Symmetrical and geometrical cycles in twelve-tone composition: developments toward a new model

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 (from now on TTT). 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. The authors propose a model for 12-tone composition that assumes an interactive approach between the horizontal and the vertical statements toward a new pre-compositional system based on geometrical and symmetrical issues. This model is being implemented in PWGL for Computer Aided Composition (CAC) in order to assist the extrapolation of the Motivic/Harmonic fundamental requirements of the model. Finally, the empiric outcome produced in the form of musical composition was analyzed, although not presented in its entirety in the scope of this paper.info:eu-repo/semantics/publishedVersio

Geometria serial : um modelo compositivo para composição algorítmica assistida por computador

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

A culture of dissonance : Wassily Kandinsky, atonality, and abstraction

textA Culture of Dissonance: Wassily Kandinsky, Atonality, and Abstraction by Lynn Edward Boland, Ph.D. Supervisor: Linda D. Henderson Wassily Kandinsky's interest in music as a source for abstraction in painting has often been noted in the scholarship on his art. However, no studies have sufficiently explained how the artist employed musical strategies, especially as he was developing his abstract style in the first decade of the twentieth century. Kandinsky's looked primarily to Arnold Schoenberg's new musical idioms and theories, and he was deeply inspired by highly dissonant music, but his ideas were set within a much broader context that further suggested and encouraged the expressive and transformative power of dissonance. By the late nineteenth century, extended passages of dissonance were common in musical compositions. At the same time, the concept of dissonance as a positive force was suggested in a wide range of late nineteenth-century literature, including the writings of Friedrich [should be this spelling throughout] Nietzsche, occult authors, popular texts on physics and experimental psychology, as well as within music and art theory. Close readings of Kandinsky's theoretical texts and selected works of art provide insights into how he might have understood and employed these concepts in his formation of an abstract style. Kandinsky's paintings Impression III (Concert) of 1911 and Composition VII of 1913 are the primary artistic foci of this study, along with his book Concerning the Spiritual in Art and the anthology Der Blaue Reiter, which he co-edited. This dissertation will seek to restore the concept of musical dissonance and its application in the visual arts to its historical context for Kandinsky. This will facilitate more informed formal analyses of Schoenberg's music and Kandinsky's paintings, which, in turn, suggest strategies of atonal musical composition applied to abstract painting. Additionally, this dissertation will establish an artistic context of visual dissonance that goes beyond Kandinsky, including artistic movements in France and Russia, allowing additional comparisons and a consideration of the larger impact of these ideas.Art Histor