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.

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.

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 …

In 1873, Brahms completed the two op. 51 quartets. These were not the first string quartets Brahms composed, hut they were the first that Brahms allowed to be published. He found the string quartet difficult; as he confided to his friend Alwin Cranz, he sketched out twenty string quartets before producing a pair he thought worthy of publishing. Questions arise: what aspect of the string quartet gave Brahms so much trouble, and what in the op. 51 quartets gave him the inclination to publish them for the first time in his career? The op. 51 quartets are essential to understanding the evolution of Brahms's compositional technique. Brahms had difficulty limiting his massive harmony and polyphony to four solo strings. This difficulty was compounded by his insistence on deriving even the accompaniment from the opening main motivic material. This study investigates the manner in which Brahms distributes the main motivic material to all four voices in these quartets, while at the same time highlighting each voice effectively in the dialogue.

The purpose of the study is the investigation of the topics of transposition and the transposed major and minor modes as discussed principally by selected French authors of the final twenty years of the seventeenth century and the first three decades of the eighteenth. The sources are relatively varied and include manuals for singers and instrumentalists, dictionaries, independent essays, and tracts which were published in scholarly journals; special emphasis is placed on the observation and attempted explanation of both irregular signatures and the signatures of the minor modes. The paper concerns the following areas: definitions and related concepts, methods for singers and Instrumentalists, and signatures for the tones which were identified by the authors. The topics are interdependent, for the signatures both effected transposition and indicated written-out transpositions. The late Baroque was characterized by much diversity with regard to definitions of the natural and transposed modes. At the close of the seventeenth century, two concurrent and yet diverse notions were in evidence: the most widespread associated "natural" with inclusion within the gamme; that is, the criterion for naturalness was total diatonic pitch content, as specified by the signature. When the scale was reduced from two columns to a single one, …

While musical sources and documents from throughout the Middle Ages reveal that mode was an enduring and consciously derived trait of monophonic chant, modality in later polyphony shares neither the historical span nor the theoretical clarity of its monophonic counterpart. Modern theorists are left with little more than circumstantial evidence of the early development of modality in polyphony. This study attempts to shed light on the problem by detailed analysis of a select body of paraphrase masses from the early sixteenth century. First, it correlates the correspondence between the paraphrased voice and the original chant, establishing points of observation that become the basis of melodic analysis. Then, these points are correlated with known rules of counterpoint. Exceptions are identified and examined for their potential to place emphasis on individual mode-defining pitches. A set of tools is derived for quantifying the relative strength of cadential actions. Levels of cadence are defined, ranging from full, structural cadences to surfacelevel accentuations of individual pitches by sixth-to-octave dyadic motions. These cadence levels are traced through the Missae de beata virqine repertoire from c. 1500-1520, a repertoire that includes masses of Josquin, Brumel, La Rue, Isaac, and Rener. While the Credos, based on two chant …

This investigation traces the history and development of music theory in Mexico from the date of the first Mexican treatise available (1776) to the early second half of the nineteenth century (1866). This period of ninety years represents an era of special importance in the development of music theory in Mexico. It was during this time that the old modal system was finally abandoned in favor of the new tonal system and that Mexican authors began to pen music treatises which could be favorably compared with the imported European treatises which were the only authoritative source of instruction for serious musicians in Mexico.

The songs of Hugo Wolf represent the culmination of the Romantic German Lied tradition. Wolf developed a personal chromatic harmonic style that allowed him to respond to every nuance of a poetic text, thereby stretching tonality to its limits. He was convinced, however, that despite its novel nature his music could be explained through the traditional theory of harmony. This study determines the degree to which Wolf's belief is true, and begins with an evaluation of the current state of research into Wolf's harmonic practice. An explanation of my analytical method and its underlying philosophy follows; historical perspective is provided by tracing the development of three major elements of traditional theory from their inception to the present day: fundamental bass, fundamental chords, and tonal function. The analytical method is then applied to the works of Wolf's predecessors in order to allow comparison with Wolf. In the investigation of Wolf's harmonic practice the individual elements of traditional functional tonality are examined, focusing on Wolf's use of traditional harmonic functions in both traditional and innovative ways. This is followed by an investigation of the manner in which Wolf assembles these traditional elements into larger harmonic units. Tonal instability, rapid key shifts, progressive …

General-Bass in drey Accorden (1756), the first of Johann Friedrich Daube's theoretical works, is a practical instruction manual in thorough-bass accompaniment. It consists of a sixteen page preface followed by 215 pages of text and musical examples. The twelve chapters begin with a presentation of interval classification and a discussion of consonance and dissonance. Daube then explains a theory of harmony in which all "chords" are derived from three primary chords. These are illustrated with regard to their sequence in harmonic progressions, their resolutions—common and uncommon—, and their use in modulation. Seventy-two pages of musical examples of modulations from all major and minor keys to all other keys are included. Particular attention is given to the fully diminished seventh chord, which is illustrated in all inversions and in numerous modulatory progressions. Daube devotes one chapter to three methods of keyboard accompaniment. The subject matter includes textures, dynamics, proper doubling, the accompaniment of recitatives, full-voiced accompaniment, the use of arpeggiation, trills, running passages, and ornamentation in general.

The internal unity of the themes in a sonata-allegro movement and the external unity of the movements in a sonata cycle are crucial elements of Beethoven's compositional aesthetic. Numerous theorists have explored these aspects in Beethoven's sonatas, symphonies, quartets, and concertos. Similar research into the independent variation sets for piano, excluding Opus 120, has been largely neglected as the result of three misconceptions: that the variation sets, many of which were based on popular melodies of Beethoven's time, are not as worthy of study as his other works; that the type of hidden internal relationships which pervade the sonata cycle are not relevant to the variation set since all variations are, by definition, related to the theme; and that variations were composed "additively," that is, one after another, without any particular regard for their order or relationship to one another. The purpose of this study is to refute all three of these incorrect assumptions. Beethoven was concerned with the order of variations and their relationship to one another, and he was able to transcend the additive tendency in a number of ways. Some of his methods included registral connection, registral expansion, rhythmic acceleration, textural expansion, dynamics, articulation, and motivic similarities. …

With the founding of the Paris Conservatory in 1795, a diversity of instructional methods for the teaching of harmony were used. Each theory instructor insisted upon using his own system; some relied heavily upon the theories of Rameau, while others used ideas based on eighteenth century German or Italian theorists. The Conservatory administration, realizing the need to unify theoretical instruction into a single method, formed a committee to evaluate the different harmonic systems available. After considering several treatises, including the theories of Rameau, the committee chose the Traité d'harmonie of Catel as the work best suited for their purposes. This investigation deals with Catel's synthesis of various theoretical principles, concentrating on his concise, often simplistic approach to harmonic theory. The major contribution of the Traité is the classification of chords into two categories: "natural harmony" and "artificial harmony." Catel believed that only one chord exists in harmony, the dominant ninth chord, which he derived from the first nine partials of the overtone series. From this chord, he formed the basic triads of "natural harmony," describing these chords as suspensions ("prolongations") of "natural harmony."

Antoine Reicha stands as an important figure in the growing systematization of musical form. While Traite de melodie (1814) captures the essence of eighteenth-century concern with tonal movement and periodicity, Reicha's later ideas as represented in Traite de haute composition musicale (1824-26) anticipate descriptions of thematic organization characteristic of his nineteenth-century successors. Three important topics emerge as crucial elements: melody, thematic development, and schematic categorization of complete pieces.

Allen Forte's theory of pitch-class set structure has provided useful tools for discovering structural relationships in atonal music. As valuable as set—theoretic procedures are for composers and analysts, the extent to which set relationships are perceptible by the listener largely remains to be investigated. This study addresses the need for aural-perceptual considerations in analysis, reviews related research in music perception, and poses questions concerning the aural perceptibility of set relationships. Specifically, it describes and presents the results of a computer-assisted experiment in testing the perceptibility of set-equivalency relationships.

This dissertation contains the first complete Latin-English translation of one of the most controversial music theory treatises of the fifteenth-century: the Musica Practica (Bologna, 1942) of Bartolomeo Ramos de Pareia. its title as well as its content illustrate the Renaissance transformation from the abstract mathematical approach of "musica speculativa" to that of an emphasis upon the everyday demands of the practicing musician. Although Ramos provides traditional explanations of the modes, counterpoint, "musica ficta," and white mensural notation, his innovations in temperament, solmization, mutation, and the gamut set this treatise apart from other ffifteenth-century music treatises. Ramos's rejection of traditional Pythagorean-Boethian-Guidonian explanations, coupled with his strong polemic criticisms of the auctoritas, resulted in a treatise that remained at the center of heated debate well into the sixteenth century.

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 problem with which this investigation is concerned is that of presenting a concise English translation of the book which Martin Agricola wrote in 1528 in German on the musical instruments and practices of his time. In addition to the translation itself, there is a major section devoted to a comparison of the material of Musica instrumentalis deudsch with other books and treatises on the same and related subjects which were written at approximately the same time or within the next hundred years. Agricola states that the purpose of his book was to teach the playing of various instruments such as organs, lutes, harps, viols, and pipes. He also noted that the material was prepared expressly for young people to study. To facilitate the accomplishment of this purpose Agricola wrote the book in short, two-lined, rhymed couplets so that the youths might quickly memorize the material and thus retain the instructions better.

The purpose of this study is to provide a practical English translation of Vincenzo Galilei's significant treatise on ancient and modern music (1581). In spite of the important place this work holds in the history of music, it has never before been made available in its entirety in any language other than the original Italian. This volume includes the front matter and chapters 1-3.

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 …

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, …

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 …

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.

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 …