Esta dissertação pretende verificar a utilização das relações musicais simétricas nos Estudos no 1, no 10, no 11, e no 12 de Heitor Villa-Lobos que se apresentam em diversas camadas de sua composição, como na elaboração melódica, na estruturação harmônica, na execução técnica e na disposição formal. Partindo da noção matemática e geométrica de simetria descrevemos como suas operações podem ser observadas em várias estruturas musicais para determinar uma gama de ferramentas que, somadas às técnicas das recentes teorias de análise musical, foram utilizadas para analisar os quatro Estudos. Desta maneira, pudemos determinar quais os tipos de relações de simetria são mais relevantes em cada um dos Estudos e quais são comuns a mais de um ou a todos eles. Concluímos com base em inúmeros resultados coletados destas análises que as relações de simetria e suas diversas operações desempenham um papel fundamental na composição destes quatro Estudos / This dissertation intends to investigate the use of musical symmetric relations at Heitor Villa- Lobos Etude no. 1, no. 10, no. 11, and no. 12 featured in several layers of its composition such as the melodic elaboration, the harmonic structure, the technical approach and the formal disposition of the sessions. From the mathematical and geometrical notion, we could show how the symmetry operations can be observed in several musical structures and so determine a range of tools that, together with the techniques of the recent theories of music analysis, were used to analyze these four Etudes. Thus, we could determine which types of symmetry relations are more relevant in each Etude and which is common to more than one or all of them. We conclude on the basis of numerous results collected from these analyses that the relations of symmetry and its various operations play an important role in the composition of these four Etudes

Esta dissertação pretende verificar a utilização das relações musicais simétricas nos Estudos no 1, no 10, no 11, e no 12 de Heitor Villa-Lobos que se apresentam em diversas camadas de sua composição, como na elaboração melódica, na estruturação harmônica, na execução técnica e na disposição formal. Partindo da noção matemática e geométrica de simetria descrevemos como suas operações podem ser observadas em várias estruturas musicais para determinar uma gama de ferramentas que, somadas às técnicas das recentes teorias de análise musical, foram utilizadas para analisar os quatro Estudos. Desta maneira, pudemos determinar quais os tipos de relações de simetria são mais relevantes em cada um dos Estudos e quais são comuns a mais de um ou a todos eles. Concluímos com base em inúmeros resultados coletados destas análises que as relações de simetria e suas diversas operações desempenham um papel fundamental na composição destes quatro Estudos / This dissertation intends to investigate the use of musical symmetric relations at Heitor Villa- Lobos Etude no. 1, no. 10, no. 11, and no. 12 featured in several layers of its composition such as the melodic elaboration, the harmonic structure, the technical approach and the formal disposition of the sessions. From the mathematical and geometrical notion, we could show how the symmetry operations can be observed in several musical structures and so determine a range of tools that, together with the techniques of the recent theories of music analysis, were used to analyze these four Etudes. Thus, we could determine which types of symmetry relations are more relevant in each Etude and which is common to more than one or all of them. We conclude on the basis of numerous results collected from these analyses that the relations of symmetry and its various operations play an important role in the composition of these four Etudes

The 10 Etudes for Guitar by Giulio Regondi represent the pinnacle of technical achievement for nineteenth century guitar performance. Dense textures, large stretches, fast scales and arpeggios, and obscure modulations are used in combinations that were unrivalled among his contemporaries. The etudes were not published until the late twentieth century and have not had generations of guitarists solving their challenges and teaching them to younger generations of students. Right-hand fingerings are virtually non-existent in published versions, but a thorough study of period sources yields several strategies; examples from each etude are provided. Modern right-hand scale philosophy, such as playing scales with "a," "m," and "i" in the right-hand are addressed and further example provided to give players several solutions to choose from. Right-hand fingering implies articulation and several interpretations are analyzed for each etude where they exist. Left-hand fingerings are sporadically present in modern editions but are often lacking in the most difficult passages. Stretching techniques from other string instruments can be applied to the guitar and one technique in particular can be applied to the most difficult stretches in Regondi in numerous instances. For some of the most challenging textures several solutions are given. The etudes of Regondi can prepare the guitarist for challenges found in playing music that is not written for the guitar or even by guitarists which consists of a substantial portion of the modern concert guitarist's repertoire. His music pushes what is possible on the guitar and borderlines what many would call idiomatic. This paper establishes a small number of techniques that will allow players to solve any challenge presented in the etudes from multiple technical viewpoints.