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Universidade Federal Do Estado Do Rio De Janeiro Centro De Letras E Artes Programa De Pós-Graduação Em Música Doutorado Em Música UNIVERSIDADE FEDERAL DO ESTADO DO RIO DE JANEIRO CENTRO DE LETRAS E ARTES PROGRAMA DE PÓS-GRADUAÇÃO EM MÚSICA DOUTORADO EM MÚSICA ANÁLISE PARTICIONAL: UMA MEDIAÇÃO ENTRE COMPOSIÇÃO MUSICAL E A TEORIA DAS PARTIÇÕES PAUXY GENTIL-NUNES RIO DE JANEIRO, 2009 ii ANÁLISE PARTICIONAL: UMA MEDIAÇÃO ENTRE COMPOSIÇÃO MUSICAL E A TEORIA DAS PARTIÇÕES por PAUXY GENTIL-NUNES Tese submetida ao Programa de Pós- Graduação em Música do Centro de Letras e Artes da UNIRIO, como requisito parcial para obtenção do grau de Doutor, sob a orientação da Professora Dra. Carole Gubernikoff RIO DE JANEIRO, 2009 iii iv Para meus pais, Maria Emília Andrade Nunes e (in memoriam) Pauxy Gentil Nunes, com gratidão. v AGRADECIMENTOS Aos colegas Tom Moore e Jean-Pierre Caron pela generosa ajuda nas traduções do resumo. Aos alunos da turma de Composição 2005 da UFRJ, hoje colegas, Gustavo Guerreiro, (pela cessão da partitura editorada de Ferneyhough), Frederico Omar Ribeiro, Rodrigo Andrade, Antonio Albuquerque, pela vivacidade e entusiasmo com que abraçaram e enriqueceram as propostas ligadas ao presente trabalho. Aos amigos e colegas Marina Spoladore e Paulo Dantas, por terem compartilhado, de forma brilhante, os momentos de criação e execução de Baile. Ao colega e compositor Alexandre Carvalho, pela amizade, motivação e pela importante interlocução no momento de início da pesquisa. Aos colegas compositores Caio Senna, Leonardo Fuks, Marcos Lucas, Marcos Nogueira e Roberto Victorio pela participação durante o processo, com idéias, motivação e interlocução. A todos os professores e funcionários do PPGM, que com seu esforço deram sentido ao caminho percorrido. Às pessoas que me apoiaram e me acolheram, em momentos bons e em momentos difíceis, durante o período do Doutorado - César Tavares, Flávio Vieira Jacques, Luana Ribeiro Andrade, Noara Paoliello, Prof. Rubens Cirino (UERJ). À amiga e mestra Carole Gubernikoff, pela confiança, competência e entusiasmo inspirador. vi Os aspectos das coisas que são, para nós, os mais importantes ficam escondidos devido à sua simplicidade e familiaridade. (L. Wittgenstein) vii GENTIL-NUNES, Pauxy. Análise particional: uma mediação entre composição musical e a teoria das partições. 2009. Tese (Doutorado em Música). Rio de Janeiro: Programa de Pós- Graduação em Música, Centro de Letras e Artes, Universidade Federal do Estado do Rio de Janeiro RESUMO A análise particional é proposta como abordagem original da composição musical, fundamentada na convergência entre a teoria das partições de inteiros, de Leonhard Euler (1748), e a análise textural de Wallace Berry (1976). Seu principal objetivo é construir uma topologia completa das configurações texturais, e assim promover a criação de novas formalizações de práticas composicionais. Para isso, são estabelecidas relações entre as partições, através da análise de sua estrutura interna. Alguns conceitos e ferramentas originais são desenvolvidos, como os índices de aglomeração e dispersão, os particiogramas, os indexogramas, e os processos de redimensionamento, revariância, transferência, concorrência e reglomeração. Três aplicações analíticas são propostas: particionamento rítmico, melódico e por eventos. A partir delas, são analisadas pequenas peças de alguns autores de música de concerto (Beethoven, Schöenberg, Webern, Bach, Gentil-Nunes, Ferneyhough), com a finalidade de verificar a pertinência analítica da teoria, através da comparação com outros tipos de análise. PALAVRAS-CHAVE: Partições de Inteiros / Composição / Análise Musical viii GENTIL-NUNES, Pauxy. Partitional analysis: mediation between musical composition and the theory of integer partitions. 2009. Thesis (Doctor Degree in Music). Rio de Janeiro: Programa de Pós-Graduação em Música, Centro de Letras e Artes, Universidade Federal do Estado do Rio de Janeiro ABSTRACT Partitional analysis is proposed as an original approach to musical composition and analysis, based on a convergence between the theory of integer partitions, by Leonhard Euler (1748), and textural analysis, by Wallace Berry (1976). Its main objective is to build a complete topology of textural configurations, and thus to promote the creation of new formalizations of compositional practices. For this purpose, relations between partitions are established through analysis of internal structures. Various original concepts and tools are explored, including indices of agglomeration and dispersion, partitiograms, indexograms, and processes of resizing, revariance, transfer, concurrence, and regglomeration. Three analytical applications are presented - rhythmic, melodic and event partitioning. Based on these applications, short pieces by a few composers of classical music (Beethoven, Schoenberg, Webern, Bach, Gentil-Nunes, Ferneyhough) are analyzed, in order to verify the analytical relevance of the theory, through comparison with other types of analysis. KEYWORDS: Integer Partitions / Composition / Musical Analysis ix GENTIL-NUNES, Pauxy. Analyse partitionelle: une médiation entre la composition musicale et la théorie des partitions d’un entier. 2009. Thèse (Doctorat en Musique). Rio de Janeiro: Programa de Pós-Graduação em Música, Centro de Letras e Artes, Universidade Federal do Estado do Rio de Janeiro SOMMAIRE L’analyse partitionelle est proposée comme une approche originale de la composition musicale, fondée sur la confluence de la théorie des partitions d’un entier, de Leonhard Euler (1748), et sur l’analyse de la texture, de Wallace Berry (1976). Son principal objectif est de construire une topologie complète des configurations texturelles, et ainsi, promouvoir la création de nouvelles formalisations de pratiques compositionelles. A cet effet, quelques relations entre les partitions sont établies à partir de l’analyse de ses structures internes. Quelques concepts et outils originaux sont développés, tels les indices de agglomération et dispersion, les partitiogrammes et indexogrammes; et les processus de redimensionment, de revariance, d’agglomération, de dispersion, de transfert, de concurrence et de regglomeration. Trois applications analytiques sont proposées : partitionement rythmique, mélodique et par évenements. Celles-ci sont utilisées dans l´analyse de petites pièces de compositeurs de musique de concert (Beethoven, Schöenberg, Webern, Bach, Gentil-Nunes, Ferneyhough), visant la vérification de la pertinence analytique de la théorie, en comparaison avec d´autres types d’analyses. MOTS-CLÉ: Partitions d’un entier / Composition / Analyse musicale x SUMÁRIO LISTA DE FIGURAS ............................................................................................................ xii LISTA DE TABELAS ....................................................................................................... xxiii LISTA DE EQUAÇÕES .................................................................................................... xxiv INTRODUÇÃO ........................................................................................................................ 1 1 - FUNDAMENTOS ............................................................................................................... 6 1.1 - A teoria das partições .................................................................................................. 6 Representações de partições ............................................................................................ 11 Diagrama de Hasse, reticulado de Young e relações entre partições ............................. 13 1.2 - Berry e a representação das texturas ....................................................................... 17 1.3 - A função das taxonomias exaustivas ........................................................................ 22 Forte e a teoria dos conjuntos ......................................................................................... 22 Morris e os espaços de altura .......................................................................................... 26 2 - CONCEITOS .................................................................................................................... 31 2.1 - Concepção pragmática .............................................................................................. 31 2.2 - Topologia das configurações texturais ..................................................................... 33 Índices de aglomeração e dispersão ................................................................................ 33 Particiograma .................................................................................................................. 38 2.3 - Indexograma e condução dos índices no tempo ...................................................... 52 2.4 - Limites da teoria ........................................................................................................ 57 2.5 - PARSEMAT: uma ferramenta para a análise particional .................................... 62 Programação ................................................................................................................... 62 Estrutura .......................................................................................................................... 65 Utilização ......................................................................................................................... 76 3 - PARTICIONAMENTO RÍTMICO ................................................................................ 82 3.1 - Três análises de particionamento rítmico...............................................................
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