces in which diatonic-related objects are precisely specified as pc segments and these objects are related by transformations unavailable in mod-12 or considered trivial in mod-7. These spaces are labeled chromatic, whole-tone, octatonic, mystic, Guidonean, and dasian spaces. One can think of these spaces as hybrid because at the local level they share intervallic patterns with diatonic collections, but become chromatic at the inter-regional level.

The paper explores how, in every space, moving from one pc to another non-adjacent pc can be precisely defined by TICK operations, which have two possible outcomes: either the pc is mapped into the same pc in a different location in the cycle (channeling), or it is mapped into the pc a semitone away (chromatic inflection). TICKs can be thought as “modulating” the space because they transform a pc (or a pc segment) into similar “neighborhoods” tonal theory would see as related by modulation. Any move in the space can be generalized by establishing a relationship between TICK operations and stepwise motion—from a given pc to its immediate neighbor. The variety of hybrid spaces models transformations between numerous scales or pc sets which, given their arrangement into steps and half steps, are pervasive in post-tonal diatonic music: whole-tone, octatonic, diatonic, “mystic chord,” heptatonia secunda, heptatonia tercia, etc. The paper concludes by briefly considering some of the spaces’ analytic potential.

A common feature of axial symmetry is the equal distribution of pitches around an axis to create musical lines that mirror each other. As the pitches converge and diverge from a fixed axis voices move in contrary motion. However, wedges may not result from absolute mirror symmetry, but may be produced by several lines moving in similar motion. For example, if two (or more) voices move in the same direction by different interval cycles, say a rising whole-tone scale simultaneously with a rising chromatic scale, then the intervallic distance between the two voices will steadily increase and decrease in size, thus generating a unique kind of wedging motion. Because two voices move in the same direction by different interval cycles, I call this a cyclic wedge. With any cyclic wedge there is a point whereupon all the voices merge, and I refer to this “axis” as the convergence point. In my presentation, I consider the relevance of cyclic wedges and convergence points in the fifth movement from Arnold Schoenberg’s Serenade Op. 24, Josef Berg’s String Quartet, Alban Berg’s String Quartet Op. 3, and Jean Papineau-Couture’s Dialogues pour violon et piano.

In his book Generalized Intervals and Transformations, David Lewin presents the idea of “interval” first in terms of a generalized interval system (GIS), and then in terms of a simply transitive group (STRANS) action on a set. He remarks that the first perspective is Cartesian and observer-oriented whereas the second perspective is gestural and subject-oriented. He also notes that the second is more general: while a GIS captures our historically grounded idea of interval as distance or measurement, a STRANS action captures both the idea of interval as distance and of interval as transformation.

Understanding this philosophical distinction calls on a student to compare the formal definitions of a GIS and of a STRANS action. The pedagogical difficulty of presenting the mathematics can be reduced if students are asked first to perform activities with familiar materials: (1) to translate ordinary-language statements about music from “Cartesian” into “transformational” language, (2) to invent systems both within and without the zone of the theory using the usual T/I operations, (3) to construct graphs induced by voice-leading relations that the student invents via brainstorming. This paper’s broad aim is to increase the ways we can respond to a large question which may arise in any theory course: why does music theory take the specific form it does?

A simple compositional trick for writing canons can shift classroom attention away from the usual obsessive struggle to compose consonances between pairs of dux and comes notes to the long-range musical issues of form, harmony, and motive. The basic trick, for a canon at the unison or octave, is to separate two dux notes that are one time interval of the canon apart by the interval of a third (ascending or descending), thereby assuring an imperfect consonance between the canonic voices at each time interval of the canon. A single note can then fill in this ascending or descending third by step. It is instructive to examine the frequency of this figure, but ultimately, the figure’s musical interest, both analytically and compositionally comes from the myriad ways that it can be embellished.

Three pieces—the minuet from Mozart’s String Quintet in C Minor, K. 406, the Credo from Haydn’s Lord Nelson Mass, and Contrapunctus XIII from Bach’s The Art of the Fugue all display a continuous fascination with the filled-in third’s utility. In fact, the repeated figure provides a skeletal frame for each composer’s piece. These three pieces demonstrate that a dux shaped primarily of filled-in thirds is not a mere crutch for the novice. Analytically and compositionally, an awareness of this pattern as a common canonic frame can help to demystify the canonic form, leading to the realization that the real puzzle of canons is to make music from limited musical choices.

The intellectual ability to read musical symbols and auralize a performance, or conversely to hear a performance and visualize the printed music, is highly prized among musicians. Aural skills classes have traditionally focused on developing these abilities through sight-singing and dictation, respectively. True aural skills, however, must go beyond deciphering and encoding; they must involve musical interpretation. Unfortunately, most aural skills programs barely address skills of interpretation, let alone emphasize their development with a methodical curriculum.

In my presentation, I will suggest some basic-level classroom exercises that promote the development of critical listening skills in a musical context. I will also summarize a sample lesson plan incorporating contextual listening for a relatively advanced aural skills class.

The Variations2 Digital Music Library project is a major research initiative being carried out at Indiana University, under a four-year NSF grant. The goal of Variations2 is to establish a second-generation digital library testbed system for music, which will provide on-demand audio; high-resolution scanned score images; symbolically encoded score files; and tools to enable music instructors to effectively use the digital library’s content to enhance classroom lectures and student activities, as well as to support distance learning. These Multimedia Music Theory Teaching (MMTT) tools will provide in a single application a number of capabilities otherwise available only in separate programs: a media player; a score viewer capable of zooming without loss of image quality; a music notation editor; a digital timeliner that enables the creation of interactive form diagrams; drawing tools for annotating scores and diagrams with text and shapes; labeling tools that allow for the quick creation of analytical symbols such as figured bass and scale degrees; tools for creating various types of questions and the automatic evaluation of student answers; and lesson management tools that provide the ability to save, retrieve, share, and submit lessons. The various media formats can have their display/playback synchronized, perhaps at the measure level. In addition to enabling instructors to more effectively prepare classroom lesson using digital content, instructors will also be able to create interactive lessons which will enhance their students’ abilities to develop critical listening skills and give them the opportunity to integrate visual, aural, and tactile modes of learning.

Charles Ives’s 1906 sketch, Rube Trying to Walk 2 to 3!!, served as an important compositional model for several of Ives’s later pieces. However, the nature of the relationship between the sketch and some of these pieces seems to have been overstated in the literature, and this paper seeks to rectify some of these errors by providing a detailed comparison of each of the relevant passages from these later pieces with the earlier sketch. The first part of the paper will present some analytical comments on the sketch, focusing especially on the multi-layered 2-against-3 rhythmic relationships suggested by the title. Next the sketch will be compared with the five later pieces that derive from or are related to this sketch. Finally, this paper will provide evidence to suggest that Rube Trying to Walk 2 to 3!! is about baseball, specifically Hall-of-Fame pitcher Rube Waddell, not just about some “Rube” from the country.

Despite the use of harmonic/collectional vocabularies foreign to the common-practice era, many post-tonal compositions generate interesting narratives defined by their pitch centers. This analysis of the first Allegro section of Appalachian Spring (“Eden Valley”) traces one such narrative. Many of Aaron Copland’s works exhibit alternation between musical units that emphasize tonal centers and those that are tonally ambiguous. The latter may have tonal implications for the rest of the work; that is, it may be an integral part of this composer’s style to use music lacking clear tonal centers to generate large-scale tonal structures. By focusing on the techniques used in these passages, and the ways in which they relate to one another, we may come to a better conception of Copland’s tonal design.

In this Allegro the opening tonal center is A, but by the section’s end it has yielded to F. These fundamental tonalities are represented as such by passages employing functional harmonic progressions emphasizing those major keys. In the context of this music, functional progression defines the most emphatic assertion of a given tonal center. However, functional harmony constitutes only one of several tonal techniques employed in this Allegro. To investigate this multi-faceted movement from A to F this paper will examine individually each of the tonal techniques juxtaposed in this section. Some techniques will be shown to suggest their own “paths” to F, though the way in which Copland has positioned various contrasting passages also gives rise to a larger, more complex tonal structure that constitutes movement from A to F.

In the thirties, Cole Porter’s “Love for Sale” was better known for its lyrics than for its music. This song about prostitution, with its references to soiled love and the price of paradise, was famously banned in Boston and even raised a few eyebrows on Broadway. I will demonstrate some ways in which Porter musically depicted his tawdry lyrics, coupling ambiguous and non-functional harmonic structures with disguised and incomplete contrapuntal lines. For comparison, portrayals of “true love” in two of Porter’s more normative torch songs will also be considered.

The role of rhetoric in the music of J. S. Bach has remained problematic, particularly the two central issues of how we understand rhetoric within a larger aesthetic context and how we interpret specific applications of the figures within historically informed analysis. Here I propose an approach that takes rhetoric as a mode of language fundamentally distinct from other modes (such as logic), and therefore assumes a different mode of operation and meaning. Commentary, elaboration, amplification, presence, and persuasion are various terms that have been used to describe this unique epistemological domain. And if we take music to be a kind of language (which has been one of the most influential metaphors in the history of Western music) then exactly how that language works will be a crucial matter.

Several musical excerpts from the St. Matthew Passion and the keyboard works will illustrate Bach’s use of figures and how these rhetorical events suggest musical meaning or formal function. In addition, eighteenth-century treatises offer a theoretical basis for Bach’s rhetorical turns of phrase. Included in the examples are figures that: 1) elaborate important words in the text, through repetition and commentary; 2) extend diminution beyond its usual scope; 3) expand the rhythmic profile of the strict treatment of dissonance; and 4) articulate formal function. Significantly, these various roles frequently involve the expansion of a phrase and thus suggest connections to recent work on phrase rhythm—for although Bach’s music largely predates the phrase-rhythm norms of later tonal music, it nevertheless presents rhythmic techniques of great interest.

Chapter 16, section 6, of Johann Joachim Quantz’s Versuch einer Anweisung die Flöte traversiere zu spielen (1752) concerns the duties of the keyboardist in accompaniment, and includes a short original composition entitled “Affettuoso di molto.” This piece features an unprecedented variety of musical dynamics—alternating abruptly from loud to soft extremes and utilizing every intermediate gradation. The extreme density of dynamic surprises is remarkable: most comparable pieces from the period were published without any dynamic indications whatsoever, and no other eighteenth-century treatise spells out dynamic prescriptions as explicitly. Quantz’s dynamics are seemingly intended to document an ideal concept of dynamic shaping, and may also be taken as an indication of contemporary performance practice. Most suggestively, Quantz’s discussion of this example provides an analytic rationale for the various dynamic levels specified in the musical score: specific levels of relative amplitude are prescribed for particular classes of harmonic events, depending on their relative dissonance. Quantz defines his categories in the language of the thoroughbass theorists of the time, but his categorization of dissonant chords speaks to a harmonic understanding related to or derived from emerging Rameauvian ideas of chordal structure. The transmission, co-option and revision of Rameauvian theory at the hands of Marpurg, Sorge, Daube and eventually Kirnberger represents an intellectual tradition with which Quantz is not usually associated; some kind of a link would seem to be suggested, however, by his categorization of dissonance and the theoretical understanding upon which it appears to be based.

Fétis is widely recognized as the music theorist who popularized the concept of tonality. Modern scholarship that has addressed his theory of harmony has focused with few exceptions on the sources and characteristics of the principle of tonality, which is the philosophical basis of his theory. The present paper discusses a dimension of Fétis’s theory of harmony that has thus far received no attention in the scholarly literature: the social aspects of its emergence. Two points are discussed specifically: first, the “unveiling” of the theory in a series of popular lectures by Fétis in Paris, and second, the place of Fétis’s theory as challenger to the harmonic theory of Catel, which was the institutional status quo for Parisians of Fétis’s generation. This ideological battle between the theories of Fétis and Catel was played out in a journalistic debate between Fétis and Joseph Zimmerman, a friend of Fétis but disciple of Catel. Zimmerman accepted Fétis’s principle that tonality was the organizing force of harmony; the sources of conflict were details of chord generation. The majority of the disagreements between Fétis and Zimmerman concerned the derivations of the seventh chords built on the second scale degree in major and minor keys. An examination of the generation of these chords in each theoretical system provides a clear view of their points of conflict.

One of the most important elements in Anton Bruckner’s pedagogy was Sechter’s harmonic theories; however, they are viewed as objectionable now since they lead to the addition of theoretical pitches not literally notated in the score. In addition, the level of complexity found in Brucker’s music appears so much greater than the harmonic exercises found in Bruckner’s and Sechter’s writings that any relationship appears negligible.

Several studies over the past fifteen years, however, have pointed to a closer relationship between Bruckner’s analytic work and his compositional output. Following their lead, I will argue that a linking element between Bruckner’s harmonic pedagogy and his compositional practice can be found in the relationship between strict and free composition. To see this, we must view the strict/free relationship in a dynamic manner rather than in a static manner.

The relationship between strict composition and free composition is dependent upon the concept of transforming a simpler underlying idea into a more complex one. Using compositional principles derived from the primary documents of Bruckner’s circle, enigmatic passages from the first movement of Bruckner’s Eighth Symphony will be reduced to demonstrate the relationship to Sechter’s strict harmonic underpinning. The primary principles used for that purpose include: 1) the existence of a diatonic foundation for all chromaticism, 2) enharmonic reinterpretation, 3) harmonic ellipsis (i.e., the omission of an expected chord in a progression), 4) modulation and 5) region ambiguity.

Heinrich Schenker’s Ursatz exemplifies the traditional functional roles of outer voices in tonal music, with the upper voice as principal bearer of melody and the lower voice as provider of harmonic support. What would happen if these traditional roles were reversed? Is this kind of role reversal possible? In this study, I examine exceptional pieces in which the lowest sounding voice is the principal bearer of the melody. My principal focus is on piano compositions in which the melody is played by the left hand. Among the issues I consider are: what happens to the bass line in these works; what role do the upper voices play; and can the fundamental line be positioned entirely in a lower voice?

The analyses in this study show that, rather than role reversal, the melodic bass is generally forced into a dual role, in the form of a compound melody with both a functional bass and melodic tenor. The upper voices provide an accompaniment that can sometimes be interpreted as Urlinie tones, but a stronger case can often be made for an Urlinie in the tenor. In support of this approach, I cite Carl Schachter’s concept of a “submerged Urlinie,” defined as “a fundamental line that is introduced in the middle of the texture rather than on top.” The dynamic tension that may emerge between a lower voice that attempts to take on a melodic Urlinie role and a competing upper voice that may resist such attempts is what I term “Urlinie Envy.”

In Brahms Studies 3 (2001), Peter H. Smith explores motivic-metric process in the opening movements of the Horn Trio Op. 40 and the Clarinet Trio Op. 114 and discovers significant relationships among metric displacement, tonal organization, and formal design. In each of these movements, the concluding section provides substantial, though not complete, resolution of previous metric dissonances. Brahms’s oeuvre contains many similar trajectories from motivic-metric instability to stability; probably the most celebrated one involves the opening neighbor-note motive from the first movement of the Second Symphony. The analytical literature on Brahms’s instrumental music has comparatively little discussion of dissonances that do not resolve within a movement, even though these situations are not rare in this repertoire. This paper will explore such metric dissonances in the second movement of the Piano Trio in C Minor, Op. 101, the last of Brahms’s many scherzo-type movements in the key of C minor. The paper will conclude by briefly considering the expressive motivation for the unresolved metric dissonance in this movement, the role of the contrasting middle section in making non-resolution an effective outcome for the movement, and the interaction of metric dissonance with tonal structure.

  While the flattened borrowed chords (bIII, bVI, and bVIII) and the Neapolitan triad (bII) have provided composers with coloristic harmonic resources for centuries, the pivotal role of primary triads (I, IV, and V) makes them less subject to such alterations. Whereas harmonies such as the flat-submediant may be used to embellish and “darken” an underlying simple harmonic palette, alteration of primary triads potentially undermines the fundamental progression and the tonality of the music.

Richard Bass has demonstrated how “harmonic shadows” in the music of Prokofiev allow the composer to explore simultaneously two harmonic structures in keys one semitone apart (as C major and D-flat major). This paper demonstrates that Shostakovich used similar devices and proposes that such shadow structures are not limited to semitone relations but may be extended to more remote alterations. Analysis of Shostakovich’s Prelude in C-Sharp Minor, Op. 34, No. 10 shows how not only flat-tonic relations (C natural, bI) but also triply flat relations (B-flat, bbbI) operate by proxy to the fundamental tonic. There is no modulation in the common sense of the term; the tonal center remains but briefly skewed. Such an unusual treatment of harmonies is idiomatic of Shostakovich, Prokofiev, and other Russian composers.

Shostakovich’s late works have been described as sparse and austere, lacking the bombast that often marked his earlier music. Many have also observed in them the advent of twelve-tone melodies. Another defining feature is a frequent emphasis on interval classes 1 and 5, a trait that links Shostakovich with such diverse composers as Webern, Stravinsky, Bartok, and Ruggles, all of whom wrote passages or entire pieces rooted in ic1 and ic5. Previous scholars have recognized the importance of these interval classes in late Shostakovich. Yet no one has pursued in depth the nature of their interaction. This paper does so by drawing on the concept of dual interval space (DIS).

A DIS is a two-dimensional pitch-class space in which each axis corresponds to a distinct interval class. A DIS provides a conceptual framework for analysis: if two interval classes underlie some piece (or section of it), we can envision that music inhabiting the DIS generated by those two interval classes. In addition, we can illuminate musical processes by means of transformations involving translations and flips in a DIS, revealing musical symmetries beyond those associated with conventional pitch-class operations.

After introducing the theoretical groundwork and considering several small-scale examples, the paper explores pitch structure in “Noch” (“Night”), one of the final songs in the Suite on Verses of Michelangelo. This song features an intriguing mix of ic1/ic5 activity and octatonicism. The analysis reveals connections between these disparate aspects of pitch structure, in the process demonstrating how ic1/ic5 space can offer a useful lens through which to explore octatonicism in the song.

Traditional techniques of music analysis are based on the assumption of a governing unity in the musical language. Thus the musical collage, which by definition subverts the concept of unity by juxtaposing fragmentary quotations from different musical styles within a single composition, poses the most stimulating questions for the analyst: What is the relationship between the disparate elements in a collage? What are the structural implications of combining such a variety of disparate elements? Finally: What theoretical tool should be used to analyze music with such diverse musical idioms?

Technical discussion of the first movement of George Rochberg’s Music for the Magic Theater has for the most part been limited to a description of the motivic recurrence of the 3–1 [0, 1, 2] trichord. In my discussion I will demonstrate, by using transformational graphs, that the role of the chromatic trichord goes far beyond mere motivic recurrence as it is eventually established as one of the most important harmonic sonorities and voice-leading structures of the piece. In this way it underlies and connects all of the disparate elements in the piece including even those sections and motives that do not apparently contain it. Furthermore, the chromatic trichord provides the logic behind the large-scale organization by determining the structure of the large-scale transformations involved.

In this way it becomes apparent that transformational theory and motivic analysis (both of which are analytical tools that have been applied with success to a variety of repertoires) can reveal surprising sources of unity and continuity by traversing distinct musical languages and thus elucidate the logic behind the combination of the latter on many different levels of structure in a musical collage.

In an article in Music Theory Spectrum (vol. 12/1, 1990) David Lewin defined a Klumpenhouwer network (K-net) as “any network that uses T and/or I operations to interpret interrelations among pcs.” A K-net is a graphic representation of the intervallic relationships among elements of a set. Lewin suggested that K-nets may be applicable to aspects of George Perle’s twelve-tone tonality, a theory based on the conjunction of interval cycles and inversional symmetry. Perle responded in a letter to the editor (Spectrum, vol.15/2, 1993), noting several points of intersection involving trichordal and tetrachordal pc segments. More recently, David Lewin, Philip Lambert, David Headlam, and Philip Stoecker have continued the dialogue to some extent (Spectrum, vol. 24/2, 2002). Their discussions only touch on the various relationships between K-nets and Perle’s cyclic sets (entities formed by alternating inversionally related interval cycles).

This paper explores how K-nets are applicable at deeper levels of Perle’s theory, that of array relationships. The paper first examines the relationship among cyclic set segments and complexes, then progresses to chords generated by rotating the component cyclic sets of a single array, and then arrives at the more abstract level of relationships among different arrays, observing the various types and degrees of isographies that obtain. The paper concludes with suggestions for further study at the hierarchical levels of synoptic modes and keys. Such investigations will confirm the structural integrity and cohesion that permeate all levels of Perle’s twelve-tone tonality.

Bernard (1993), Mead (1994 and 1995), and Capuzzo (2000) offer important explorations of the role of pitch and contour spaces in Elliott Carter’s music. The significance of registral distribution is heightened when Carter uses compositional strategies are based on all-interval twelve-tone chords. The presentation explores the role of register and spacing in the formal processes of Carter’s music. The paper offers tools to show the registral spacings of the twelve-tone chords by developing the concepts of SP-collections, SP-mosaics, and SP-types based on spacing (SP) and it sums introduced in Morris (1987). The focus is Carter’s orchestral piece Remembrance (1988), which is based on twenty-nine all-interval twelve-tone chords proceeding at a steady pace. The paper illustrates how these chords are a source of the work’s processes on various structural levels and in various musical dimensions, considering also how the chords’ registral spacings relate to their instrumentation. The paper concludes by discussing the roles of the pc-, p-, and c-structures to illustrate how the work’s formal processes may be perceived by a listener, suggesting that in this regard the interaction between the underlying pc-organization and the musical surface is important: the underlying pc-organization provides a syntactical context within which the surface strategies take place.

Since the rise of dynamic psychiatry beginning in the late nineteenth century, Wagner’s operas have attracted psychologically attuned analytical perspectives. Elements intrinsic to Wagner’s works encourage such studies and the view that Wagner was ahead of his time in his psychological insights. What could be considered the study of psychology in Wagner’s own time seems unscientific, even bizarre, when compared with modern dynamic psychiatry. The serious interest in animal magnetism and a general idealistic tone have not encouraged favorable assessments through most of the twentieth century. Yet since the 1960s, the history of psychology has been largely rewritten to illustrate the indebtedness of modern dynamic psychiatry to ideas developed from the 1770s to the mid-1800s. Regardless of certain errors in judgement, this heady mixture of philosophy, psychology and aesthetics found expression in artworks such as Wagner’s Tristan und Isolde.

This paper reconsiders Wagner’s relationship to psychological ideas of his time and their possible avant-garde influence on Tristan und Isolde. Since Der fliegende Holländer, Wagner had explored means of coordinating psychologically intricate material with progressive ideas about musical form and tonal planning. As is well known, Wagner’s reading of Schopenhauer impacted his creativity in the mid-1850s. Examined here is Schopenhauer’s concept of the unconscious and the conscious as mediated through the allegorical dream state. As vivid aesthetic metaphors, such ideas support a framework of differentiated psychological spaces in Tristan und Isolde that bear ties to developments in Wagner’s harmonic and tonal practices. The paper concludes with a psychologically-oriented consideration of the principles of associative tonality, reassessing the function of tonal pairs in Tristan und Isolde previously explored by Robert Bailey, Lawrence Kramer and John Daverio.

Edvard Grieg is one of the nineteenth century’s masters of song composition, and the song cycle Haugtussa, Op. 67, represents one of the composer’s highest achievements in the genre. The text is a story of a love and loss taken from Arne Garborg’s novel of the same title. This paper uses a semiotic approach to explore Grieg’s musical interpretation of the poetic narrative.

Grieg employs a “love motive,” a three-note descending figure, throughout the song cycle. The motive is consistently denotative of love, but it has different connotations from one song to the next. Initially the motive connotes joy, but it is gradually transformed into a symbol of loss, mirroring the text as love is tarnished by betrayal.

I will use the “semiotic square” put forward by A. J. Greimas to map the various feelings expressed in the songs and to trace the narrative path of the protagonist’s emotions from initial joy to obsession, loss, and final resignation, examining both the literary content of the songs and Grieg’s musical interpretation of the text. The paper demonstrates that Greimas’s semiotic square and the concept of the narrative path are effective and engaging when applied to the study of both music and text.

Theorists have developed analytical systems that describe the structure and function of music of the common practice period, of serial music, and of nonserial, atonal music, but until recently no system designed specifically for the analysis of post-tonal diatonic music has existed. In 1979, John Clough designed such a system in his article “Aspects of Diatonic Sets,” and since then scholars, most notably Mathew Santa, have used these ideas as a basis for their own theories and analyses. The following paper is also based on Clough’s theories, but differs from previous scholarship in that it makes more significant use of Clough’s system of chord notation. As its name implies, chord notation is primarily used to describe vertical sonorities, but there is no theoretical reason why this nomenclature should be limited only to chords, for it is actually a generalized way of describing the interval content within a given set of mod-7 pitches. Therefore, it can also be applied to the horizontal dimension to reveal the underlying set of intervals that comprise a given melody. This, in turn, reveals which interval sets are of particular structural significance to the music, because of their appearance in both dimensions. Furthermore, this nomenclature also has the potential to reveal how melodies and harmonies evolve as the structure of the music evolves, and, by extension, how closely the melodies and harmonies are related.

To illustrate these points, this paper applies these theories in new ways to segments of the first and second movements of Ralph Vaughan Williams’s Fifth Symphony.