Music Theory Midwest

Arthur J. Komar Student Award

2011 - Lincoln, NE
Christopher Brody (Yale University)
The V–I Paradigm in Bach's Binary Dances and a New Subject Category for Fugal Gigues

Conventionally, tonal structure in Bach's binary dance movements is described as a first reprise modulating from I to V (or i to v for minor-key pieces), followed by a second reprise modulating from V to I. As this paper demonstrates via a comprehensive survey, that stereotype is mistaken with respect to the tonal structure of second reprises, which, in fact, normally do not begin in a non-tonic key at all. Instead, second reprises usually begin with what I term the V–I paradigm, in which the reprise begins on an active dominant in the tonic key, which then proceeds without overt cadential rhetoric to a tonic chord. Only after this reiteration of dominant-to-tonic harmonic motion, which occurs in about 70% of Bach’s binary dances whose first reprises end in the key of V, does the second reprise proceed with the tonicization of a secondary key area and an eventual cadence in tonic. Because the V–I paradigm occurs in a variety of prolongational contexts, I argue that it functions as a schema in the sense recently popularized by Robert O. Gjerdingen (2007). The V–I paradigm also serves as the structural underpinning for the subjects of certain fugues: those in the second reprises of binary gigues in Bach’s keyboard suites. As such, the V–I paradigm allows us to construct a supplement to the otherwise exhaustive categorization of subjects and exposition patterns described by William Renwick (1995).

2010 - Oxford, OH
Benjamin Anderson (Northwestern University)
Schema Versus Archetype: How the Concepts Differ and Why We Need Both

Music theorists often use the words archetype and schema interchangeably: both words describe a musical pattern learned from the experience of listening. These words, however, have quite different epistemological underpinnings. In the context of style analysis, Leonard B. Meyer describes an archetype as a pattern that is "stable over time" and that "may help to illuminate the nature of the changes that have occurred in the history of...music." Schema, on the other hand, comes from a cognitive bent and Robert O. Gjerdingen defines it simply as a "mental representation." There may be merit in keeping these terms separate, with "schema" operating within a style and "archetype" transcending styles. This paper will first compare two Galant schemata—the Prinner and the Romanesca—with two analogous schemata from the vastly different music of Elton John—schemata that I have termed the Levon and the Chameleon. Then the style-specific features of these two pairs of structurally similar schemata will be removed to approximate the two metastylistic archetypes: the 4-3-2-1 stepwise bass descent archetype and the stepwise octave bass descent archetype. Finally, I will briefly discuss two possible uses for archetypes: archetypes as analytic tools used to detect changes in musical styles and archetypes as superordinate schemata abstracted from listening to a diverse repertoire of music.

In the forty-five years since composer Arthur Berger called for a "new branch of music theory" to address the language of post-tonal repertoires, the proliferation of analytical tools for examining the structure of such works has been considerable. There remains, however, a considerable gap between the analytical results provided by such tools and their relevance to musical performance—a gap that I contend is far narrower in tonal analysis. In this paper, I propose that the comprehension of even the most basic atonal structures is largely unhelpful to a musician in developing an informed and meaningful performance. To fill this gap, I propose a multifaceted analytical approach grounded in the field of musical meaning, an approach that utilizes recent theories of musical gesture, embodiment, and intertextuality.
Defending his twelve-tone method in 1936, Arnold Schoenberg wrote that he instructed his students to, "...use the same kind of form or expression, the same themes, melodies, sounds, rhythms, as you did before." This paper takes Schoenberg's compositional advice as analytical imperative. Focusing on one of the most over-analyzed works of atonal music in the repertoire, the second movement of Webern's Piano Variations, op. 27, this discussion avoids any mention of row forms, inverted canons, pitch-class symmetries, or fixed-registral dyads. Rather, using Peter Stadlen's 1936 performance edition as a starting point, I suggest specific gestural and topical prototypes, establishing the movement's connection to the past through various recompositions. My aim is to demonstrate that the movement derives its meaning from the expressionistic distortion of these prototypes.

2008 - Bowling Green, OH
Michael Vidmar-McEwen (Indiana University)
Franz Schubert & the Etherealized Mechanical

Critical responses to Schubert's music have traditionally been preoccupied with appraising his craft in relation to the Beethovenian ideal. They have especially focused on judging the worthiness of Schubert's sonata forms; these are found to be lacking, a result of their supposedly excessive length, repetitiveness, and propensity to become "lost" in temporally directionless memory-worlds. Recently, some authors--inspired by Adorno's 1928 essay, "Schubert"--have taken a more affirmative approach to these traits, focusing on the power of those very moments at which Schubert appears to be lost. So far, most have identified modulations as the primary activator of  Schubert's dream-spaces.

I demonstrate in this paper that Schubert frequently opens his characteristic interior spaces not just with kaleidoscopic modulation and arresting melody, but by recourse to a continuum of increasingly etherealized mechanical topics. Drawing on Elaine Sisman's work on memory and Carolyn Abbate's study of mechanical music, I show how Schubert's sensitivity to texture and timbre allowed him to create a range of mechanical style types, arrayed from the most grotesque (the Gothic horror of Der Leiermann), up through Arcadian musettes and tinkling music-boxes, to encounters with transcendent angelic voices. Schubert's use of mechanical topics to create his memory-worlds takes on even richer meaning when it is considered in light of the composer's cultural and biographical circumstances, including Romantic conceptions of memory and the pastoral, musical automata, Biedermeier Viennese psychology, and Schubert's own cautious involvement with Mesmerism.

  Experiencing a minimalist work has seldom been described as an active process. Yet, there are certain pieces that seem to imply a participatory role for the listener in virtue of their structural design. In this paper I examine Steve Reich's Drumming, exploring how the formal plan of the work suggests a participatory listening strategy—one that is both active and creative. Through a procedure Reich calls "pointing out," resulting patterns are highlighted from the successive phase relationships; in effect allowing new melodies to emerge from the music in a slow crescendo, and then fade out just as gradually. Though from a listener's perspective, even after these patterns fade they are still mentally present. These "trace melodies" are then overwritten by new resulting patterns, creating the temporal equivalent of a palimpsest. At a certain point, the performers cease to point out these melodies, yet the sustained phase relationship suggests that the listener should take on this role. Building on the work of Cohn, Horlacher, and Rink, I demonstrate how Part I of Drumming has a teleological formal shape, providing both a crescendo of attack points and an increasing variety of possible resultant patterns. Yet, it becomes the responsibility of the listener to mentally contribute to this composite, and without this participation the structure is anti-climactic; it is the listener who completes the formal process. After exploring how Drumming encourages the listener to take on this active role, I conclude by pointing out some of the rewards that come from engaging the piece in this way.

Musical scholarship on the relationship between analysis and performance continues to flourish. The first wave of this research, conducted throughout the 1980s and early 1990s with predecessors in Schenker, sought to establish a correspondence between marked structural events and their interpretation in performance. A second, more recent wave, dissatisfied with the formalism of such analyses, has sought to balance the contributions of the analyst and the performer in a more holistic musical understanding.

The rise of performance-driven analysis mirrors the growing work on musical agency. As yet, these two streams remain distinct. This paper seeks to examine the relationship between agency and performance using the first movement of Schubert's Sonata in A Minor, D. 845, as a text. I will propose an agential reading of the piece and demonstrate how various performances by established pianists recast and ultimately enrich that reading. By modulating the marked oppositions within their jurisdiction (i.e., expressive timing, dynamics, and articulation), performers can attenuate the listener's sense of narrative or refute it altogether.
No performer projects all aspects of my agential analysis; however, I do not assert that my reading is the only possible narrative. Rather, my aim is to show how the concept of agency can be a useful tool for comparing different performances. By speculating on the expressive motivations of performance choices, a theorist can interpret the microstructural variables behind such easy labels as "romantic," "passionate," or "mechanical." This approach complements hermeneutic analysis by according the performer a more equal role in the creation of musical meaning.

In recent music discourse, scholars have struggled to explain the sudden harmonic shifts, remote tonal regions, and discontinuity of musical gestures in Schubert's music. In an effort to rationalize these idiosyncrasies by relating them to a unified whole, some scholars have retooled pre-existing analytical systems by extending concepts of diatony; others have sought to devise new systems altogether, or have turned to hermeneutic models. What seems to fuel this drive toward integrating disparate musical events is an aesthetic of unity. This paper asks what other options might be available to us and how pursuing an alternative to an aesthetic of unity can affect our understanding of Schubert's music.

Using the Moment Musical, Op. 94, No. 2, as a case in point, my paper will suggest that certain pieces can be thought of in terms of irony, fostering a double-consciousness by engaging in a dialogic relationship with themselves and with formal and harmonic structures drawn from the past. The paper will (1) provide an alternative to perceiving Schubert's music as a monologic, unified consciousness, whereby idiosyncratic musical events are explained as contributing to a greater, continuous whole; (2) show how Schubert's use of tonality and form can coexist with notions of conventional diatony and form, and need not be understood either as a derivative of these customary procedures or as independent from them.

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.

The paper examines a simple, but (in the words of Edward T. Cone) subtle and refined example of discontinuity in Stravinsky's neoclassical style: the "Hymne" from the Serenade in A for piano. It reconsiders the established view that harmonic relations within self-contained "blocks" (or short sections) are functionally disconnected from those arising between juxtaposed blocks. Inspired by the internal structure of the 8-note diatonic collection that opens the movement, and by other surface features, the paper proposes a pitch framework, I call the Guidonian space, that captures all the 12 diatonic collections in a cyclic string of 36 pitch-classes. The harmonic system that results from the Guidonian arrangement models both superimpositions and juxtapositions of diatonic-affiliated collections used in the piece, but without the necessity of mediating these through complete diatonic collections. The paper proposes an operation (called MODULATE) that traces intra-space transformations of material based on common tone retention and incremental chromatic inflection. Since the operation acts at the level of the entire space, it allows for the transformation between collections of different cardinality. Analytical findings show that both superimpositions and juxtapositions of material are structured by a consistent value of MODULATE, suggesting that the piece's formal discontinuities rest upon a coherent harmonic syntax expressed at both local and large-scale levels.

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."

This paper investigates a link between metric displacements and romantic longing (Sehnsucht) in selected Lieder by Schubert, Schumann, and Brahms. Sybille Reichert has shown that expressions of Sehnsucht generally involve movement outwards, towards the infinite, followed by a return to the self. Metric displacements have the potential to generate "energy profiles" (Lewin) that correlate with this gesture of longing. The correlation is inevitably loose, however, for while the resolution of metric displacements brings about a relative state of rest, the longing subject who returns to him- or herself achieves neither resolution nor rest. The songs presented here compensate for this discrepancy in a variety of ways.

In Schubert's "Wandrers Nachtlied II" metric displacements reflect the outward movement of the Wanderer's longing. They cease with the turn to self-consciousness, but their "kinetic energy" is transferred to the vocal line, and the singer reaches up to his or her melodic climax in the final phrases. Ultimately Schubert's song achieves a state of rest that lies outside of the "temporal actuality" of the poem. Metric displacements in Schumann's "Intermezzo" are introduced as the poet gazes inward at an image of his beloved, intensified as he sings a song which flies out towards her, and resolved as he returns to the image in his heart. Schumann's postlude, however, undermines the sense of full closure. In Brahms's "Immer leiser wird mein Schlummer" the dying protagonist performs her urgent longing for the beloved with metric displacements, and her life energy dissipates as the displacements resolve.

A distinctive compositional signature for Bartók's post-1926 contrapuntal style consists of the superposition of strands in different keys. Analytical approaches to this music seem to divide along a standard tonal/atonal boundary. However, both approaches suppress the individuality and coherence of diatonic strands, the first by reducing chromaticism into diatonicism, the second by scattering diatonicism into chromaticism.

This paper proposes an alternative framework in which to conceive superposed diatonic spaces, without specifying diatonic collections nor appealing to pitch-centers. The starting point is the analytical tradition inspired by Bart—k's notion of polymodal chromaticism, and its subsequent crystallization as a prolongational model, the Lydian-Phrygian polymode. It is suggested that polymodes can be viewed independently of pitch-centric constraints, through a space I call dasian, after the dasian scale discussed in the medieval Enchiriadis treatises. The dasian space is a 48-element cycle, in which the twelve diatonic pitch-spaces are represented. It is thus a hybrid space: diatonic at the regional level and chromatic when gradually venturing outside each region. However, subsegments are defined not by their key affiliation, but by their (sometimes multiple) location within the cycle. Hence, the space draws its coherence not from the differentiation between key areas, but from its intervallic coherence and autonomous patterning. The navigation of the dasian system (through stepwise motion, and through an operation I call channeling) during mm. 1-38 of Bartók's Piano Sonata, mvt. III, retains the individual diatonic strands within the dasian space, as the music engages in a process of coherent exploration of that space.

Few have denied the value of performing a musical work. Yet more often than not we tend to dismiss the performer's role as a mere conduit through which we can hear the "work." The variety and nature of recorded interpretations has challenged musicologists and theorists alike to reconsider the nature of a musical work, its theory, and the entire system of values by which we evaluate music.

In this paper, I propose a radical shift away from perceiving the musical score as the single arbiter of a musical work and toward a view in which the performance and score collaborate to create a final work. It is my contention that we do not yet sufficiently understand the importance of performance; we credit the score for saying more than it really does. I examine a six-bar phrase from the third movement of Beethoven's "Waldstein" Sonata, Op. 53. and its development within the Rondo as performed by Arthur Schnabel, Ernst Levy, and most importantly, Josef Hofmann; Hofmann presents a three-note motive, a motive which, although not absent in the score, is not present in any other performances. Once brought to our attention, the motive governs our hearing of the entire movement and its overall structure. Drawing on the work of the cognitive linguist Ronald Langacker, I discuss the ways in which our perception of an otherwise unnoted motive might determine musical meaning.

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.

A simple algebraic framework is proposed for studying triadic transformations. Included are the "neo-Riemannian" transformations P, L,and R, and other transformations recently studied by Cohn, Hyer, and Lewin. Hyer's group of 144 transformations is extended to a group of 288, in which composition of transformations may be defined in a simpler and more unified fashion. The 144 non-Hyerian transformations include some of particular musical importance, such as the "diatonic mediant" transformation. Briefly, each transformation is represented by a sign (indicating mode-preserving or mode-reversing) and two transposition levels (one for major triads, one for minor). The study of the structure of this group generalizes some results of Cohn about the self-inverse property of some neo- Riemannian transformations, and provides some clarification of the relationship between those transformations that behave in characteristically "neo-Riemannian" ways and others (such as the "dominant" transformation) that do not--a relationship that some have found disturbing. The group may be regarded as the group of intervals in a suitable Generalized Interval System in the sense of Lewin. The methods presented are readily adaptable to transformations of set classes other than triads and to equal-tempered systems other than that with 12 notes.

The author views late works of Morton Feldman through the window of the metaphor 'living on the edge.' Analysis of the 1983 work Clarinet and String Quartet shows how fleeting hints of process, ordering and pattern engage the listener's perception at the threshold of intelligibility, and create a narrow 'zone of possibility' in which much of the activity of the piece takes place. In many ways the music adheres to the dictum formulated by Cage, Feldman, and their associates of the early 1950's: that sounds were to be heard 'as sounds themselves.' However, the author shows how the construction and presentation of material both validates and questions this idea.

Voiceleading parsimony is a term employed in recent work by Richard Cohn (1996) to describe situations in which every voice in a motion between two simultaneities is either retained as a common tone or moves incrementally, a half-step in chromatic space. This paper explores three relations of parsimonious voiceleading in Scriabin's nontonal music. The Pn-relation is a formalization of parsimonious voice-leading between chords for which there exists a one to one mapping, where n denotes the number of voices moving by half-step. P2-relations hold between any Teven-related Mystic chords (set-class 6-34), a common chord sequence in Scriabin's music. Split voice-leading which holds between a single pc and a dyad consisting of that pc's upper and lower neighbors, for example between {F} and {E,F#), is formalized as a split-relation. This relation employs a grouping based on registral proximity, and thus provides an alternative to the assumptions of one-to-one mapping of most theories of voice-leading. A Generalized Interval System of splitrelations is developed which demonstrates: (1) that T6-related acoustic collections (set-class 7-34), sister sonority of the Mystic chord, possess the potential for parsimonious voiceleading via splitrelations; and (2) an explicit means of describing the function of the acoustic collection as a mediating structure between whole-tone and octatonic collections. A generalized relation is developed which allows any instance of voice-leading parsimony to be decomposed into its constituent Pn- and splitrelations. Examples from Scriabin's Etude, op. 65, no. 3, demonstrate the inherent potential for parsimonious voiceleading of his preferred pitch structures, suggesting a relational network which obtains among them.

Felix Mendelssohn's incidental music for A Midsummer Night's Dream (1843) adds a powerful nonverbal narrative dimension to Shakespeare's play, sometimes furthering and other times suspending or transforming the dramatic narrative. More than any of the other movements, the Nocturne poses a potential conflict between musical and dramatic narratives by temporarily halting the staged action. While the mortal lovers on stage rest as the result of supernatural intervention, the audience too is forced to take a pause from the dramatic action by the external intervention of Mendelssohn's nondiegetic music. By being thus musically drawn into the Dream, the audience is--like the characters on stage--subject to some harmless deception, revealed in the following act through a surprising conjunction of music and words.

Morton Subotnick's A Key to Songs (1985) is the first piece in a trilogy of works each based on a separate collage "novel" by the Surrealist artist Max Ernst; A Key to Songs is based on the 1934 novel Une semaine de bont", ou les sept "l"ments capitaux (A Week of Kindness, of the Seven Deadly Elements). In each piece of the trilogy, Subotnick attempts to represent musically the bizarre worlds of Ernst's collage novels. In A Key to Songs, the methods of representation include imitating Ernst's collage technique and drawing upon some musical corollaries of the primary influences on Ernst's collages. Subotnick collages direct quotations and the stylistic variations from 19th century German Romantic lieder together in rapidly alternating sections, creating a formal collage of themes which is camouflaged by the surface smoothness of the music; in addition, Subotnick collages the acoustic and electronic instruments together, creating hybrid sounds. The result is an overall collage of 19th century Romanticism with Subotnick's contemporary computer music, and a collage technique analogous to that of Ernst's and including influences ranging from Freudian psychology to literary theory.

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