This dissertation contains a comparison from a historical and theoretical perspective of the passacaglia from the Piano Trio in E Minor, Op. 67, written by Dmitri Shostakovich (1906-1975), and the passacaglia from the Piano Trio in A Minor, written by Maurice Ravel (1875-1937).Before the history and theory discussion of these two movements begins, a background is given on the passacaglia form and its origins. References are made to the beginnings of the passacaglia in Italy and Spain, as well as the gradual evolution of the form into the keyboard music of the 17th century. Early published examples of passacaglias are displayed in chapter two.The third and fourth chapters of this dissertation are the focus of the comparison, where historical and theoretical information is discussed and deciphered. In the history section, details of the life of the composer during the time he wrote the piece are provided. The theory section contains a concentrated examination and comparison (enhanced by musical examples) of melody, harmony, rhythm, texture, and form, as used by Ravel and Shostakovich in these two passacaglias.It was concluded in this dissertation that both of these master composers used the passacaglia form successfully in their piano trios. As a result, they contributed musical masterpieces in the genre of the piano trio for musicians and scholars alike to investigate, study, and perform. / School of Music

The purpose of this thesis is to investigate the use of isorhythm in two of Arnold Schoenburg's chamber works, the Third and Fourth String Quartets. The study of rhythm in twelve-note music has been generally relegated to a position less prominent than that held by the study of any of the other important aspects of the style. This condition is due probably to the fact that rhythm underwent less change with the advent of the twelve-note school of composition than melody, counterpoint, or harmony experienced. However, Rufer states that "rhythm has a special formal function in Schoenberg's twelve-note music, in addition to its motivic function and to that of creating subdivisions.

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This thesis presents an analysis of Copland's first major serial work, the Quartet for Piano and Strings (1950), using pitch-class set theory and tonal analytical techniques.

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.

This thesis is concerned with the historical context and evaluation of the string quartets of Franz Berwald. It will establish the environment within which Berwald composed these quartets, and show the results of his efforts. The material for this investigation was gathered from musical scores and literature about music. Chapter I gives an introduction to the thesis and a short biographical sketch of Berwald. Chapter II surveys the string quartet in the first half of the nineteenth century, citing the work of major composers. This chapter concludes with an examination of the influences on Berwald's musical styles. Chapter III surveys Berwald's musical output and describes the Quartet in G Minor. Chapter IV describes his last two quartets. The evaluations and conclusions are presented in Chapter V.

The purpose of the present study is to determine the stylistic characteristics of Beethoven's early piano trios. For the purposes of this study, the term "piano trio" is defined as any work for three instruments in which a piano participates. Of the twelve such trios written by the composer, the first six are dealt with. There is in addition a brief discussion of a trio of uncertain origin. These six piano trios were composed over a span of about ten years (1785-1795), between the ages of fifteen and twenty-five. Although there is a great deal of uncertainty as to the exact time and place of origin of these trios, the first three are generally considered to have been written in Bonn, and the last three in Vienna.

Este trabalho versa sobre desenvolver a habilidade de “reconhecer características ou propriedades de fenômenos ondulatórios ou oscilatórios, relacionando-os a seus usos em diferentes contextos” (BRASIL, 2009, p.8) de uma forma menos tradicional. O objetivo foi abordar o conteúdo de acústica utilizando instrumentos musicais (violão, guitarra, flauta, xilofone, lira...). A partir de ondas estacionárias em tubos sonoros e cordas vibrantes, foram elucidados os conceitos de altura, intensidade e timbre, relacionando com os conceitos básicos de ondas – frequência, comprimento de onda, amplitude, velocidade de propagação das ondas em cordas de diferentes densidades lineares, entre outros. Também foram trabalhadas notas musicais e conceitos bem básicos de formação de acordes. A proposta foi aplicada com os dois nonos anos de um colégio particular bastante tradicional de Novo Hamburgo: o Colégio Marista Pio XII. Nesta fase final do Ensino Fundamental, o colégio disponibiliza aos seus alunos cinco períodos de Ciências da Natureza, distribuídos em: um de Biologia, dois de Física e dois de Química. A ideia é que fossem trabalhadas Competências e Habilidades comuns aos componentes curriculares, por meio de sequências didáticas. O trabalho foi aplicado em um total de seis encontros, cada um com duração de 50 min. Alguns desses períodos foram dedicados a aulas puramente expositivas, outros deles com aulas expositivas dialogadas, com a utilização de uma espiral de caderno, uma guitarra, um cavaquinho, instrumentos de sopro e do computador, onde interpretamos as frequências fundamentais emitidas pela vibração das cordas e do ar em tubos sonoros com o software Spectrogram1. Como referencial teórico, utilizamos a teoria sócio-interacionista de Vygotsky e alguns conceitos de alfabetização científica. A discussão e o manuseio de instrumentos musicais em pequenos grupos fizeram com que os alunos interagissem entre si e com o professor, favorecendo a construção do conhecimento e a interação de signos. A partir dessas interações aluno - instrumentos musicais, professor - aluno e aluno – aluno, o objetivo era abrir espaço para questionamentos, discussões e reflexões, de maneira que o conhecimento fosse sintetizado por todos. Como referência para o planejamento de ensino, construção do significado das aulas e análise das interações, utilizamos uma ferramenta analítica de Mortimer e Scott (2002). / This work is about developing the ability to "recognize characteristics or properties of wave or oscillatory phenomena, relating them to their uses in different contexts "(BRASIL, 2009, p.8), in a less traditional way. The objective was to approach the content of acoustics using musical instruments (guitar, electric guitar, flute, xylophone, lyre ...). From stationary waves in sound tubes and vibrating strings, concepts of height, intensity and timbre, were elucidated, relating them to the basic concepts of waves - frequency, wavelength, amplitude, velocity of wave propagation in strings of different linear densities, among others. Musical notes and basic concepts of chord formation were also seen. The proposal was applied with two groups of nineth graders from a very traditional private school in Novo Hamburgo: Marista Pio XII school. In this final phase of elementary school, the school offers its students five classes of Science a week, distributed in one of Biology, two of Physics and two of Chemestry. The idea was work with common skills to these curricular components, through didactic sequences. The work was applied out in a total of six classes, each lasting 50 min. Some of these were devoted to purely expository presentation, others with dialogic lectures, with the use of the spiral of a notebook, a guitar, another small kind of guitar, wind instruments and a computer where we interpret the fundamental frequencies emitted by the vibration of the strings and air in sound tubes with the Spectrogram software2. As a theoretical reference, we use Vygotsky's socio-interactionist theory and some concepts of scientific literacy. The discussion and manipulation of musical instruments in small groups led the students to interact with each other and with the teacher, favoring the construction of knowledge and interaction. From these student - musical instruments, teacher - student and student – student interactions, the objective is to open space for questions, discussions and reflections, so that knowledge was synthesized by all. As a reference for teaching planning, construction of meaning and interaction analysis, l we used an analytical tool by Mortimer and Scott (2002).

O escopo deste mestrado é de se familiarizar com a chamada {\\it correspondência AdS/CFT}, que tem sido um dos mais importantes desenvolvimentos na física teórica nas últimas décadas. De acordo com essa correspondência, deformações das geometrias do lado da gravidade (ou lado \"AdS\") devem ser mapeadas para operadores das teorias de calibre duais (ou lado \"CFT\"). Em particular, nos temos estado interessados em explorar uma entrada particular no dicionário AdS/CFT, a relação entre os operadores 1/2 BPS em ${\\cal N}=4$ super Yang-Mills, e as chamadas {\\it geometrias bubbling} no lado da gravidade. A fim de fazer isso, apresentamos primeiramente as noções de ${\\cal N}=4$ SYM e soluções de Supergravidade. Portanto, podemos expor mais claramente o sentido da correspondência AdS /CFT, e depois mostrar a derivação das geometrias 1/2 BPS duais a estados 1/2 BPS em ${\\cal N}=4$ SYM como um exemplo. / The scope of this Master program was to get acquainted with the so-called {\\it AdS/CFT correspondence}, which has been one of the most important developments in theoretical physics in the last decades. According to this correspondence, deformations of the geometries in the gravity side (or \"AdS\" side) must be mapped to states of the dual gauge theories (or \"CFT\" side). In particular, we have been interested in exploring a particular entry in the AdS/CFT dictionary, namely, the relation between 1/2 BPS operators in ${\\cal N}=4$ super Yang-Mills, and the so-called {\\it bubbling geometries} on the gravity side. In order to do that, we first present the notions of N=4 SYM and Supergravity solutions. In this way, we can expose the statement of the AdS/CFT correspondence, and later show the derivation of 1/2 BPS geometries dual to 1/2 BPS states in N=4 SYM as an example of this one.

Orbits of charged particles under the effect of a magnetic field are mathematically described by magnetic geodesics. They appear as solutions to a system of (nonlinear) ordinary differential equations of second order. But we are only interested in periodic solutions. To this end, we study the corresponding system of (nonlinear) parabolic equations for closed magnetic geodesics and, as a main result, eventually prove the existence of long time solutions. As generalization one can consider a system of elliptic nonlinear partial differential equations whose solutions describe the orbits of closed p-branes under the effect of a "generalized physical force". For the corresponding evolution equation, which is a system of parabolic nonlinear partial differential equations associated to the elliptic PDE, we can establish existence of short time solutions. / Bahnen von geladenen Teilchen, die sich unter dem Einfluss eines Magnetfeldes bewegen, werden in der Mathematik durch magnetische Geodäten beschrieben. Sie ergeben sich als Lösungen eines Systems (nichtlinearer) gewöhnlicher Differentialgleichungen zweiter Ordnung. Wir interessieren uns ausschließich für periodische Lösungen. Dazu studieren wir das zugehörige System (nichtlinearer) parabolischer Differentialgleichungen für geschlossene magnetische Geodäten. Als Hauptresultat beweisen wir die Existenz von Langzeitlösungen. Verallgemeinernd betrachten wir noch ein System von elliptischen nichtlinearen partiellen Differentialgleichungen, dessen Lösungen die Orbiten von geschlossenen p-Branen unter dem Einfluss einer verallgemeinerten physikalischen Kraft beschreiben. Für die entsprechende Evolutionsgleichung, welche ein System von parabolischen nichtlinearen partiellen Differentialgleichungen ist, das dem elliptischen Problem zugeordnet ist, können wir die Existenz von Kurzzeitlösungen beweisen.