This thesis uses two different musical analytical systems, one of Heinrich Schenker and one of Paul Hindemith, to analyze tonality within "Die Gurre Lieder" and "Fourth String Quartet" by Arnold Schoenberg.

Diversos dos conflitos da atualidade são apresentados pela mídia e em discursos políticos como um confronto entre civilizações incompatíveis. A oposição entre Ocidente e Oriente é muitas vezes apresentada nesses discursos como um conflito de longa duração, nascido a partir da própria formação da religião islâmica e pontuado ao longo da história pelo enfrentamento entre impérios cristãos e muçulmanos. Isso é particularmente preocupante para os historiadores, já que esse discurso não leva em consideração as transformações ocorridas nas sociedades humanas ao longo do tempo. Ao longo da história, houve muitos encontros entre o Islã e o Ocidente, em diferentes situações e com cada um deles desempenhando papeis diferentes. A presente dissertação de mestrado tem como objetivo analisar a interação entre Oriente e Ocidente no plano discursivo e político a partir da imagem que se fez do Império Otomano nas obras do historiador britânico Arnold Joseph Toynbee (1889-1975) na primeira metade do século XX. / Media and political discourses present many of nowadays conflicts as a clash between incompatible civilizations. The opposition between West and East is often depicted in these discourses as a long time conflict born with Islam itself and punctuated along history by the skirmish between Christian and Muslim empires. This is particularly worrisome to historians since it does not take in to account the transformations that have occurred in human societies over time. Throughout history, there have been many encounters between Islam and the West, in different situations and with each civilization playing different roles. Our objective in this dissertation is to analyse the interaction between East and West in political and discursive plans from the image about the Ottoman Empire in British historian Arnold Joseph Toynbees texts during the first half of the twentieth century.

Diversos dos conflitos da atualidade são apresentados pela mídia e em discursos políticos como um confronto entre civilizações incompatíveis. A oposição entre Ocidente e Oriente é muitas vezes apresentada nesses discursos como um conflito de longa duração, nascido a partir da própria formação da religião islâmica e pontuado ao longo da história pelo enfrentamento entre impérios cristãos e muçulmanos. Isso é particularmente preocupante para os historiadores, já que esse discurso não leva em consideração as transformações ocorridas nas sociedades humanas ao longo do tempo. Ao longo da história, houve muitos encontros entre o Islã e o Ocidente, em diferentes situações e com cada um deles desempenhando papeis diferentes. A presente dissertação de mestrado tem como objetivo analisar a interação entre Oriente e Ocidente no plano discursivo e político a partir da imagem que se fez do Império Otomano nas obras do historiador britânico Arnold Joseph Toynbee (1889-1975) na primeira metade do século XX. / Media and political discourses present many of nowadays conflicts as a clash between incompatible civilizations. The opposition between West and East is often depicted in these discourses as a long time conflict born with Islam itself and punctuated along history by the skirmish between Christian and Muslim empires. This is particularly worrisome to historians since it does not take in to account the transformations that have occurred in human societies over time. Throughout history, there have been many encounters between Islam and the West, in different situations and with each civilization playing different roles. Our objective in this dissertation is to analyse the interaction between East and West in political and discursive plans from the image about the Ottoman Empire in British historian Arnold Joseph Toynbees texts during the first half of the twentieth century.

This is a study of the ways in which the past is inscribed in sound. It is also an examination of the role of concert music in the invention of cultural memory in the wake of the Second World War. And finally, it is a study of the creation and early American reception of A Survivor from Warsaw, a cantata written in 1947 that became the first major musical memorial to the Holocaust. It remains uniquely significant and controversial within the larger oeuvre of its composer, Arnold Schoenberg (1874-1951). Historians interested in the chronologies and modalities of Holocaust memory have tended to overlook music’s role as a carrier of meaning about the past, while other media of commemoration have received far greater scrutiny, be they literary, cinematic, or architectural. And yet, A Survivor from Warsaw predated almost all of its sibling memorials, crystallizing and anticipating the range of aesthetic and ethical concerns that would define the study of postwar memory and representation for decades to come. It also constituted a uniquely personal memorial that may be read not only as a work of Holocaust art but also as a profoundly autobiographical document, one that sheds light on constellations of particularist identities often hidden beneath the “universalist” veil of one of the twentieth-century’s most iconic musical figures. Ultimately, this study seeks to articulate an under-examined linkage between modernism and memory, while arguing methodologically for the importance of sound in the contemporary practice of cultural history.

Für das Verständnis einer Vielzahl von Problemen von der Himmelsmechanik bis hin zur Beschreibung von Molekülen spielen Systeme mit mehr als zwei Freiheitsgraden eine entscheidende Rolle. Aufgrund der Dimensionalität gestaltet sich ein Verständnis dieser Systeme jedoch deutlich schwieriger als bei Systemen mit zwei oder weniger Freiheitsgraden. Die vorliegende Arbeit soll zum besseren Verständnis der klassischen und quantenmechanischen Eigenschaften getriebener Systeme mit zwei Freiheitsgraden beitragen. Hierzu werden dreidimensionale Schnitte durch den Phasenraum von 4D Abbildungen betrachtet. Anhand dreier Beispiele, deren Phasenräume zunehmend kompliziert sind, werden diese 3D Schnitte vorgestellt und untersucht. In einer sich anschließenden quantenmechanischen Untersuchung gehen wir auf zwei wichtige Aspekte ein. Zum einen untersuchen wir die quantenmechanischen Signaturen des klassischen "Arnold Webs". Es wird darauf eingegangen, wie die Quantenmechanik dieses Netz im semiklassischen Limes auflösen kann. Darüberhinaus widmen wir uns dem wichtigen Aspekt quantenmechanischer Kopplungen klassisch getrennter Phasenraumgebiete anhand der Untersuchung dynamischer Tunnelraten. Für diese wenden wir sowohl den in der Literatur bekannten "fictitious integrable system approach" als auch die Theorie des resonanz-unterstützen Tunnelns auf 4D Abbildungen an. / Systems with more than two degrees of freedom are of fundamental importance for the understanding of problems ranging from celestial mechanics to molecules. Due to the dimensionality the classical phase-space structure of such systems is more difficult to understand than for systems with two or fewer degrees of freedom. This thesis aims for a better insight into the classical as well as the quantum mechanics of 4D mappings representing driven systems with two degrees of freedom. In order to analyze such systems, we introduce 3D sections through the 4D phase space which reveal the regular and chaotic structures. We introduce these concepts by means of three example mappings of increasing complexity. After a classical analysis the systems are investigated quantum mechanically. We focus especially on two important aspects: First, we address quantum mechanical consequences of the classical Arnold web and demonstrate how quantum mechanics can resolve this web in the semiclassical limit. Second, we investigate the quantum mechanical tunneling couplings between regular and chaotic regions in phase space. We determine regular-to-chaotic tunneling rates numerically and extend the fictitious integrable system approach to higher dimensions for their prediction. Finally, we study resonance-assisted tunneling in 4D maps.

This study examines the relativistic aspects of Arnold Schoenberg's harmonic and aesthetic theories in the light of a framework of ideas presented in the early writings of Ludwig Wittgenstein, the logician, philosopher of language, and Schoenberg's contemporary and Austrian compatriot. The author has identified correspondences between the writings of Schoenberg, the early Wittgenstein (the Tractatus Logico-Philosophicus, in particular), and the Vienna Circle of philosophers, on a wide range of topics and themes. Issues discussed include the nature and limits of language, musical universals, theoretical conventionalism, word-to-world correspondence in language, the need for a fact- and comparison-based approach to art criticism, and the nature of music-theoretical formalism and mathematical modeling. Schoenberg and Wittgenstein are shown to have shared a vision that is remarkable for its uniformity and balance, one that points toward the reconciliation of the positivist-relativist dualism that has dominated recent discourse in music theory. Contrary to earlier accounts of Schoenberg's harmonic and aesthetic relativism, this study identifies a solid epistemological core underlying his thought, a view that was very much in step with Wittgenstein and the Vienna Circle, and thereby with the most vigorous and forward-looking stream in early twentieth century intellectual history.

Orientadora: Profa. Dra. Mariana Rodrigues da Silveira / Dissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Matemática , Santo André, 2018.

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, Technik, und Kunst seiner Darstellung (the Gedanke manuscripts), written over the course of several years from the 1920s to the early 1930s. After emigrating to the United States in 1933, Schoenberg immediately began teaching and writing in an attempt to arrive at a comprehensive approach to his pedagogy. The remainder of Schoenberg's textbook publications, with the exception of Models for Beginners in Composition, were left unfinished, were edited primarily by Leonard Stein and published after Schoenberg's death in 1951. Preliminary Exercises in Counterpoint, Fundamentals of Musical Composition, and Structural Functions of Harmony complete his ouevre of theory publications. An examination of the Stein notes offers contributing evidence to Schoenberg's lifelong pursuit to find a comprehensive approach for teaching an understanding of the musikalische Gedanke. With the addition of an analysis of the first movement of Mozart's G minor Symphony, K. 550, which Schoenberg used often to illustrate examples of basic concepts as liquidation, transition, neutralization in the minor key, the role of the subordinate theme, retransitions, codettas, melodic and harmonic overlapping, and motivic analysis, this study focuses on Schoenberg's comprehensive approach to both analyzing the musical work and teaching methods of composing.

De traditionella begravningsplatserna kräver stora ytor. Urbanisering och befolkningsökning gör att detta utrymme inte längre finns att tillgå i tätbebyggda områden. Detta projekt tar sin utgångspunkt i denna problematik och de konsekvenser den fått för de begravningspraktiker som är etablerade i vårat samhälle. Projektets avsikt är att pröva en långsiktig lösning i form av en alternativ begravningspraktik med stadens förutsättningar som utgångspunkt. Detta innebär att jag föreslår ett nytt gravskick, en ny ritual samt visar hur dessa kan gestaltas.  Projektarbetet inleddes med skrivandet av en uppsats där jag undersökte begravningsritualen och den plats där den utövas. Jag utvecklade en modell för att beskriva kopplingen mellan ritualens handlingar och platsens betingelser. Modellen tog sin utgångspunkt i antropologen Arnold van Genneps teorier om begravningsritualer. Modellen användes för att analysera Sigurd Lewerentz förslag till ett kombinerat krematorium och begravningsplats i Helsingborg. Därefter tog en designprocess vid som innebar att jag formgav ett arkitektoniskt lösningsförslag. Under denna process använde jag den modell som utvecklades i uppsatsen som ett redskap för att pröva och motivera mina val.  Resultatet av projektet kan beskrivas som ett förslag på en modifierad minneslund placerad i centrala Stockholm. Av intresse för fortsatt undersökning är dels de problemområden jag identifierat i mötet mellan begravningsplatsen och den urbana kontexten, dels den metod jag använt för att omsätta den teoretiska modellen till fysisk gestaltning. / Traditional cemeteries requires large areas. Urbanization and increased population means that this space is no longer available in urban contexts. This project has its starting point in the aforementioned problem and the consequences it has had for existing burial customs.  The purpose of the project is to examine a long-term solution in the form of an alternative burial practice based on the conditions of the contemporary city. This means that I propose a new burial custom, a new ritual and show how these might staged architectonically.  The project began with the writing of an essay in which I examined the relationship between the burial ritual and its associated space. In order to do this, I developed a model which describes the connection between the ritual act and spatial circumstances. This model is based on the anthropologist Arnold van Genneps theories concerning rituals of passage. It was used to analyze Sigurd Lewerentz proposal for a combined crematorium and cemetery in Helsingborg. I then used the conclusions drawn from the analysis as the basis for a design process which resulted in the architectonic solution proposal. The model was a central tool for verifying and motivating my choices during the design processes.  The result can be described as a modified memorial park placed in central Stockholm. Of interest for further investigation is the problem areas which I have identified in the meeting between the cemetery and the urban context as well as the method I used to translate the theoretical model to physical form.

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