Please use this identifier to cite or link to this item: http://hdl.handle.net/2445/110488
Title: Una formulació matemàtica de les modulacions musicals
Author: Villalón Forns, Helena
Director: Bayer i Isant, Pilar, 1946-
Keywords: Transformacions de Fourier
Tesis
Tor (Geometria)
Ones sonores
Modulació (Música)
Torus (Geometry)
Theses
Fourier transformations
Sound-waves
Modulation (Music)
Issue Date: 8-Jul-2016
Abstract: It has always been mentioned that Mathematics and Music are deeply connected, but sometimes it can be difficult to precise the how and the why. As we all know, music transmission’s way is the sound, which can be represented by means of Fourier analysis as a sum of sinusoidal waves multiplied by amplitude factors. These factors are given by Fourier coefficients and, musically, they provide the harmonics of a fundamental sound and determine the timbre of a musical instrument. The purpose of this project is to use Fourier analysis in an alternative way in order to obtain a representation in coordinates of triad chords, by means of the Fourier transform of their characteristic functions. Since we identify a triad chord with a tonality, this work has allowed us to shape and visualize musical modulations in a different way from that of the traditional tonal harmony.
Note: Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2016, Director: Pilar Bayer i Isant
URI: http://hdl.handle.net/2445/110488
Appears in Collections:Treballs Finals de Grau (TFG) - Matemàtiques

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