Le but principal de ce mémoire est de calculer la mesure de Mahler logarithmique d’une famille de polynômes à trois variables x^n + 1 + (x^(n−1) + 1)y + (x − 1)z. Pour réaliser cet objectif, on intègre des régulateurs définis sur des complexes motiviques polylogarithmiques. Pour comprendre ces régulateurs, on explore les propriétés des polylogarithmes et démontre quelques identités polylogarithmiques. Ensuite, on utilise les régulateurs afin de simplifier l’intégrante. Notre résultat est une formule qui relie la mesure de Mahler de la famille de polynômes susmentionnée au dilogarithme de Bloch–Wigner et à la fonction zêta de Riemann. / The main purpose of this thesis is to compute the logarithmic Mahler measure of the three variable polynomial family xn + 1 + (xn−1 + 1)y + (x − 1)z. In order to accomplish this, we integrate regulators defined on polylogarithmic motivic complexes. To understand these regulators, we explore the properties of polylogarithms and show some polylogarithmic identities. The regulators are then applied to simplify the integrand. Our result is a formula relating the Mahler measure of the family of polynomials to the Bloch–Wigner Dilogarithm and the Riemann zeta function.

The Light is a twenty-four minute composition for two narrators and chamber orchestra. The two narrators perform the roles of the Apostle John and Moses. After an overview of the piece and a brief history of pieces incorporating narrators, the essay focuses on my compositional process, describing how orchestration, drama, motive, and structure work together in the piece. The Light is organized as a series of five related scenes. In the first scene, God creates light. In the second scene, God places Adam and Eve into the Garden of Eden to tend it, allowing them to eat from any tree except the tree of the knowledge of good and evil. The serpent appears, Adam and Eve succumb to his evil influence, and God banishes them from the Garden of Eden. Many generations have passed when Scene Three begins. Moses relates a story from Israel's journey in the wilderness after leaving Egypt. The people had become frustrated with Moses and with God. When God sent serpents among them as punishment, they appealed to Moses to pray for them. God's answer was for Moses to make a bronze serpent and place it on a pole. Whoever looked at the serpent would live. In Scene Four, John relates his vision of final redemption. New Jerusalem descends from heaven, with the River of Life and the Tree of Life ready to bring healing to the nations. Sadly, some people are not welcomed into the city, and the drama pauses to give respectful consideration to their fate. Finally, the fifth scene celebrates the eternal victory over sin, death, and the serpent of Eden. As I composed The Light, I had in mind the dramatic profile, the general motivic progression and the fundamental structural progression. However, most of the intricate interrelationships among orchestration, drama, motive, and structure were the result of informed intuition. Throughout the piece, each of these four elements interacts with the others, sometimes influencing and sometimes responding to them. My hope is that these subtle tensions propel the composition forward toward its ultimate resolution.

This dissertation presents an analysis of Akrodha (1998), a multiple percussion solo in two movements, composed by Kevin Volans. The analysis is focused on the motivic content and subsequent iterations written within the tempos that provide the structural form of the piece. The structural tempos are supported by the presence of various motifs that serve as the tempos' characteristic traits, thereby giving the tempos more tangibility. As the work develops, these motifs reappear either as note-for-note reiterations or as variations that still maintain the unique qualities of the motifs. For comparison, similar analyses of Mr. Volans' other multiple percussion solos, She Who Sleeps with a Small Blanket (1985) and Asanga (1997), are also presented to further explore Mr. Volans' use of motifs as they relate to structural tempos. In addition, a comprehensive performance practice of Akrodha is presented based on a synthesis of considerations and methods from individuals involved in the piece's development and early performances. These include Dr. Volans himself, Jonny Axelsson (for whom Akrodha was written), and Robyn Schulkowsky (for whom She Who Sleeps with a Small Blanket and Asanga were written), as well as the author's personal experiences. This dissertation provides a deeper understanding of Akrodha for the scholar and provides performance guidance for the performer to enhance the ability to replicate the musical spirit of Kevin Volans' compositional intentions.

Der Beitrag bietet eine Einführung in die Schichtenlehre Heinrich Schenkers ohne Anspruch auf Vollständigkeit. Die Darstellung fokussiert grundlegende Ereignisse in Vorder- Mittel- und Hintergrund, ohne die Lehre vom Ursatz explizit zu berühren (letztere ist nach Auffassung des Autors aufgrund ihres hohen Abstraktionsniveaus als Einstieg nicht geeignet). Nach Klärung einiger für die schenkerianische Analyse zentraler Begriffe wie ›Stufe‹, ›Auskomponierung‹ und ›Tonikalisierung‹ wird sich unterschiedlichen Verfahren der ›Modulation‹ in Exposition und Durchführung diverse Sonatensätze von Wolfgang Amadé Mozart zugewandt. Gezeigt werden gängige kontrapunktische Verfahren (5–6–5-Fortschreitung und chromatischer Stimmtausch) sowie die Bedeutung ›motivischer Parallelismen‹ für den Zusammenhang zwischen thematischer Motivik und harmonischem Stufengang. / This article offers an introduction into Heinrich Schenker’s method of graphic analysis (without any claim of completeness). The approach focuses on fundamental events in the fore-, middle- and background without explicitly addressing the concept of the Ursatz, which the author considers inappropriate for an introduction due to its high level of abstraction. After defining some terms central to Schenkerian analysis like Stufe, Auskomponierung, and Tonikalisierung, different treatments of “modulation” in the expositions and developments of various sonatas by Wolfgang Amadé Mozart will be examined. Common contrapuntal patterns (e.g., 5–6–5 progression and chromatic voice exchange) and the significance of “motivic parallelisms” for the relationship between thematic motives and harmonic progression will be shown.

We find formulas for the Segre-MacPherson classes of Schubert cells in T-equivariant cohomology and the motivic Segre classes of Schubert cells in T-equivariant K-theory. In doing so we look at the pushforward of the projection map from the Bott-Samelson (Kempf-Laksov) desingularization to the Grassmannian. We find that the Segre-MacPherson classes are stable under pullbacks of maps embedding a Grassmannian into a bigger Grassmannian. We also express these formulas using certain Demazure-Lusztig operators that have previously been used to study these classes. / Doctor of Philosophy / Schubert calculus was first introduced in the nineteenth century as a way to answer certain questions in enumerative geometry. These computations relied on the multiplication of Schubert classes in the cohomology ring of Grassmannians, which parameterize k-dimensional linear subspaces of a vector space. More recently Schubert calculus has been broadened to refer to computations in generalized cohomology theories, such as (equivariant) K-theory. In this dissertation, we study Segre-MacPherson classes and motivic Segre classes of Schubert cells in Grassmannians. Segre-MacPherson classes are related to Chern-Schwartz-MacPherson classes, which are a generalization to singular spaces of the total Chern class of the tangent bundle. Motivic Segre classes are similarly related to motivic Chern classes, which are a K-theory analogue of Chern-Schwartz-MacPherson classes. This dissertation also studies the relationship between Schubert varieties and their Bott-Samelson desingularizations, specifically their (T-equivariant) cohomology and K-theory rings. Since equivariant cohomology (or K-theory) classes can be represented by polynomials, we can represent the Segre-MacPherson (or motivic Segre) classes as rational functions. Furthermore, we use certain operators that act on such polynomials (or rational functions) to find formulas for the rational function representatives of the aforementioned classes.

Made available in DSpace on 2014-06-11T19:22:20Z (GMT). No. of bitstreams: 0 Previous issue date: 2006-08-07Bitstream added on 2014-06-13T19:48:36Z : No. of bitstreams: 1 mannis_gdb_me_ia.pdf: 3194427 bytes, checksum: 2374fc542cb39f88a904a9fe24e7d7ef (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / O presente trabalho de mestrado tem como seu principal objetivo demonstrar que a aplicação de diferentes métodos analíticos a uma mesma obra e sua posterior comparação é uma metodologia eficaz para o estudo da linguagem musical, em particular de uma obra específica e que, através deste procedimento, informações de interesse teórico e interpretativo, que vão além da aplicação isolada de cada método, podem ser alcançadas. Para tanto, foi feita a análise de um movimento de grande duração inserido em uma obra extensa, composta pelo austríaco Gustav Mahler (1860-1911): a Sinfonia nº3. Sobre esta obra foram realizadas três análises: formal segundo Schoenberg e Rosen; motívica, segundo Réti; e schenkeriana, segundo Salzer.Os métodos foram comparados entre si, de modo a identificarem-se as convergências e divergências entre eles; com base nas divergências e convergências, foramindicadas possibilidades de leitura da obra. Ao final, estes resultados foram confrontados com gravações realizadas por grandes orquestras, tendo à frente regentes reconhecidos como grandes intérpretes da obra de Mahler, verifinco como foram solucionados os problemas de divergência analítica e observando, ainda, se as convergências podem ser confirmadas em suas interpretações. / The present Master's Degree dissertation seeks to demonstrate that the utilization of different analytical methods to a single opus, and their posterior comparation, in an efficient method for the study of musical language, particularly of an specific opus, and that, through this procedure, information on theoretical and interpretative interest that go beyond the isolated utilization of each method can be reached. Therefore, three analysis of the first movement of Gustav Mahler's 3rd Symphony were made. The three analysis were; formal, according to Schoenberg and Rosen; motivic according to Réti; and schenkerian, according to Salzer. The methods were compared to each other so it would be possible to identify similarities and differences amont them. Then, based on these similarities and differences, possibilities of reading of the work were indicated. In the end, these results were confronted with recording made by great orchestras, conducted by great maestros well-known as great interpreters of Mahler's opus, verifying how the problems of analytical diffrences were resolved and observing as well if the similarities coud be confirmed in their interpretations.

音樂分段在研究音樂分析相關的領域是很重要的研究題目。音樂的分段可以提供作音樂結構分析、音樂瀏覽、音樂內容查詢與音樂摘要等應用。本論文的研究目的就是對音樂作自動分段，以幫助使用者能快速瀏覽音樂的內容。因此，我們針對音樂的主題作主題式的分段。 音樂的主題是取決於作曲者的動機，動機是構成音樂主題的基本因素。為了能夠以主題為基礎作音樂分段，我們必須找出決定音樂主題的因素。動機會有規則性的出現在整首音樂當中，所以我們可以利用動機出現的規則來探勘音樂的動機。 我們提出一個以主題對音樂作分段的方法，總共分為四個主要的步驟。第一，我們從原始的音樂資料擷取出主旋律的部分。第二，將主旋律做粗略分段。我們利用探勘Non-trivial重複樣式的技術[17]，來找出粗略段落。第三，從粗略段落中探勘動機。我們利用Stein所提出來的動機變化規則，修改傳統探勘重複序列的方法，做動機的探勘。最後，我們利用探勘出來的動機對主旋律作精細分段。我們針對MIDI音樂檔案利用提出來的方法，實做出一個系統，找出音樂的主題段落。 先前研究在評估實驗結果時，多採用Precision與Recall去評估實驗的結果。然而，這樣的評估方法並不能表現出實驗結果與正確答案之間的相似程度。所以我們提出新的評估方法，根據實驗結果與正確答案之間的相似程度來評估實驗的準確率。根據實驗結果顯示，我們的方法準確率約65%。 / Music segmentation is one of the important issues in music analysis. Music segmentation can be utilized for music structure analysis, music browsing, content-based music retrieval, and music summarization. In this theis, we proposed a music segmentation method based on the music theme to provide users the capability to browse music segments by theme. Motives, the concepts of the composer, are the basic elements of music themes. Music themes were constructed by motives. In order to segment music by themes, we have to discover motives. Most motives repeated in the music by some motivic treatment rules. Therefore, motives can be discovered by these rules. We proposed the theme segmentation method. There are four steps. Firstly, we extract main melody from original music. In the second step, rough segments are generated from main melody by mining non-trivial repeating patterns. Then, motives are detected from rough segments. We modify the mining algorithm for discovering frequent patterns by applying motivic treatment rules proposed by Stein. Finally, we segment main melody based on the generated motives. Moreover, a system for segmentation of music in MIDI format was implemented. Concerning the effectiveness evaluation of music segmentation, precision and recall are used in previous research. We proposed an effectiveness measure and corresponding algorithm to evaluate the accuracy of music segmentation. Experimental results show that our proposed music segmentation method achieves 65% accuracy.

Saxophonist Chris Cheek has been a reference for his work as a sideman with some of the most established jazz artists in the international jazz scene of the last twenty-five years. Despite his importance, there is lack of detail in the available publications about Cheek. The short length and journalistic character of the publications only produce surface descriptions of Cheek's style. There is a need to further describe the melodic elements present in Chris Cheek's style in order to have a better understanding of the implications and importance of these elements across the history of jazz saxophone and jazz pedagogy. In the past, several scholarly works have described the improvisational styles of jazz musicians using a multitude of analytical tools. The design of those studies often fails to provide a comprehensive view of the improviser's style because of the limited scope of the analyzed sources or the specific focus of the analysis. This analytical study presents a comprehensive view of Chris Cheek's style through the motivic and voice-leading analyses of six improvisations by the saxophonist. This design allows the study to discern between motivic development processes, melodic structures, formulaic material, and harmonic structures that belong to the saxophonist's idiom. By presenting the elements in Cheek's style, this study is able to show the importance of motivic and voice-leading coherence in jazz pedagogy as well as the importance of Cheek's style as a reference for lyricism.

This dissertation aims to examine the motivic voice leading of the first two movements of Korngold's Violin Concerto, Op. 35 to illuminate the interwoven motives within the underlying structures of the movements. The analysis principally concentrates on two main motives: the motivic tritone and rising-third motives. Moreover, the analysis of Korngold's motivic writing further investigates the semantics that are evoked by the technical aspects. With his exceptional ability to interconnect music to narratives both in operas and films, Korngold never ceased to express the recurring themes of love and revival also in his instrumental music. It is noteworthy that he borrowed only the "love themes" from his film scores for the first two movements of the violin concerto. The violin concerto was the first work written after Korngold returned to absolute music after a decade of composing for films to ensure his and his family's survival during the war. After the Anschluss, during his exile in California as a Jewish refugee, Korngold's love for his homeland Austria, his philanthropic concern for humanity, and longing for peace became his primary focus; these concerns are reflected in his Violin Concerto through his use of specific motives. By researching the historical and biographical materials, as well as employing linear analysis, this study seeks to explore the meanings of the linear motives in Korngold's music; more specifically, it attempts to show how particular motivic figures and tonal structures express the composer's ideas of transcendental "love." It argues that an in-depth understanding of both the technical and semantic aspects is also the first and foremost requirement for performing this piece.

According to the American League of Orchestras' most recent report, Michael Daugherty is one of the ten most performed American composers of concert music in modern times. He has received six GRAMMY awards, including awards for Best Contemporary Classical Composition in 2011 and 2017. Characteristics of Daugherty's music are diverse: colliding tonalities and blocks of sound, driving polyrhythmic counterpoint, and jazz and pop elements. His music can be minimalistic at times and at others, stirringly melodic. Amongst this eclecticism, a fascination with American iconography remains a consistent hallmark of his music, exemplified by titles such as American Gothic, Jackie O, or Lost Vegas. Daugherty has stated that his goal is to create sophisticated, abstract music that is also catchy or memorable, with melodies and cultural allusions that audiences can "hang their hat on." Despite widespread success, relatively little scholarly work has been done on Daugherty's music, providing an opportunity for further research. The primary goal of this study is to add to the literature on Michael Daugherty by providing an analysis and conductor's guide of his first choral-orchestral work, Mount Rushmore. It is a genuine show piece, galvanizing and colorful, modestly demanding of the listener, and appreciated by individuals of diverse musical backgrounds. The work also contains multitudes, offering layers of musical complexity and extensive historical symbolism for those who wish to engage further. Daugherty's Mount Rushmore offers immediate appeal and an excellent return on investment. Using interviews with the composer as well as detailed formal, harmonic, and historical-textual analysis, this paper provides in-depth information and guidance to future conductors who wish to present an appealing choral-orchestral work by a prominent, living American composer. Conductors who program Daugherty's Mount Rushmore will find it valuable for their ensemble and community for years to come.