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2 TCC FLÁVIA E LUAN.Pdf UNIVERSIDADE FEDERAL FLUMINENSE INSTITUTO DE COMPUTAC¸ AO~ DEPARTAMENTO DE CIENCIA^ DA COMPUTAC¸ AO~ FLAVIA´ ELIAS ROCHA LUAN SIMOES~ CARDOSO EDOπ : Uma biblioteca em Python para m´usicamicrotonal Niter´oi 2021 UNIVERSIDADE FEDERAL FLUMINENSE INSTITUTO DE COMPUTAC¸ AO~ DEPARTAMENTO DE CIENCIA^ DA COMPUTAC¸ AO~ FLAVIA´ ELIAS ROCHA LUAN SIMOES~ CARDOSO EDOπ : Uma biblioteca em Python para m´usicamicrotonal Trabalho de Conclus~aode Curso apresentado `aUniversidade Federal Fluminense como re- quisito parcial para a obten¸c~aodo Grau de Bacharel em Ci^enciada Computa¸c~ao. Orientador: JORGE PETRUCIO VIANA Co-orientador: BRUNO LOPES VIEIRA Niter´oi 2021 i Ficha catalográfica automática - SDC/BEE Gerada com informações fornecidas pelo autor C268e Cardoso, Luan Simões EDOpi: Uma biblioteca em Python para música microtonal / Luan Simões Cardoso, Flávia Elias Rocha ; Jorge Petrucio Viana, orientador ; Bruno Lopes Vieira, coorientador. Niterói, 2021. 56 f. : il. Trabalho de Conclusão de Curso (Graduação em Ciência da Computação)-Universidade Federal Fluminense, Instituto de Computação, Niterói, 2021. 1. Sistemas Microtonais. 2. Teoria dos Grupos. 3. Computação Musical. 4. Biblioteca Python. 5. Produção intelectual. I. Rocha, Flávia Elias. II. Viana, Jorge Petrucio, orientador. III. Vieira, Bruno Lopes, coorientador. IV. Universidade Federal Fluminense. Instituto de Computação. V. Título. CDD - Bibliotecário responsável: Debora do Nascimento - CRB7/6368 Fl´avia Elias Rocha Luan Sim˜oes Cardoso EDO⇡ : Uma biblioteca em Python para m´usica microtonal Trabalho de Conclus˜ao de Curso apresentado `aUniversidade Federal Fluminense como re- quisito parcial para a obten¸c˜aodo Grau de Bacharel em Ciˆencia da Computa¸c˜ao. Aprovada em10/05/2021 XX/XX/2021. BANCA EXAMINADORA Prof. Dr. Jorge Petrucio Viana - Orientador, IME-UFF (Presidente) Prof. Dr. Bruno Lopes Vieira - Co-orientador, IC-UFF Prof. Dr. Pauxy Gentil-Nunes, EM-UFRJ Profa. Dra. Isabel Leite Cafezeiro, IC-UFF Agradecimentos (Fl´avia) Aos meus pais, que fazem de tudo pela minha felicidade. Aos meus irm~aose cunhadas, que s~aomeus melhores amigos e foram minhas compa- nhias nos momentos mais descontra´ıdosdo meu ´ultimoano. Ao meu sobrinho Miguel, por ter um olhar cheio de ternura e ao gatinho Frajola, por ser t~aocompanheiro. Aos amigos Gabriela, Z´e,Paulo Augusto, Fabr´ıcio, Alexandre, Andr´ee Julia, que desfrutaram do doce e do amargo da faculdade comigo. Aos amigos Paulinho, Rapha e Bruno. Nossos momentos foram um privil´egio. Ao professor Pauxy, por ter sido t~aoatencioso conosco. A` minha dupla, Luan, por ter mantido o brilho nos olhos durante todo o trabalho e ter sido t~aocompreensivo e generoso. Ao professor Petrucio, por ter orientado este trabalho e me feito entender o que ´euma universidade. Sua amizade vale muito mais do que mil r´eis. Agradecimentos (Luan) A` minha m~aeLuciene, por ter conseguido me educar com carinho e cuidado, mesmo nos momentos dif´ıceis, garantindo todas as condi¸c~oese oportunidades que me fizeram chegar at´eaqui. A Andr´e,meu pai, e ao meu irm~aoPedro, que sempre me apoiaram e motivaram, e compreenderam minha aus^encianestes ´ultimosmeses. A` Lara, por ser meu amor-poema, por me ensinar tanto e me inspirar e motivar com sua luta, sua resist^enciae seu cora¸c~ao. Ao meu afilhado Miguel, a quem espero poder ensinar, um dia, tudo que tive a oportunidade de aprender. A` Fl´aviae aos professores Petr´ucioe Pauxy, pelos tantos encontros, discuss~oes,re- flex˜oese ensinamentos no curso deste trabalho. A` Professora Karina Mochetti, por ter mudado minha vis~aoda Ci^enciada Com- puta¸c~aoe enxergado potencial em mim quando eu mais precisava. Ao meu amigo Matheus Marotti, que esteve ao meu lado nesta longa caminhada, desde os tempos de ensino m´edio. Aos meus amigos artistas Juan, Marina, Camila, Julieta, e a todos os membros do Coro C^enicoCanta Mais, por tanto contribu´ıremcom a minha concep¸c~aode arte. A` M´usica,por nunca ter desistido de mim, mesmo nas tantas vezes em que eu achei que devia desistir dela. A` crian¸caque me habita, por me lembrar, a todo momento, quem eu sou. Resumo Os sistemas microtonais t^emsido alvo de interesse de m´usicose pesquisadores nas ´ultimasd´ecadas. O desenvolvimento dessas pesquisas vem sendo beneficiado pelo avan¸co das ferramentas digitais no campo da Computa¸c~aoMusical. No presente trabalho, apre- sentamos o conceito de Sistema Microtonal, atrav´esde uma an´alisealg´ebricados compo- nentes b´asicosdas rela¸c~oesintervalares crom´aticas subjacentes `asescalas musicais. Base- ados nessa an´alise,desenvolvemos uma biblioteca na linguagem de programa¸c~ao Python para auxiliar pesquisadores, compositores e estudantes na investiga¸c~aoe aplica¸c~aopr´atica de sistemas microtonais. Nossa investiga¸c~ao´ebaseada nos trabalhos de Gerald Balzano, Paul Zweifel, Mark Gould e Kristie Kennedy. Palavras-chave: Sistemas Microtonais. Teoria dos Grupos. Diagrama de Balzano. Com- puta¸c~aoMusical. Biblioteca Python. Abstract Microtonal systems have been used and studied by musicians and researchers in recent decades. The development of digital tools in the field of Computer Music increased the interest in this academic and artistic domain. In the present work, we define the concept of Microtonal System, through an algebraic analysis of the basic components of the chromatic interval relations underlying the musical scales. Based on this analysis, we developed a library in the Python programming language to assist researchers, composers and students in the investigation and practical application of microtonal systems. Our research is based on the works of Gerald Balzano, Paul Zweifel, Mark Gould and Kristie Kennedy. Keywords: Microtonal Systems. Group Theory. Balzano Diagram. Computer Music. Python Library. Lista de Figuras 2.1 Teclas do piano na extens~aode uma oitava . 18 2.2 Ciclo Crom´atico. 18 2.3 Ciclo de Quintas com as cromas da Escala Diat^onicade D´oMaior em destaque 19 2.4 Ciclo de Quintas com as cromas da Escala Pentat^onicade D´oMaior em destaque. 20 2.5 Diagrama de Balzano do Z12 com a Escala Diat^onicaem destaque. 28 3.1 Diagrama de classes de EDOπ ......................... 38 4.1 Interface gerada pela Matplotlib para exibi¸c~aoda G-Escala de Z27, com G =5....................................... 48 4.2 Diagrama de Balzano referente `aescala mostrada na Figura 4.1. 49 Sum´ario 1 Introdu¸c~ao 11 1.1 Motiva¸c~ao . 11 1.2 M´usicaMicrotonal . 12 1.3 Objetivos e Organiza¸c~aodos Cap´ıtulos . 14 2 Fundamenta¸c~aoTe´orica 16 2.1 O Sistema 12-EDO ............................... 16 2.1.1 Semitom e a Escala Crom´atica. 16 2.1.2 Ciclo de Quintas e a Escala Diat^onica . 18 2.1.3 Intervalos de ter¸cae as tr´ıades. 21 2.2 Abordagem alg´ebrica . 21 2.2.1 O Conjunto Zn ............................. 22 2.2.2 Ciclo de Quintas Generalizado . 23 2.2.3 Escala Diat^onicaGeneralizada . 26 2.2.4 Diagrama de Balzano . 28 3 Biblioteca proposta 31 3.1 Caracter´ısticasda biblioteca . 31 3.1.1 Linguagem . 31 3.1.2 Depend^encias . 32 3.1.3 Testes . 33 3.1.4 Licen¸ca . 34 Sum´ario ix 3.2 Bibliotecas e softwares correlacionados . 34 3.2.1 Scala ................................... 35 3.2.2 music21 ................................. 35 3.2.3 SCAMP ................................. 36 3.2.4 edoJS .................................. 37 3.3 EDOπ ..................................... 37 3.3.1 TonalSystemElement . 39 3.3.1.1 Atributos . 39 3.3.1.2 M´etodos . 39 3.3.2 Scale . 40 3.3.2.1 Atributos . 41 3.3.2.2 M´etodos . 41 3.3.3 GCycle . 42 3.3.3.1 Atributos . 42 3.3.3.2 M´etodos . 42 3.3.4 BalzanoDiagram . 43 3.3.4.1 Atributos . 43 3.3.4.2 M´etodos . 44 3.3.5 TonalSystem . 44 3.3.5.1 Atributos . 44 3.3.5.2 M´etodos . 44 4 Cen´ariosde uso 46 4.1 Usu´ariosfinais . 46 4.2 Cen´ario1 . 47 4.3 Cen´ario2 . 49 4.4 Cen´ario3 . 50 Sum´ario x 5 Perspectivas 52 Refer^encias 54 Cap´ıtulo1 Introdu¸c~ao 1.1 Motiva¸c~ao N~ao´ede hoje que a Ci^enciada Computa¸c~ao,como ferramenta para desenvolver solu¸c~oes,tem sua aplica¸c~aonas mais diversas ´areasdo conhecimento. Assim, n~aosur- preende que, t~aologo os m´etodos e conceitos tecnol´ogicosse desenvolvam, j´ase busquem aplica¸c~oespr´aticasinterdisciplinares para estes. Com respeito `am´usica,n~ao´ediferente. A ´areada Ci^enciada Computa¸c~aoque busca solu¸c~oespara problemas musicais chama-se Computa¸c~aoMusical e seu surgimento remonta `asprimeiras t´ecnicasde convers~aodo som em sinal el´etrico,ainda no fim do s´eculoXIX [7]. A Sociedade Brasileira de Computa¸c~aopossui uma comiss~aoespecial para a ´areade Computa¸c~aoMusical, que organiza bienalmente o Simp´osioBrasileiro de Computa¸c~ao Musical (SBCM). O evento interdisciplinar re´unem´usicos,cientistas da computa¸c~aoe outros interessados e, nele, s~aoapresentados os desenvolvimentos recentes da ´area. J´a ocorreram 17 desses simp´osios. A Computa¸c~aoMusical, ao contr´ariodo que se pode pensar, n~aose limita a forne- cer ferramentas t´ecnicasauxiliares para as tarefas de an´alise, grava¸c~aoe distribui¸c~aode m´usicas.Este vasto campo adentra tamb´ema pr´opriaforma de se fazer m´usicaem v´arios g^eneros,viabilizando novas pr´aticas,tais como a M´usicaEletroac´ustica,a Composi¸c~ao Algor´ıtmicae a Composi¸c~aoAuxiliada por Computadores, que influenciaram a est´etica da m´usicade concerto e da m´usicacomercial a partir da segunda metade do s´eculoXX. Alguns dos m´etodos de composi¸c~aocom o uso de computadores s~aodescritos por Edu- ardo Reck Miranda em [22] e incluem a utiliza¸c~aode Algoritmos Gen´eticos,Gram´aticas Formais e Redes Neurais.
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