Gustav Mahler's Seventh Symphony seems to belie traditional notions of symphonic unity in that it progresses from E minor in the first movement to C major in the Finale. The repertoire of eighteenth and nineteenth century composers such as Haydn, Beethoven, and Brahms indicates that tonal holism is a significant factor for the symphonic genre. In order to reconcile Mahler's adventurous key scheme, this dissertation explores a multidimensional harmonic model that expands upon other concepts like Robert Bailey's double-tonic complex and transformation theory. A multidimensional musical object is a nexus of several interconnected chords that occupy the same functional space (tonic, dominant, or subdominant) and can be integrated into a Schenkerian reading. Mahler's Seventh is governed by a three-dimensional tonic object that encompasses the major and minor versions of C, E, and A-flat and the augmented triad that is formed between them. The nature of this multidimensional harmony allows unusual formal procedures to unfold, most notably in the first movement's sonata form. To navigate this particular sonata design, I have incorporated my own analytical terminology, the identity narrative, to track the background harmonic events. The location of these events (identity schism, identity crisis, and identity reclamation) is critical to the …

Hymnus Paradisi (1938), a large-scale choral and orchestral work, is well-known as an elegiac masterpiece written by Herbert Howells in response to the sudden loss of his young son in 1935. The composition of this work, as noted by the composer himself and those close to him, successfully served as a means of working through his grief during the difficult years that followed Michael's death. In this dissertation, I provide linear analyses for Howells' Hymnus Paradisi as well as its predecessor, Howells' Requiem (1932), which was adapted and greatly expanded in the creation of Hymnus Paradisi. These analyses and accompanying explanations are intended to provide insight into the intricate contrapuntal style in which Howells writes, showing that an often complex musical surface is underpinned by traditional linear and harmonic patterns on the deeper structural levels. In addition to examining the middleground and background structural levels within each movement, I also demonstrate how Howells creates large-scale musical continuity and shapes the overall composition through the use of large-scale linear connections, shown through the meta-Ursatz (an Ursatz which extends across multiple movements creating multi-movement unity). Finally, in my interpretation of these analyses, I discuss specific motives in Hymnus Paradisi which, I hypothesize, …

Max Reger was a prolific composer on the threshold of modernism. The style of his extensive musical output was polarizing among his contemporaries. A criticism of Reger's music is its complex and dense musical structure. Despite writing tonal music, Reger often pushes the boundaries of tonality so far that all sense of formal organization is seemingly imperceptible. In this dissertation, I offer what I observed to be a new way of discerning Reger's motivic relationships and formal structures within and between movements. There are three primary tools and methods I incorporated to make these observations: Schoenberg's developing variation; melodic contour analysis as discussed by Elizabeth West-Marvin and Diana Deutsch; and Janet Schmalfeldt's motivic cyclicism stemming from internal themes. In this dissertation I examine five different musical works by Reger: D minor Piano Quartet, Clarinet Quintet, Piano Concerto, String Quartet, op. 121 and E minor Piano Trio, op. 102. My analysis shows how Reger relies on melodic contours of his motives to connect musical moments across entire movements and entire works with multiple movements. These motives are developed and often mark structurally significant moments providing the organization often perceived as missing in Reger's music.

Although music of the twentieth and twenty-first centuries makes frequent use of non-isochronous meter (meters involving beats of different length, such as 5/4 and 7/8), most studies on meter and metric dissonance focus on isochronous meters (meters involving beats of the same length, such as 4/4 and 9/8). This dissertation bridges this gap by developing two methodologies to account for metric dissonance involving non-isochronous pulses: modified ski-hill graphs and the composite beat attack point system. Modified ski-hill graphs, adapted from Richard Cohn's ski-hill graphs, illustrate metric states involving non-isochronous pulses and reveal degrees of dissonance in musical passages that share time spans, as in 5/4 grouped 3+2 vs. 5/4 grouped 2+3. The composite beat attack point system uses rhythmic notation to illustrate metric states involving any pulse duration or time span, revealing specific points of dissonance and consonance, relative strength of dissonance and consonance, and patterns of dissonance and consonance. The methodology is used to closely examine the treatment of metric dissonance in Holst's "Mars," from The Planets, Ligeti's Hungarian Rock (Chaconne), and Ligeti's Désordre. The analyses focus on passages where the metric dissonance becomes ever more pronounced and ends up obliterating any sense of meter.

Beethoven's rich compositional language evokes unique problems that have fueled scholarly dialogue for many years. My analyses focus on two types of paradoxes as central compositional problems in some of Beethoven's symphonic pieces and piano sonatas. My readings of Beethoven's Piano Sonata No. 27 (Op. 90), Symphony No. 4 (Op. 60), and Symphony No. 8 (Op. 93) explore the nature and significance of paradoxical unresolved six-four chords and their impact on tonal structure. I consider formal-tonal paradoxes in Beethoven's Tempest Sonata (Op. 31, No. 2), Ninth Symphony (Op. 125), and Overture die Weihe des Hauses (Op. 124). Movements that evoke formal-tonal paradoxes retain the structural framework of a paradigmatic interrupted structure, but contain unique voice-leading features that superimpose an undivided structure on top of the "residual" interrupted structure. Carl Schachter's observations about "genuine double meaning" and his arguments about the interplay between design and tonal structure in "Either/Or" establish the foundation for my analytical approach to paradox. Timothy Jackson's reading of Brahms' "Immer leiser word meine Schlummer" (Op. 105, No. 2) and Stephen Slottow's "Von einem Kunstler: Shapes in the Clouds" both clarify the methodology employed here. My interpretation of paradox involves more than just a slight contradiction between two …

Philip Glass's minimalist opera The Voyage commemorates the 500th Anniversary of Christopher Columbus's discovery of America. In the opera, Philip Glass, like other composers, expresses singers' and non-singers' words and activities by means of melodies, rhythms, chords, textures, timbres, and dynamics. In addition to these traditional musical expressions, successions of reiterating materials (RMs, two or more iterations of materials) and non reiterating materials (NRMs) become new musical expressions. However, dividing materials into theses two categories only distinguishes NRMs from RMs without exploring relations among them in successions. For instance, a listener cannot perceive the functional relations between a partial iteration of the RM and the NRM following the partial RM because both the partial RM and the NRM are NRMs. As a result, a listener hears a succession of NRM followed by another NRM. When an analyst relabels the partial RM as partial loop, and the NRM following the partial RM as loop breaker, a listener hears the NRM as a loop breaker causing a partial loop. The musical functions of loops and loop breakers concern a listener's expectations of the creation, sustaining, departure, and return to the norm in successions of loops and loop breakers. When a listener associates …

Through an examination of 402 songs that charted in the top 20 of the Billboard year-end charts between the years 1990 and 2009, this dissertation builds upon previous research in form of popular song by addressing the following questions: 1) How might formal sections be identified through melody, harmony, rhythm, instrumentation, and text? 2) How do these sections function and relate to one another and to the song as a whole? 3) How do these sections, and the resulting formal structures, relate to what has been described by previous theorists as normative? 4) What new norms and trends can be observed in popular song forms since 1990? Although many popular songs since 1990 do follow well-established forms, some songwriters and producers change and vary these forms. AAA strophic form, AABA form, Verse-Chorus form, Verse-Chorus with Prechorus and/or Postchorus sections, Verse-Chorus-Bridge form, “Other, with a Chorus” and “Other, without a Chorus” forms are addressed. An increasing number of the songs in each of the above listed forms are based on a repeating harmonic progression or no harmonic progression at all. In such songs, the traditional method of identifying sections and section-functions through harmonic analysis is less useful as an analytical tool, …

The Czech-born music theorist, Václav Philomathes, wrote the Musicorum libri quattuor in 1512 while attending the University of Vienna. This didactic treatise became one of the most widely published theory treatise of its time with 26 copies of five editions remaining today and covers the topics of Gregorian chant practice, Solmization, Mensural Notation, Choir Practice and Conducting, and Four-voice Counterpoint. Of particular note, is the section on choir practice and conducting, of which there is no equivalent prior example extant today. This dissertation provides a Latin-English translation of Philomathes’s work, as well as produces a critical commentary and comparison of the five editions while positioning the editions within the context of the musico-theoretical background of early-to-mid-16th century scholarship in Central Europe.

Heinrich Baryphonus (1581-1655) and Heinrich Grimm’s (1592/3-1637) didactic treatise, Pleiades musicae (1615/1630), provides a vivid testimony to the state of music education and music theory pedagogy in Protestant Germany in the early seventeenth century. Published initially by Baryphonus for use at the Gymnasium in Quedlinburg and reissued in an expanded format by Grimm for use at the Gymnasium in Magdeburg, the text examines the fundamentals of pitch, intervals, counterpoint, and, in the second edition, triadic theory and composition. Throughout the remainder of the seventeenth century and into the eighteenth century, music theorists including Johann Andreas Herbst (1588-1666), Otto Gibel (1612-1682), and Andreas Werckmeister (1645-1706), used the document as a source for their own musical writings, solidifying its status as a significant contribution to the field of music theory. Recently, scholars such as Carl Dahlhaus, Benito Rivera, and Joel Lester have found value in Pleiades musicae for its role in the early stages of the development of triadic theory and the emergence of harmonic tonality. However, with the exception of the passages on triadic theory, the treatise continues to be relatively unknown. In order to understand the full extent of Baryphonus and Grimm’s contributions to the history of music theory, and …

The use of algorithms in compositional practice has been in use for centuries. With the advent of computers, formalized procedures have become an important part of computer music. David Cope is an American composer that has pioneered systems that make use of artificial intelligence programming techniques. In this dissertation one of David Cope’s compositions that was generated with one of his processes is examined in detail. A general timeline of algorithmic compositional practice is outlined from a historical perspective, and realized in the Common Lisp programming language as a musicological tool. David Cope’s compositional output is summarized with an explanation of what types of systems he has utilized in the analyses of other composers’ music, and the composition of his own music. Twentieth century analyses techniques are formalized within Common Lisp as algorithmic analyses tools. The tools are then combined with techniques developed within other computational music analyses tools, and applied toward the analysis of Cope’s prelude. A traditional music theory analysis of the composition is provided, and outcomes of computational analyses augment the traditional analysis. The outcome of the computational analyses, or algorithmic analyses, is represented in statistical data, and corresponding probabilities. From the resulting data sets part of …

Tonality is a term often used to describe the music of the common practice period (roughly 1600-1900). This study examines the music of mid twentieth-century jazz composer Thad Jones in light of an extended common practice, explicating ways in which this music might be best understood as tonal. Drawing from analyses of three of Jones’s big band compositions: To You, Three and One, and Cherry Juice, this study examines three primary elements in detail. First is Jones’s use of chord-scale application techniques in the orchestration over various chordal qualities represented by the symbols, revealing traditional as well as innovative methods by Jones. Second is Jones’s use of harmonic progressions, demonstrating his connection to past practice as well as modern jazz variations. Third is Jones’s use of contrapuntal connections and their traditional relationship to functional tonality, but in a chromatic scale-based environment. Jones’s music is presented in this study to demonstrate a tonal jazz common practice that represents an amalgamation of traditions including twentieth-century scale-based procedures, Renaissance and early twentieth-century modality, eighteenth- and nineteenth-century voice leading schemas, and Baroque and Classical descending-fifth progressions. Also included as an appendix is a list of possible note errors in the published scores of To …

In 1924, Herbert Eimert’s Atonale Musiklehre was the first published text to describe a systematic approach to composing atonal music. It contains significant contributions to the discourse on the early development of twelve-tone composition. While Eimert uses the term “atonal” to describe his compositional approach, his definition of atonality demands that all twelve tones be present with none repeated, and that they present as complexes not ordered rows. Eimert’s discussion of atonality differs from others of the same period because he focuses on vertical sonorities and introduces “interlocking complexes”, wherein two separate statements of the aggregate can overlap by one pitch or by a set of pitches. Interlocking complexes are an important feature of Eimert’s string quartet Fünf Stücke für Streichquartett, which was published in 1925 and composed at the same time as Atonale Musiklehre was written. In the foreword to Atonale Musiklehre, Eimert clarifies that he is not the originator of the concept of atonality, rather that he absorbed the ideas of Josef Matthias Hauer and Jefim Golyscheff. Twelve-tone complexes appear first in Golyscheff’s 1914 String Trio. He refers to them as “twelve-tone duration complexes” and labels them in the score. As the name “duration complexes” implies, there are …

During the 1930s, German-born music critic and composer Gualterio Armando (1887-1973), formerly known as Walter Dahms, set to music thirty-four poems by some of the most important Hispano-American poets from the latter part of the nineteenth and first half of the twentieth century. In these songs, Armando tries to capture the spirit and idiosyncrasy of Hispano-American cultures while incorporating his own musical aesthetics. Armando’s 34 Canciones Hispanoamericanas para Canto y Piano (34 Hispano-American songs for voice and piano) display an original sound and style full of rhythms, shapes, colors, and textures found in the music of various Hispanic cultures. Nevertheless, the essence of these songs is deeply rooted in nineteenth-century German musical traditions. This eclecticism results in unique works that developed and evolved as reflections of their creator’s musical psyche. This dissertation presents an analytical study of selected songs from the 34 Canciones. The study focuses on three compositional aspects: unity within song cycles, chromaticism, and the use of pre-existing musical material. Since only one of the 34 Canciones has ever been published, this document also includes a complete edition of the thirty-four songs. Additionally, a significant part of the research incorporates a biographical sketch of the composer.

Respighi’s scarcely-known orchestral work Sinfonia Drammatica lives up to its title by evoking a narrative throughout the course of its three movements. In this dissertation, I argue how the work’s surface, subsurface, and formal elements suggest this narrative which emerges as a cycle of rising and falling dramatic tension. I explain how Respighi constructs the work’s narrative in the musical surface through a diverse body of themes that employ three motives of contour. The disposition and manipulation of these motives within the themes suggest frequent fluctuations of the level of conflict throughout the symphony as a whole. To show the involvement of musical forms in the work’s narrative, I employ an approach which integrates harmony and thematic behavior. I utilize analytical methods from the current Formenlehre, including terms from James Hepokoski and Warren Darcy’s sonata deformation theory and William Caplin’s theories of formal functions to elucidate ties between the forms of the Sinfonia Drammatica’s movements and those of conventional sonata forms of the late-eighteenth century. This dissertation also employs Heinrich Schenker’s theories of structures, voice leading, and reduction to illustrate large-scale aspects of the Sinfonia Drammatica’s narrative. The resulting analyses show Respighi’s elaborations of common structural paradigms which serve to …

Beethoven's complex manipulation of formal structures, especially his tendency to build important connections and transformative continuities between non-adjacent sections of musical works, may be seen to function as an attempt to control and sometimes to distort the listener's perception of both the narrative process of musical directionality, as well as the subjective interpretation of time itself. Temporal distortion often lies at the heart of Beethoven's complex contrapuntal language, demonstrated equally through the composer's often enigmatic disruption of phrase-periodic gestures, as well as by occasional instances of overtly incongruous temporal shifts. The "Krakow" collection of compositional sketches for Beethoven's String Quartet in E-Flat, Op. 127, provides a number of instances of "non-linear" or "multi-linear" musical continuity. The term "Krakow" sketches, when referenced in this dissertation, specifically designates the group of Beethoven manuscripts possessed by the Biblioteka Jagiellońska in Krakow, Poland, but which formerly were held by the Royal Library in Berlin. Structural voice-leading analyses are provided for selected portions of the "Krakow" collection; these analyses are then compared to voice-leading graphs and analytical reductions of the corresponding material from Beethoven's published versions of the same musical passages. In some cases the sketches supply almost complete texts, for which critical transcriptions are …

When Schenkerian theory began to influence scholarly circles in the United States, the primary - although not the only - work to which scholars had access was Schenker's last monograph, Der freie Satz. Reading textual passages and examining the many musical graphs in the companion volume of examples influenced their concept of the fundamental structure as Schenker understood it, as well as the relationship of the other levels (Schichten) to the larger structure. The problem is that most of the second generation of Schenkerian scholars were reading the 1956 second German edition, not the 1935 first German edition. The second edition had been altered for textual and musical content by Schenker's student, Oswald Jonas - so there is already a disconnect between the original version and the text scholars were reading at that time (the 1950s, 60s, and 70s). Furthermore, many younger North Americans were insufficiently fluent in German to be able to read the work in the original language. In order to make Schenker's treatise accessible to English-speaking scholars, Ernst Oster set about translating the work into English, a task completed in 1979 just after his death. The text was based on the second German edition (ed. Jonas, Vienna, …

Arnold Schoenberg's teaching career spanned over fifty years and included experiences in Austria, Germany, and the United States. Schoenberg's teaching assistant, Leonard Stein, transcribed Schoenberg's class lectures at UCLA from 1936 to 1944. Most of these notes resulted in publications that provide pedagogical examples of combined elements from Schoenberg's European years of teaching with his years of teaching in America. There are also class notes from Schoenberg's later lectures that have gone unexamined. These notes contain substantial examples of Schoenberg's later theories with analyses of masterworks that have never been published. Both the class notes and the subsequent publications reveal Schoenberg's comprehensive approach to understanding the presentation of the Gedanke or musical idea. In his later classes especially, Schoenberg demonstrated a method of analyzing musical compositions using illustrations of elements of the Grundgestalt or "basic shape," which contains the technical aspects of the musical parts. Through an examination of his published and unpublished manuscripts, this study will demonstrate Schoenberg's commitment to a comprehensive approach to teaching. Schoenberg's heritage of eighteenth- and nineteenth-century music theory is evident in his Harmonielehre and in his other European writings. The latter include Zusammenhang, Kontrapunkt, Instrumentation, Formenlehre (ZKIF), and Der musikalische Gedanke und die Logik, …

The present study develops a dynamic model of strict and free composition that views them as relative to a specific historical context. The dynamic view espoused here regards free embellishments of an earlier compositional generation as becoming the models for a strict compositional theory in a later one. From the newly established strict compositional models, succeeding generations of composers produce new free embellishments. The first part of the study develops the dynamic conception of a continuously emerging strict composition as the context necessary for understanding Anton Bruckner's compositional methodology with respect to the harmonic instruction of his teacher, Simon Sechter. In other words, I view Sechter's harmonic theories as a strict compositional platform for Bruckner's free compositional applications. Many theoretical treatises of the seventeenth, eighteenth and nineteenth centuries such as those by Christoph Bernhard, Johann Philipp Kirnberger and Sechter acknowledged that strict composition must provide the structural framework for free composition. The above procedure becomes a manner of justifying a free embellishment since a "theorist" can demonstrate or assert the steps necessary to connect it with an accepted model from a contrapuntal or harmonic theory. The present study demonstrates that the justification relationship is a necessary component for understanding any …

Composition for Arnold Schoenberg is a comprehensible presentation of a musical idea (musikalische Gedanke); the totality of a piece represents the idea. For tonal works, he defines Gedanke as a process of resolving the "tonal relation" or "tonal problem." Contrary to the numerous tonal examples illustrating the notion of Gedanke, Schoenberg hardly expounds on the Gedanke principle for his atonal and twelve-tone repertoires. This study reevaluates Schoenberg's compositional philosophy and aesthetics including Gedanke, comprehensibility, Grundgestalt, and developing variation in light of his compositional practices in Begleitungsmusik zu einer Lichtspielszene, Op. 34. Although Schoenberg denies the existence of a tonal problem and hierarchy among pitches in twelve-tone compositions, the registral placement found in Op. 34 indicates certain functionality assigned to each pitch-class, producing a sense of "departure and return." The approach here elucidates the "idea" of Op. 34, in which the large-scale formal organization unfolds through contextually emphasized tonal relations. This study also explores Schoenberg's concept of the multi-dimensional presentation of a musical idea. Even though Schoenberg's discussion of musical coherence is usually limited to the immediate musical surface, I believe that he was also aware of an extended realization of foreground motives in the sense of Heinrich Schenker's "concealed motivic …

Wladimir Vogel's (1896-1984) interest in twelve-tone composition began to develop in 1936 after hearing a series of lectures by Willi Reich, a music critic and supporter of the new music of the Second Viennese School. The transition for Vogel from a large-scale orchestral “classical” style, influenced by his study with Ferruccio Busoni in Berlin in the early 1920s, to a new technique involving dodecaphony is apparent in his instrumental writing, the third and fourth movements of the Konzert für Violine und Orchester (1937), as well as in his vocal writing, the Madrigaux for mixed a cappella choir (1938/39). Vogel's twelve-tone works exhibit tertian structures which are particularly emphasized by triads located as consecutive pitches within the rows. Emphasis on tertian structures are not limited to small-scale segmentation of the rows but can also be seen in the structural and tonal organization of complete movements and works. A primary example is the Konzert für Violoncello und Orchester (Cello Concerto) (1955) in which, on a smaller scale, the presentation of the row emphasizes both diminished and minor triads, and at the macro level, the structural triadic relationships unify passages within individual movements as well as the concerto as a whole. Since the …

The music of Béla Bartók is defined in part by its unique blend of rhythmic vitality and inventiveness, and his string quartets offer a glimpse into a consistency of technique evident throughout his compositional career. Bartók's rhythmic environments are primarily metrical, but many of his rhythmic configurations are placed in such a way as to potentially override established meter. It is necessary, therefore, to institute an analytical means by which the delineation and comparison of rhythmic structures both within and without the metrical context may be accomplished. An analytical method using Timepoint Accent Structures (TAS) allows for the comparison of rhythms resulting from patterns of accent produced by pitch onset, dynamic stress, articulation or any other accentual factors. Timepoint Grouping Structures (TGS) delineate the number of timepoints present in alternating groups/blocks in a texture, thereby allowing for the recognition of patterning created by these larger groups. By applying TAS and TGS analysis, relationships of rhythmic equivalency, rotation, retrograde, complementation, augmentation, diminution, subset, superset, exchange, compression and expansion are clearly confirmed in the string quartets. In addition, symmetrical structures and arithmetic progressions are discovered. In many ways, Bartók's rhythmic organization mimics his procedures of pitch structuring.

Many of the early writings and lectures of the German phenomenological philosopher Martin Heidegger involve investigations into the question of Being. An important part of these investigations is his examination of how we go about the everyday business of existing--doing our jobs, dealing with things in our environment, working through problems, thinking, talking--and what our ways of operating in these everyday activities tell us about our Being in general. Musicians have their own everyday musical tasks, two of the most prominent of which are composing and performing. Composers and performers, like everyone else, have a 'world'--Heidegger's word for the structure of relationships between equipment, persons, and tasks and the way in which a person is situated in that structure--and that 'world' allows them to cope with their musical environment in ways that enable them to make music as composers and performers. Analyzing music is an activity that a Heideggerian approach sees as derived from the primary musical activities of composing and performing. A music analyst trades the possibility of primary musical involvement for a kind of involvement that points out determinate characteristics; hence in adopting an analytical stance, the analyst trades doing something musical for saying something about music. In …

The late chromatic music of Chopin is often difficult to analyze, particularly with a system of Roman numerals. The study examines Schoenberg's Grundgestalt concept as a strategy for explaining Chopin's chromatic musical style. Two short Chopin works, Nocturne in E-flat major. Op. 9, No. 2, and Etude in E major, Op. 10, No. 3, serve as models in which the analytic method is formulated. Root analysis, in the manner of eighteenth-century theorist Simon Sechter, is utilized to facilitate harmonic analysis of chromatic passages. Based upon the analytic method developed, the study analyzes the last three polonaises of Chopin: Polonaise in F-sharp minor, Op. 44, Polonaise in A-flat major, Op. 53, and Polonaise-Fantasie in A-flat major, Op. 61. The Grundgestalt-based analysis shows harmonic, melodic and rhythmic connections in order to view Chopin's chromaticism and formal structure from a new perspective. With this approach, the chromaticism is viewed as essential to the larger form.

This study examines the five late keyboard works of Cesar Franck: the Prelude, Chorale, and Fugue and the Prelude. Aria, and Finale for piano, and the three organ chorales. The study focuses on harmonic and contrapuntal techniques and their interrelationships, placing the discussion in the context of an analysis of the whole piece. The primary goal is to identify the salient characteristics of each piece; a secondary goal is to identify common harmonic and contrapuntal aspects of Franck's style.