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Authors
Advisor(s)
Abstract(s)
Este trabalho desenvolve um novo modelo teórico com implementação na
prática pré-compositivo, estando na sua base relacionado com dois sistemas que
revelam duas perspectivas bem diferenciadas: o Serialismo de Schoenberg e a
Twelve-Tone Tonality de George Perle. Embora ambos de alicerce serialista,
Schoenberg via a sua série dodecafónica a funcionar como motivo, e é esta
polarização linear (horizontal) que deve trazer toda a unidade da obra; por outro
lado, a Twelve-Tone Tonality de Perle resulta em progressões de simultaneidade
harmónica (vertical) com base na interpolação e concatenação de séries cíclicas
simétricas.
Perle, compositor e teórico norte-americano, conhece o serialismo de
Schoenberg nos anos 30. Entusiasmado com o sistema procura extrair
simultaneidades duma matriz dodecafónica, mas logo percebe que essas
simultaneidades resultam de modo fortuito, ao acaso e com pouca ou nenhuma
relação1. A exceção estava nas séries com base em ciclos simétricos. Ernst Krenek,
confrontado com a primeira tentativa serialista de Perle num esboço para quarteto de
cordas, disse-lhe que tinha interpretado de um modo errado o sistema dodecafónico,
mas ao mesmo tempo tinha feito aquilo que apelidou de ‘uma descoberta’. As séries
baseadas na conjunção de intervalos cíclicos e inversões simétricas são as únicas que
possibilitam extrair simultaneidades de uma matriz dodecafónica de forma
consistente e previsível. A constatação da existência destes ciclos simétricos tinha já
começado com o estudo levado por Perle sobre a música de Alban Berg, visível em
vários livros e artigos. Perle vê-se assim conduzido a uma teoria que enfrenta
exatamente a problemática da simultaneidade, a que viria a chamar de início Twelve-Tone Modality, mais tarde com a colaboração de Paul Lansky com a designação de
Twelve-Tone Tonality.
Este estudo revela um serialismo de Schoenberg essencialmente estruturado
na perspectiva linear, enquanto os ciclos simétricos de Perle são essencialmente
estruturados em progressões verticais. Surge aqui a necessidade de desenvolver um
novo modelo compositivo decidido a beneficiar duma articulação específica entre os
sistemas de Schoenberg e de Perle, extrapolando e definindo as suas mais valias
idiossincráticas. Este modelo teórico de nome Geometria Serial, apoia-se na
direccionalidade motívica de Schoenberg e na sistematização estrutural harmónica de
Perle, mas pretende-se mais aglutinador na dicotomia melodia/harmonia, assumindo
uma abordagem interativa entre os planos horizontal e vertical, e cimentando as suas
premissas nos princípios de simetria e de geometria, centros de apoio poderosos,
como se verá ao longo do presente estudo.
Como a base deste modelo é a interação entre uma dada série e o
constrangimento das possíveis soluções harmónicas à luz do sistema, recorreu-se à
informática musical de forma a acelerar o processo de cálculo. O desenvolvimento da
sua implementação e a sua associação à Composição Algorítmica Assistida por
Computador (CAAC) é determinante na escolha da aplicação PWGL para essa mesma
implementação.
Perto do final, a composição de um número substancial de obras musicais
resultam exatamente do processo de identificação de anteriores modelos e de
transformação com o novo modelo desenvolvido. Afigura-se a sua análise e discussão
de resultados. As conclusões finais dão por terminado o processo metodológico,
abrindo no entanto portas a novas questões e perspectivas para futuros trabalhos
relacionados com as matérias abordadas e com o atual desenvolvimento desta teoria.
The development of a pre-compositional model is proposed in this study based on two systems with two design perspectives: Schoenberg’s Serialism and Perle’s Twelve-Tone Tonality. Schoenberg’s perspective reveals a linear design where the set has functions like those of a motive; on the other hand, Perle’s design result in harmonic simultaneities based on symmetric cycles. Perle met the serialism of Schoenberg in the 30s. Excited with the system, he tries to draw simultaneities of a twelve-tone matrix, but soon he realizes that these actions result fortuitously at random and with little or no relation at all. The exception was with sets based on symmetric cycles. Ernst Krenek, confronted with Perle’s first serialistic attempt – a sketch for a string quartet – told him he had misinterpreted the twelve-tone system, but at the same time he had made what he called ‘a discovery’. This misinterpretation is the symmetrical cycle. A set based on symmetric cycles offers consistent and predictable simultaneities to be extracted from a twelve-tone matrix2. The finding of the existence of symmetric cycles had already begun with the studies on Alban Berg's music, evident in several Perle’s books and articles. This study reveals that Schoenberg’s serialism is more structured in the linear perspective, while Perle’s symmetrical cycles are more structured in vertical progressions. It opens the possibility of developing a new compositional model determined by a specific relationship between Schoenberg’s motive and Perle’s harmonic structure. This theoretical model named Serial Geometry, is sustained by a motivic directionality, and by a harmonic structure based on symmetrical geometrical objects, becoming more cohesive in the horizontal/vertical (melody/harmony), dichotomies. As the basis of this model is the interaction between a given set and several possible harmonic solutions, using computer applications becomes inevitable. Once immersed in the universe of Computer-Aided Algorithmic Composition (CAAC), the selection of the PWGL application for that development and implementation was decisive. In the end, the composition of a substantial number of musical works identifies previous models and the new one with analysis and discussion of results. The final conclusions accomplish the methodological process, opening however new questions and perspectives for future work related to the topic covered, and the current development of this theory.
The development of a pre-compositional model is proposed in this study based on two systems with two design perspectives: Schoenberg’s Serialism and Perle’s Twelve-Tone Tonality. Schoenberg’s perspective reveals a linear design where the set has functions like those of a motive; on the other hand, Perle’s design result in harmonic simultaneities based on symmetric cycles. Perle met the serialism of Schoenberg in the 30s. Excited with the system, he tries to draw simultaneities of a twelve-tone matrix, but soon he realizes that these actions result fortuitously at random and with little or no relation at all. The exception was with sets based on symmetric cycles. Ernst Krenek, confronted with Perle’s first serialistic attempt – a sketch for a string quartet – told him he had misinterpreted the twelve-tone system, but at the same time he had made what he called ‘a discovery’. This misinterpretation is the symmetrical cycle. A set based on symmetric cycles offers consistent and predictable simultaneities to be extracted from a twelve-tone matrix2. The finding of the existence of symmetric cycles had already begun with the studies on Alban Berg's music, evident in several Perle’s books and articles. This study reveals that Schoenberg’s serialism is more structured in the linear perspective, while Perle’s symmetrical cycles are more structured in vertical progressions. It opens the possibility of developing a new compositional model determined by a specific relationship between Schoenberg’s motive and Perle’s harmonic structure. This theoretical model named Serial Geometry, is sustained by a motivic directionality, and by a harmonic structure based on symmetrical geometrical objects, becoming more cohesive in the horizontal/vertical (melody/harmony), dichotomies. As the basis of this model is the interaction between a given set and several possible harmonic solutions, using computer applications becomes inevitable. Once immersed in the universe of Computer-Aided Algorithmic Composition (CAAC), the selection of the PWGL application for that development and implementation was decisive. In the end, the composition of a substantial number of musical works identifies previous models and the new one with analysis and discussion of results. The final conclusions accomplish the methodological process, opening however new questions and perspectives for future work related to the topic covered, and the current development of this theory.