In this dissertation, we explore the approximate diagonalization of unital homomorphisms between C*-algebras. In particular, we prove that unital homomorphisms from commutative C*-algebras into simple separable unital C*-algebras with tracial rank at most one are approximately diagonalizable. This is equivalent to the approximate diagonalization of commuting sets of normal matrices. We also prove limited generalizations of this theorem. Namely, certain injective unital homomorphisms from commutative C*-algebras into simple separable unital C*-algebras with rational tracial rank at most one are shown to be approximately diagonalizable. Also unital injective homomorphisms from AH-algebras with unique tracial state into separable simple unital C*-algebras of tracial rank at most one are proved to be approximately diagonalizable. Counterexamples are provided showing that these results cannot be extended in general. Finally, we prove that for unital homomorphisms between AF-algebras, approximate diagonalization is equivalent to a combinatorial problem involving sections of lattice points in cones.

Elliott Carter frequently organizes the formal design of his compositions with long-range polyrhythms, such that different parts of the texture move at different, slow tempi, often arranged so that their beats coincide exactly twice, at the beginning and the end of the piece. Many theorists have commented on these tempo ratios, and pointed out how they are manifested, on a smaller time scale, in each instrument’s notated beat divisions. However, building on the work of Link and Roeder, this paper shows that in Esprit Rude/Esprit Doux, Esprit Rude/Esprit Doux II, and Retrouvailles, pieces Carter dedicated to Pierre Boulez, the polyrhythms also guide the interactive behaviour of the instruments. Furthermore, it shows that although these works are all independently complete and coherent, together they can be understood as three movements of a trilogy, whereby the progression from simultaneous melodic parts that run independently of one another in Esprit I to the near-monophonic melody lines in Retrouvailles, as well as the increase in cooperative activity (for example, melody-sharing, and the mutual building of important harmonies) represent a theme of growing reconciliation. / Arts, Faculty of / Music, School of / Graduate

This study proposes a theory of texture for Elliott Carter's song cycle A Mirror on Which to Dwell. Texture is an important structural aspect of much recent music, as is exemplified in Carter's music. The first chapter is introductory and discusses other textural theories, and the concept of auditory streams. It also provides background to Elizabeth Bishop and to the poems that Carter selected for the cycle, and introduces the song cycle as a whole. The second chapter outlines a textural theory based on streaming. Texture is defined as comprising those contextually defined aspects of sound which lead one to perceive music as consisting of distinct streams. Individual streams are defined by properties, behaviours processes. The ways in which streams are combined, and the changes that occur in the streams during the combinations constitute textural behaviours and processes. The third chapter presents the ways in which textural behaviours and processes can function. They can have symbolic functions by representing personae and actions in the text. They can also have musical functions and thus can play a role in the delineation of form. In the fourth chapter each song in the Mirror cycle is analyzed. Songs that are texturally clear are analyzed first, followed by those that are more texturally complex. Because of the close relationship between text and music in these songs, each analysis starts with a discussion of the text before turning to the music. The main textural features of each song are presented, and then the analytical discussion focuses on form and text-setting. In the conclusion an overview of the songs is presented. The songs, although formally diverse, are similar in many respects. In all of them Carter establishes the important streams, some of which have significant symbolic roles, in the opening measures. The songs are characterized by similar textural processes, which help to delineate the form of the songs and to portray musically the meaning of the text. An analysis of these songs using the textural theory presented in this study provides insight into their form and meaning. / Arts, Faculty of / Music, School of / Graduate

Pierre Elliott Trudeau's ideas on liberal democracy and political philosophy are relevant to Canadian life. He is a modern liberal democrat with a vision of the 'Good' society - what he terms the Just Society. The values of a Just Society are numerous, but perhaps, the most important are freedom, equality, and tolerance. These values are core to his theory and are often revealed in his battle against nationalism. Trudeau is radically opposed to notions of ethnic nationalism, such as French Canadian and Aboriginal nationalism, but he supports a type of civic nationalism within a federal, pluralistic system. In his dislike for nationalism, Trudeau is similar to Lord Acton, who has had a major influence on his work. Trudeau also shows thought similar to John Locke, J.S. Mill, I. Berlin, de Tocqueville, Publius, and John Rawls. / Arts, Faculty of / Political Science, Department of / Graduate

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Thesis (D. Mus. Arts)--University of Washington, 1992. / Vita. Includes bibliographical references (leaves [245]-247).

The lecture recital was given January 22, 1977. A discussion of Elliott Carter's Piano Sonata emphasized those compositional techniques which foreshadowed important compositional procedures in many of his later works. The following compositions were discussed: Concerto for Orchestra, Double Concerto for Harpsichord and Piano with Two Chamber Orchestras, 8 Etudes and a Fantasy for Woodwind Quartet, Holiday Overture, Piano Concerto, Sonata for Flute, Oboe, Cello, and Harpsichord, Sonata for Violoncello and Piano, String Quartet No. 1, String Quartet No. 2, String Quartet No. 3, Variations for Orchestra. The Piano Sonata was Ty and Schumann. In addition to the lecture recital, three public solo recitals were performed. The first solo recital, performed on April 2, 1973, consisted of works by Bartok, Debussy The second solo recital, performed on October 28, 1974, included works by Bach and Liszt. The final solo recital, performed on March 7, 1976, consisted of works by Beethoven and Chopin. All four programs were recorded on magnetic tape and are filed, along with the written version of the lecture recital, as part of the dissertation. performed.

For the purposes of expressive intent, Carter developed compositional strategies that possess qualities congruent with the musical language in his Second Quartet (1959). He employed strategies including tempo modulation, triple groupings, and large-scale ratios to assemble the musical discourse and to guide the listener's perception of large-scale continuity. I label these devices collectively as "preferential strategies" because it is Carter who selects certain pre-compositional ideas that organize musical material and demarcate structural locations. Tempo modulations that organize dual meters and triple groupings that interact in transitional and transformational ways demonstrate his concern with controlling the overall time continuity through local level organization. Large-scale ratio relations between nine interlocking sections of this four movement work illustrate how Carter employs a local strategy that projects a large-scale structure. Recognizing that Carter's ultimate compositional goal prioritizes temporal processes, these proposed preferred strategies articulate a convergence of musical elements.