One goal of music theory is to describe the resources of a pitch system. Traditionally, the study of pitch intervals was done using frequency ratios of the powers of small integers. Modern mathematical music theory offers an independent way of understanding the pitch system by considering intervals as transformations. This thesis takes advantage of the historical emergence of algebraic structures in musicology and, in the spirit of transformational theory, treats operations that form mathematical groups. Aspects of Neo-Riemannian theory are explored and developed, in particular the T/I and PLR groups as dual. Pitch class spaces, such as 12, can also be defined as torsors. In addition to surveying the group theoretical tools for music analysis, this thesis provides detailed proofs of many claims that are proposed but seldom supported.

Includes bibliographical references / Philip Glass is best known for his role in the establishment of the 1960s minimalist movement, which was characterised by an extensive reduction of musical means. Since the mid-1970s, the composer has adopted a richer, more complex musical language, and distanced himself from the minimalist label. Academic scholarship on the composer's more recent compositions is severely limited, with the result that he is often still viewed as a minimalist. This dissertation's focus is on a more recent work by Glass, the Tirol Concerto for Piano and Orchestra (2000), and thus seeks to contribute to our knowledge of the composer's more recent stylistic development and the extent to which it is minimalist. The research approach entails compositional analyses of the concerto's second movement from both literary and theoretical perspectives. The movement's conception, its background and factors that had an influence on its compositional content are explored through literature studies. This is followed by theoretical investigations of its musical characteristics through the application of functional harmonic analysis and neo-Riemannian theory. Findings from the research provide evidence that the composition's title stems from the 'Tyrolean character' that was requested by its commissioners. However, relations between the movement and the film The Truman show (1998) challenge the composer's affirmations of a Tyrolean folk-song basis. Musically, the movement consists of a simple, repetitive structural and harmonic framework that undergoes superficial variations through melodic, textural and rhythmic changes. Transformational coherence within a functional structure is an essential component of the movement's harmonic content. This dissertation concludes that the piece contains musical characteristics consistent with all of Glass's stylistic periods, including minimalism, as well as new compositional devices that have not been identified previously. It recommends further study of the composer's more recent output , especially through transformational perspectives, and a reconsideration of the ontology and appropriateness of stylistic labels such as minimalism.

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Cette thèse présente des généralisations u groupe néo-riemannien PLR, que agit sur l'ensemble des 24 triades majeures et mineures. Le travail commence par une reconstruction de l'histoire de Tonnetz, un graphe associé aux trois transformations qui génèrent le groupe PLR. La thèse présente deux généralisations du groupe PLR pour les accords de septième. Le premier agit sur le tournage des septièmes de dominantes, mineure, semi-diminuée, majeure et diminuée, le second comprend également la septième mineure majeur, majeure augmenté, l'augmentée et la septième dedominante bémol. Nous avons également classé les transformations les plus parcimonieuses parmi les 4 triades (majeure, mineure, augmentée et diminuée) et avons étudié le groupe généré par celles-ci. Enfin, nous avons introduit une approche générale permettant de définir des opérations parcimonieuses entre les accords de septième et de triade, mais aussi les opérations déjà connues entre triades et celles entre septièmes. / This thesis presents a generalizations of the neo-Riemannian PLR-group, that acts on the set of 24 major and minor triads. The work begins with a reconstruction on the history of the Tonnetz, a graph associated with the three transformations that generate the PLR-group. The thesis presents two generalizations of the PLR-group for seventh chords. The first one acts on the set of dominant, minor, semi-diminished, major and diminished sevenths, the second one also includes minor major, augmented major, augmented, dominant seventh flat five. We considered the most parsimonious operations exchanging two types of sevenths, moving a single note by a semitone or a whole tone. We also classified the most parsimonious transformations among the 4 types of triads (major, minor,augmented and diminished) and studied the group generated by them. Finally, we have introduced a general approach to define parsimonious operations between sevenths and triads, but also the operations already known between triads and those between sevenths.

A proposta desta dissertação é analisar os três movimentos das Bachianas Brasileiras Nº 1: Introdução (Embolada), Prelúdio (Modinha) e Fuga (Conversa), de Heitor Villa-Lobos, a partir de uma abordagem transformacional, seguindo a linha proposta por Steven Rings (2011) na qual, ferramentas de análise neorriemannianas são utilizadas para iluminar aspectos familiares do tonalismo. Partindo desta abordagem, os resultados da análise musical serão apresentados através de gráficos e redes transformacionais, objetivando criar um suporte analítico musical que, numa fase posterior a esta pesquisa, aponte para uma reflexão sobre a ideia de Nestor Garcia Canclini a respeito de processos de hibridação cultural (CANCLINI, 2008). / The proposal of this dissertation is to analyze the three movements of the Bachianas Brasileiras Nº 1: Introduction (Embolada), Prelude (Modinha) and Fugue (Conversa), by Heitor Villa-Lobos, based on a transformational approach, following the thinking proposed by Steven Rings (2011) in which, Neo-Riemannian analysis tools are used to illuminate familiar aspects of tonalism. Based on this approach, the results of musical analysis will be presented through graphs and transformational networks, aiming to create an analytical musical support that, at a later stage of this research, points to a reflection on the idea of Nestor Garcia Canclini regarding processes of cultural hybridization (CANCLINI, 2008).

A proposta desta dissertação é analisar os três movimentos das Bachianas Brasileiras Nº 1: Introdução (Embolada), Prelúdio (Modinha) e Fuga (Conversa), de Heitor Villa-Lobos, a partir de uma abordagem transformacional, seguindo a linha proposta por Steven Rings (2011) na qual, ferramentas de análise neorriemannianas são utilizadas para iluminar aspectos familiares do tonalismo. Partindo desta abordagem, os resultados da análise musical serão apresentados através de gráficos e redes transformacionais, objetivando criar um suporte analítico musical que, numa fase posterior a esta pesquisa, aponte para uma reflexão sobre a ideia de Nestor Garcia Canclini a respeito de processos de hibridação cultural (CANCLINI, 2008). / The proposal of this dissertation is to analyze the three movements of the Bachianas Brasileiras Nº 1: Introduction (Embolada), Prelude (Modinha) and Fugue (Conversa), by Heitor Villa-Lobos, based on a transformational approach, following the thinking proposed by Steven Rings (2011) in which, Neo-Riemannian analysis tools are used to illuminate familiar aspects of tonalism. Based on this approach, the results of musical analysis will be presented through graphs and transformational networks, aiming to create an analytical musical support that, at a later stage of this research, points to a reflection on the idea of Nestor Garcia Canclini regarding processes of cultural hybridization (CANCLINI, 2008).

Dutch composer Peter Schat’s (1935-2003) pursuit of a compositional system that could generate and preserve intervallic relationships, while allowing the composer as much flexibility as possible to manipulate musical material, led him to develop the tone-clock system. Fundamentally comprised of the twelve possible trichords, the tone clock permits each to generate a complete twelve-tone series through the “steering” principle, a concept traced to Boulez’s technique of pitch-class set multiplication. This study serves as an overview of Schat’s tone-clock system and focuses primarily on the effects of the steering function in “Genen” (2000). Furthermore, I expand on the tone-clock system by combining transformational theory with Julian Hook’s uniform triadic transformations and my proposed STEER and STEERS functions, which express the procedures of the steering principle as a mathematical formula. Using a series of transformational networks, I illustrate the unifying effect steering has on different structural levels in “Genen,” a post-tonal composition.

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Local employers believe the lack of prerequisite soft skills is inhibiting the graduates from a local community college from securing employment. The rationale of this phenomenological study was to investigate the perceptions of students and employers related to the soft skills needed to be successful in future employment. The theoretical framework was based on Mezirow's transformational and Daloz's mentorship theories. Individual face-to-face, semistructured interviews were used to gather data from 12 business and computer students and 7 employers (N=19) who were selected using purposeful random sampling. The typewritten transcripts of participants' responses were imported in MAXQDA 11, then were open coded and analyzed for emergent themes. According to emergent findings among these 19 participants, for entry-level jobs, communication was the most important and the most lacking soft skill. The recommendations informed the creation of a mandatory 3-day professional development training program, which was developed to help students enhance their soft skills before entering their future careers. This study directly affects positive social change by enhancing the quality of soft skills for future employees who enter the local work force.

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