Parsimonious voice leading is a term, first used by Richard Cohn, to describe non-diatonic motion among triads that will preserve as many common tones as possible, while limiting the distance traveled by the voice that does move to a tone or, better yet, a semitone. Some scholars have applied these principles to seventh chords, laying the groundwork for this study, which strives toward a reasonably comprehensive, usable model for musical analysis. Rather than emphasizing mathematical proofs, as a number of approaches have done, this study relies on two- and three-dimensional geometric visualizations and spatial analogies to describe pitch-class and harmonic relationships. These geometric realizations are based on the organization of the neo-Riemannian Tonnetz, but they expand and apply the organizational principles of the Tonnetz to seventh sonorities. It allows for the descriptive “mapping” or prescriptive “navigation” of harmonic paths through a defined space. The viability of the theoretical model is examined in analyses of passages from the repertoire of Frédéric Chopin. These passages exhibit a harmonic syntax that is often difficult to analyze as anything other than “tonally unstable” or “transitional.” This study seeks to analyze these passages in terms of what they are, rather than what they are not.

Film musicology is growing at a heartening pace, but the discipline is still bereft of sustained contributions from music theory. The current study seizes the opportunity presented by the underanalyzed repertoire of film music, offering an argument for applying the techniques of transformational analysis, and neo-Riemannian analysis in particular, to the interpretation of music for the moving image. Film musical style and form respond strongly to a transformational approach, which adapts well to both the triadic chromaticism characteristic of Hollywood’s harmonic practice and the dynamic and contingent condition of musical design inherent to the medium. Concurrently, the analytic tools and conceptual structure of neo-Riemannian theory benefit from exposure to a fresh repertoire with different analytic needs than those of art music. In this dissertation, the author scrutinizes the capacity for tonality to act as a unifying and dramatically potent force in film. With parameters of effective cinematic tonal design established, the adapted transformational methodology responds faithfully to the expressive and temporal qualities of the soundtrack. The author develops a model for harmonic associativity and a general hermeneutics of transformation, extrapolated from analyses of scores from John Williams, James Horner, Jerry Goldsmith, and many others. The power of the transformational approach to capture tonal phenomena through spatial representations is marshaled to perform critical readings of scores for A Beautiful Mind and Star Trek. Not only can the neo-Riemannian stance illuminate the way film music works, but it can train the listener and analyst to perceive and enjoy film with more sensitive ears. / Music

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.

Made available in DSpace on 2015-05-14T12:52:33Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 9142957 bytes, checksum: 86752beec94b26514b271847628765ae (MD5) Previous issue date: 2013-03-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / This dissertation examines the syntactic coherence of the Trimodal system of José Siqueira, through the analysis of the Quarta Sonatina for piano (1963) and Três Estudos para Flauta e Piano (1964) in light of three methodological procedures. The first of these procedures is the quantitative hierarchization of the harmonic structures, resulting in a new type of classification of the vertical entities, while proposing a method for identification and classification of the syntax of voice-leading between these structures; the second procedure is based on the concept of parsimonious connection from the Neo-Riemannian Theory and aims at investigating how the harmonic structures are connected to each other; and the third evaluates the impact of the relationship of pertinence and encapsulation between the pitchclass set in the syntactic connections between the sonorities. The application of these methodological procedures allow us to characterize a syntatic profile for the three analyzed works, revealing fundamental aspects regarding the consistency of the Trimodal system. It is still our intention that this work, which here gives a highly analytical look on a small portion of the work of Siqueira, would serve as a reference for research so that one can carry out the examination of other works of this composer, as well as other Brazilian composers who worked on the threshold between tonality and atonality, and that it would also extend its boundaries of applicability through the dialogue with other fields of research in music, especially that of musical composition, which will benefit from the modeling implemented here from a prescriptive approach. / Este trabalho examina a coerência sintática do Sistema Trimodal de José Siqueira (1907- 1985), através da análise da Quarta Sonatina para piano (1963) e dos Três Estudos para Flauta e Piano (1964) à luz de três procedimentos metodológicos. O primeiro desses procedimentos consiste na hierarquização quantitativa de estruturas harmônicas, resultando em uma nova tipologia de classificação das entidades verticais, ao mesmo tempo em que propõe uma metodologia de identificação e classificação da sintaxe de condução entre essas estruturas; o segundo procedimento se baseia no conceito de conexão parcimoniosa da Teoria Neo-Riemanniana e tem o propósito de averiguar como as estruturas harmônicas se conectam entre si; e o terceiro avalia o impacto das relações de pertinência e encapsulamento entre os conjuntos de classes de alturas nas conexões sintáticas entre as sonoridades. A aplicação desses procedimentos metodológicos nos permitirá caracterizar um perfil sintático para as duas obras analisadas, revelando aspectos fundamentais relativos à coerência do Sistema Trimodal. Ainda é nossa intenção que este trabalho, que aqui traça um olhar eminentemente analítico sobre uma pequena parcela da obra de Siqueira, possa servir como referencial de pesquisa para que se realize o exame de outras obras desse compositor, bem como de outros compositores brasileiros que trabalharam no limiar entre tonalismo e atonalismo, e que também possa ampliar suas fronteiras de aplicabilidade pelo diálogo com outros campos da pesquisa em música, mormente o da composição musical, que se beneficiará das modelagens aqui realizadas a partir de um viés prescritivo.

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O objetivo principal desta pesquisa é o aprimoramento de ferramentas teóricas desenvolvidas para a análise harmônica de obras de vanguarda do início do século XX e afins (incluindo algumas obras de Villa-Lobos), destacando a utilização da simetria intervalar como fator de coerência em amostras de músicas deste período e correlacionadas. Observaremos principalmente aspectos relacionados a presença de padrões intervalares simétricos por reflexão inerentes ao sistema cromático. Procurando estabelecer um arcabouço teórico consistente que contemplasse as demandas circunscritas nas músicas pós-tonais analisadas, buscamos entender a importância da simetria entre alturas em níveis estruturais mais profundos supondo que a proporcionalidade intervalar pudesse corroborar no delineamento harmônico das obras escolhidas. Nossa proposta de estudo é calcada em fundamentos e conceitos desenvolvidos por teóricos ligados às pesquisas sobre a teoria dos conjuntos, com destaque para os textos de Joseph Straus (2005). Em outra esfera, elencamos ferramentas teóricas de uma segunda abordagem metodológica que cada vez mais ganha destaque entre musicólogos que atuam no campo da análise de obras pós-tonais - a teoria neorriemanniana - em particular observando os conceitos apresentados por David Lewin (1982; 1987) e os seus desdobramentos discutidos por Richard Cohn (1998; 2012), autor em torno do qual gravita a vertente secundária conhecida como teoria transformacional. A partir da intersecção entre estas duas correntes teóricas pós-tonais escolhidas, desenvolvemos uma terceira proposta metodológica aparentemente inédita - que chamaremos neste trabalho de teoria da inversão - um desdobramento decorrente do aperfeiçoamento de conceitos da teoria neorriemanniana de David Lewin e Brian Hyer que envolvem a reflexão intervalar de conjuntos de alturas, parâmetros não contemplados pela recente teoria transformacional de Dmitri Tymoczko (2007; 2011) e Richard Cohn (1998; 2012). No âmbito desta proposição, seguindo a suposição levantada por Robert Morris (2007) de que existem aspectos fundamentais em comum entre as principais correntes teóricas dedicadas à música pós-tonal, exploramos alguns apontamentos deste autor que nos direcionaram à apropriação de ferramentas pertencentes à teoria dos grupos - campo de conhecimento oriundo da matemática, especializada no estudo de simetria utilizando estruturas algébricas conhecidas como matrizes. Deste processo surge a descoberta de um conglomerado de classes de conjuntos que podem ser alinhados em uma mesma rede de projeções por inversão. Avaliando os aspectos inerentes a este sistema apresentado, identificamos a construção de toda uma estrutura em disposição espelhada, revelando a existência de uma simetria transversal que abrange um grande número de conjuntos de alturas inerentes ao universo das doze alturas, confirmando a hipótese levantada por Robert Morris. Verificamos ainda outras correlações entre os conjuntos correspondentes presentes nesta rede de projeções por inversão - relações por multiplicação pelo fator M5 e M7 e invariância entre entradas de vetores intervalares (RAHN, 1980; OLIVEIRA, 2007) - que corroboram a constatação desta dimensão simétrica envolvendo o campo harmônico cromático. Outra proposta neste trabalho foi a ampliação na gama de possibilidades de utilização de redes de alturas (Tonnetze) - ferramenta emblemática da teoria neorriemanniana - apresentando outras opções de conjuntos para os desdobramentos por inversões, indo além dos convencionais conjuntos 3-11 (tricorde Maior e menor) e 4-27 (tetracordes Maior 7 e meio diminuto) recorrentes em formatações tradicionais. Seguindo neste propósito, desenvolvemos aprofundamentos abrangendo a remota rede de alturas de Euler com o tetracorde 4-20 e o Tonnetz tridimensional de Gollin (1998), alinhando esta pesquisa também aos resultados encontrados por Henri Pousseur ([1968], 2009) em suas \"redes harmônicas\" e aos conceitos desenvolvidos por George Perle (1977) e sua \"teoria dos ciclos intervalares\". / The main objective of this research is to improve the theoretical tools developed for the harmonic analysis of the early works of the early 20th century and related works (including some works by Villa-Lobos), highlighting the use of interval symmetry as a coherence factor in samples of pieces from this period and correlated. We will mainly observe aspects related to the presence of symmetrical interval patterns by reflection inherent to the chromatic system. We will mainly observe aspects related to the presence of symmetrical interval patterns by reflection inherent to the chromatic system. In order to establish a consistent theoretical framework that contemplates the circumscribed demands in the analyzed post-tonal pieces, we sought to understand the importance of symmetry by comparing pitches at deeper structural levels, assuming that the interval proportionality could corroborate the harmonic delineation of the chosen works. Our proposal is based on fundamentals and concepts developed by theorists related to research on pitch-class set theory, especially the texts of Joseph Straus (2005). Our study proposal is based on fundamentals and concepts developed by theorists related to research on pitch-class set theory, especially the texts of Joseph Straus (2005). In another sphere, we have ellipped theoretical tools of a second methodological approach that is increasingly prominent among musicologists working in the field of post-tonal analysis - neo-Riemannian theory - in particular, observing the concepts presented by David Lewin (1982, 1987) and its ramifications discussed by Richard Cohn (1998, 2012), author around which gravitates the secondary slope known as transformational theory. From the intersection between these two post-tonal theoretical currents chosen, we have developed a third methodological proposal that is apparently unpublished - which we will call inversional pitch-class set theory - an unfolding resulting from the refinement of David Lewin and Brian Hyer\'s concepts of neo-Riemannian theory involving interval analysis of sets of pitch-class sets, parameters not contemplated by the recent transformational theory of Dmitri Tymoczko (2007; 2011) and Richard Cohn (1998, 2012). In this context, following the assumption made by Robert Morris (2007) that there are fundamental aspects in common among the main theoretical currents dedicated to post-tonal music, we explore some notes of this author that have directed us to the appropriation of tools belonging to the theory of groups - field of knowledge from mathematics, specialized in the study of symmetry using algebraic structures known as matrices. From this process comes the discovery of a conglomeration of pitch-class sets that can be aligned in the same inversional pitch-class set network. Evaluating the inherent aspects of this system, we identified the construction of a whole structure in a mirrored arrangement, revealing the existence of a transversal symmetry that covers a substantial number of pitch-class sets inherent to the universe of the twelve pitches, confirming the hypothesis raised by Robert Morris. We also verified other correlations between the corresponding sets in this inversional pitch-class set network - relations by multiplication by the factor M5 and M7 and invariance between interval vectors (RAHN, 1980; OLIVEIRA, 2007) - which corroborate the observation of this symmetrical dimension involving the chromatic harmonic field. Another proposal in this work was the expansion of the range of possibilities of use of pitch-classes networks (Tonnetze) - emblematic tool of the neo-Riemannian theory - presenting other options of sets for the inversion unfolding, going beyond the conventional sets 3-11 (Major and minor chord) and 4-27 (Major 7th and half-diminished 7th chords) recurrent in traditional formatting. Following this, we developed deepening studies covering the remote pitch-class network of Euler with the tetrachord 4-20 and Gollin\'s three-dimensional Tonnetz (1998), aligning this research also with the results found by Henri Pousseur ([1968], 2009) about his harmonic networks and the concepts developed by George Perle (1977) and his \"interval cycles theory\".

Ce travail de recherche propose une description du style mélodique et harmonique du groupe britannique Portishead et s’appuie sur l’analyse du répertoire complet, soit 33 chansons réparties sur trois albums (11 chansons par albums). Étant donné que le corpus étudié est restreint, il est possible de procéder à une analyse statistique qui permet de dégager une grammaire mélodico-harmonique. L’hypothèse de ce travail de recherche repose sur l’idée que l’évolution du langage musical de Portishead s’articule autour de procédés mélodiques et harmoniques favorisant un élargissement d’un cadre tonal équivoque. Pour ce faire, Portishead a recours à plusieurs procédés mélodiques et harmoniques qui entretiennent l’équivoque tonale. Or, ces procédés sont similaires, sans toutefois être identiques, aux six procédés répertoriés par Sylvain Caron (Caron 2002) au sujet de la grammaire de Gabriel Fauré. Par la mise en œuvre de plusieurs outils d’analyses, nous procédons à une étude comparée et contextualisée de certains mécanismes mélodique et harmonique qui font émerger l’équivoque, tant chez Fauré que chez Portishead. Ces outils d’analyse, comme l’analyse des vecteurs de ruptures mélodico-harmoniques, l’analyse paradigmatique ou l’analyse néo-riemannienne, ont été bonifiés afin de rendre compte de certaines particularités liées au corpus étudié. Ce travail de recherche est divisé en deux parties précédés d’une introduction, d’une notice biographique et d’une revue de littérature analytique. La première partie se divise en trois chapitres et s’intéresse spécifiquement au traitement mélodique équivoque. La deuxième partie, constituée des deux derniers chapitres, abordent les procédés d’équivoque harmonique. Ce travail de recherche a démontré que même si un siècle sépare les compositions de Gabriel Fauré et Portishead, l’équivoque se manifeste par une grammaire musicale commune. Nous constatons aussi que l’équivoque articule le discours formel et conditionne les rapports structurants de tension – détente de l’œuvre. / This research provides a description of the melodic and harmonic style of the British band Portishead. It is based on analysis of the full repertoire or 33 songs over three albums (11 songs per album). Since the entire corpus is analyzed, one may be able to detect chronologically trends and perform statistical analysis of the evolution of the melodic- harmonic grammar and aesthetics of the group. The hypothesis of this research work is based on the idea that the evolution of the musical language of Portishead revolves around melodic and harmonic processes favoring an expansion of tonal ambiguity frame. To do this, Portishead uses several melodic and harmonic processes that maintain tonal ambiguity. However, these processes are similar, but not identical, to the six processes listed by Sylvain Caron (Caron 2002) about the grammar of Gabriel Fauré. For the implementation of various analysis tools, we perform a comparative and contextualized study of certain melodic and harmonic mechanisms that brings out the ambiguity, both in Fauré than Portishead. These analysis tools, such as analysis of melodic-harmonic vectors of ruptures, paradigmatic analysis or neo-Riemannian analysis were enhanced to reflect certain particularities of the studied corpus. This research consists of two parts preceded by an introduction, a manual and a review of literature analystique. The first part is divided into three chapters and focuses specifically on clear melodic treatment. The second part, consisting of the last two chapters address the ambiguity of harmonic processes. This research has shown that even if a century separates the compositions of Gabriel Fauré and Portishead, ambiguity is manifested by a common grammar. We also notice that ambiguity revolves formal speeches and determines the structuring of tension – release relationships.