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The Mathematics of Music: Analysis of Music using Numerical Methods and Fourier Tranforms
KTH, School of Engineering Sciences (SCI).
KTH, School of Engineering Sciences (SCI).
2018 (English)Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesisAlternative title
Musikens matematik : Analys av musik med hjälp av numeriska metoder och fouriertransformer (Swedish)
Abstract [sv]

Det här arbetet har varit utformat som ett projekt där vi har studerat matematiken och fysikenbakom musik. Vi har också arbetat med programmering i MATLAB för att med hjälp avnumeriska metoder analysera ljud och enklare sekvenser av musik. Arbetet har därmedresulterat i både denna rapport samt den MATLAB-kod vi har skrivit för att kunna utföra våraanalyser.Rapporten börjar med att ge en teoretisk bakgrund till den matematik och den teori somprojektet grundar sig på. Detta inkluderar en genomgång av fouriertransformen, den diskretafouriertransformen (DFT), den snabba fouriertransformen (FFT) samt en del musikteori.Den beskriver vidare vår arbetsgång där vi från enkla till mer avancerade analyser ochmodeller lyckats analysera melodier spelade på ett piano. Rapporten avslutas sedan med endiskussion av hur man kan utveckla modellerna vidare för analys av mer komplexamusikstycken.

Abstract [en]

In this project we have studied the mathematics and physics of music. We have also usednumerical methods and programming in MATLAB to analyse sounds and simpler sequencesof music. The project has therefore resulted in both this report as well as the MATLAB codewe have written to perform our analyses.The report begins by giving a theoretical background to the mathematics and the theory thatthe project is based on. This includes a review of the Fourier Transform, the Discrete FourierTransform (DFT), the Fast Fourier Transform (FFT) and some musical theory. Furthermore itdescribes the process where we from simple to more advanced analyses and models havesucceeded in analysing melodies played on piano. The report is then concluded with adiscussion of possible ways to develop our models further to enable analyses of morecomplex pieces of music

Place, publisher, year, edition, pages
2018. , p. 25
Series
TRITA-SCI-GRU ; 2018-116
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:kth:diva-231733OAI: oai:DiVA.org:kth-231733DiVA, id: diva2:1229776
Supervisors
Examiners
Available from: 2018-07-02 Created: 2018-07-02 Last updated: 2018-07-02Bibliographically approved

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CiteExportLink to record
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Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf