Thesis (Ph. D.)--State University of Iowa, 1963. / Includes bibliographical references (leaves 480-501).

Inaug.-Diss.--Halle. / Vita. Includes bibliographical references.

How have we come to hear melody as going “up” or “down”? Why does the Western world predominantly adopt spatial terms such as “high” and “low” to distinguish musical notes while other non-Western cultures use non-spatial terms such as “large” and “small” (Bali), or “clear” and “dull” (South Korea)? Have the changing concepts of motion and space in people’s everyday lives over history also changed our understanding of musical space? My dissertation investigates the Western concept of music space as it has been shaped by social change into the way we think about music today. In our understanding of music, the concept of the underlying space is so elemental that it is impossible for us to have any fruitful discourse about music without using inherently spatial terms. For example a term interval in music denotes the distance between two combined notes; but, in fact, two sonic objects are neither near nor far from each other. This shows that our experience of hearing interval as a combination of different notes is not inherent in the sound itself but constructed through cultural and social means. In Western culture, musical sound is often conceptualized through various metaphors whose source domains reflect the society that incubated these metaphorical understandings. My research investigates the historical formation of the conceptual metaphor of music. In particular, I focus on historical formation of the three underlying assumptions we bring to our hearing of music: (1) “high” and “low” notes and motion between them, (2) functionality of musical chords, and (3) reliance on music notation. In each chapter, I contextualize various music theoretical writings within the larger framework of philosophy and social theory to show that our current understanding of musical sound is embedded with the history of Western culture.

Made available in DSpace on 2017-07-21T20:56:28Z (GMT). No. of bitstreams: 1 Rodovlas Santos.pdf: 2016733 bytes, checksum: 6e68081442d6100ecc8c130cb6cb6a1a (MD5) Previous issue date: 2015-10-01 / Music is without any doubt one of the main ways to express culture, gender and personal tastes. Western music in general has the same musical basis which has its core in simple mathematical concepts. This study aims to bring mathematical concepts to high and elementary school students through the history of music. This essay proposes a literature review about the importance and the contributions of Pitagoras in the construction of Diatonic Scale and the influence that pitagorian studies exert in the Equal Tempered Scale, used nowadays. This paper is based in official documents such as PCN and PCNEM (National Curricular Parameters and National Curricular Parameters of High School) and curricular guidelines about the study of Mathematics allying mathematical subjects to daily life concepts, in this case, musical concepts. Activities that can be reproduced by Mathematics teachers even when the teacher does not have advanced musical knowledge are studied in this paper, for example, studying fractions aiming to build a monochord with the program Geogebra exploring sound concepts described by exponential and trigonometric functions. / A música é sem dúvida uma das principais formas de manifestação cultural, de gêneros e gostos diversos a música ocidental tem em geral uma mesma base musical e esta base tem seu cerne em conceitos matemáticos simples. Esse trabalho objetiva trazer esses conceitos matemáticos ao conhecimento de alunos do ensino médio e fundamental através da história da música. Propõe-se uma revisão bibliográfica da importância e das contribuições de Pitágoras na construção da escala Diatônica e da influência que os estudos pitagóricos exerceram na escala Temperada, que é atualmente utilizada. O estudo apresenta-se norteado por documentos oficiais como PCN e PCNEM (Parâmetros Curriculares Nacionais e Parâmetros Curricular Nacionais do Ensino Médio) e diretrizes curriculares a respeito do estudo da matemática, aliando conteúdos matemáticos a conceitos do cotidiano, nesse caso a conceitos musicais. Nesse trabalho, são tratadas atividades que podem ser reproduzidas por professores de matemática sem que o mesmo necessite de conhecimentos avançados sobre música, tais como o estudo de frações na construção de um monocórdio e com auxílio do programa Geogebra é explorado conceitos de sons descritos através de funções exponenciais e trigonométricas.

Erweiterte Fassung (2019) des gleichnamigen Beitrages aus Wahrnehmung – Erkenntnis – Vermittlung. Hildesheim, Zürich, New York: Olms Verlag, 2013 (Fs. Auhagen), 248-259