Texte remanié de: Tesi dott.--Istituto di filologia moderna--Università degli studi di Milano. / Bibliogr. p. 241-262. Glossaire. Index. Avant-titre : "Un puoco grossetto di loquela"

Dissertation--Munich, 1997. / Bibliogr. p. 579-596.

<p>This dissertation consists of two parts: a chamber opera and an article on the work of Claude Vivier.</p><p>"Cardano" is a new chamber opera by composer Bryan Christian about the work and tragic life of the Renaissance polymath Gerolamo Cardano (1501-1576). Scored for three vocal soloists, an actor, and an eleven-part ensemble, "Cardano" represents a coalescence of Christian's interests in medieval and Renaissance sources, mathematics, and intensely dramatic vocal music. Christian constructed the libretto from fragmented excerpts of primary sources written by Cardano and his rival Niccolo Tartaglia. The opera reinvigorates Cardano's 16th-century scientific and philosophical models by sonifying and mapping these models to salient musical and dramatic features. These models prominently include Cardano's solution to the cubic equation and his horoscope of Jesus Christ, which was deemed so scandalous in the 16th century that it ultimately led to Cardano's imprisonment under the Roman Inquisition in 1570 - the opera's tragic conclusion. Presenting these ideas in opera allows them to resound beyond the music itself and project through the characters and drama on stage. In this way, the historical documents and theories - revealing Cardano's unique understanding of the world and his contributions to society - are given new life as they tell his tragic story.</p><p>Claude Vivier's homophonic treatment of combination tones--what he called les couleurs--demands an extension of traditional methods of harmonic and spectral analysis. Incomplete explanations of this technique throughout the secondary literature further demand a revised and cohesive definition. To analyze all variations of les couleurs, I developed the analytical concept of combination-tone classes (CTCs) and built upon Angela Lohri's (2010) combination tone matrix to create a dynamic CTC matrix, from which CTC sets may be extracted. Intensive CTC set analysis reveals a definitive correlation between CTC set and formal sections in Vivier's composition "Bouchara." Although formally adjacent CTC sets are often markedly varied, all sets share a subset of lower-order CTCs, aiding in perception of spectral cohesion across formal boundaries. This analysis illuminates the interrelationships of CTC sets to their parent dyads, their orchestration, their playing technique, and form in "Bouchara." CTC set analysis is compared with Vivier's sketches for "Bouchara," which suggest that les couleurs were intended as integral components of the work's musical structure.</p> / Dissertation

[pt] Resposta a uma preocupação importante na resolução de equações, a impossibilidade de determinar, no conjunto dos números reais, as raízes quadradas de números negativos, o conjunto dos números complexos é estudado em detalhes. O rigor nas demonstrações dos teoremas e propriedades é prioritário para um bom entendimento do assunto. A história dos números complexos permite ao leitor visualizar como e porque surgiram estes números. Seu aparecimento não foi por acaso, e sim, pela necessidade de resolução de equações cúbicas. / [en] Response to a major concern in solving equations, the impossibility of determining, in the set of real numbers, the square roots of negative numbers, the set of complex numbers is studied in details. The rigour in statements of theorems and properties is a priority for a good understanding of the subject. The history of complex numbers allow the reader to see how and why these figures emerged. His appearance was no accident, and yes, by the necessity of solving cubic equations.

Made available in DSpace on 2016-04-28T14:16:21Z (GMT). No. of bitstreams: 1 Alessandro Menegat.pdf: 795829 bytes, checksum: 94bc3d43f28b9c27945251528cbeb43c (MD5) Previous issue date: 2015-03-17 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / This work aims to address some aspects of Niccolò Tartaglia's (1500-1556) different arguments on the trajectories of projectiles. On one hand, at Nova Scientia (1537), the author explained that the trajectories were composed by two straight lines and a circular arc; on the other, at Quesiti et Inventioni Diverse (1546), the same trajectories were presented only as curves. These two different approaches to the trajectory of projectiles suggested to some historians that Tartaglia had changed his mind, leaving, in a way, his old beliefs. Thus, based on original documents, this paper seeks to resume Tartaglia arguments in order to understand the reasons which would have led him to change his approaches in those two works. Despite other factors, we present evidence that Tartaglia had, around 1540, come in contact with works that had almost none circulation before. With this in mind, our work provides evidence that there is some continuity between the arguments of Tartaglia on the trajectories in these two works / Este trabalho tem por objetivo tratar alguns aspectos das diferentes argumentações de Niccolò Tartaglia (1500-1556) sobre as trajetórias dos projéteis. Na Nova Scientia (1537), as trajetórias seriam compostas por duas retas e um arco de circunferência. Já nos Quesiti et Inventioni Diverse (1546), elas são apresentadas completamente curvas. Esses dois enfoques diferentes dados ao tema sugeriram a alguns historiadores que Tartaglia teria mudado de ideia, abandonando, de certa maneira, suas antigas convicções. Desse modo, baseado em documentos originais, este trabalho busca retomar os argumentos de Tartaglia de modo a compreendermos as razões que o teriam levado a dar dois diferentes enfoques nas duas obras. Dentre outros fatores, apresentamos indícios de que Tartaglia passou a contar, por volta de 1540, com obras anteriormente desconhecidas e que pouco circulavam até então. Tendo isso em vista, nosso trabalho fornece indícios de que podemos observar certa continuidade entre as argumentações de Tartaglia sobre as trajetórias nessas duas obras