(Tartu Ülikool, 2013) Simson, Mai; Abel, Mati, juhendaja; Tartu Ülikool. Matemaatika-informaatikateaduskond; Tartu Ülikool. Matemaatika instituut
The aim of this bachelor’s thesis is to give an overview of some mathematical applications
which can be used in music. The thesis is mainly based on three books: “Simple
Gamma” by Georgi Evgenevitš Šilov, “Occidents’ History of Music” by Igor Garšnek
and “Music: A Mathematical Offering” by Dave Benson.
The thesis consists of four chapters. In the first chapter we give definitions to different
terms that are used in the thesis.
The second chapter briefly describes the common history in music and mathematics.
The aim of the third chapter is to explain the construction of the musical scale using
logarithms and chain fractures.
The final chapter focuses on different mathematical applications used in music. We
will discuss Iannis Xenakis’s theory about the algebraic qualities of the intervals, the
theory that Pierre Boulez used to compose his “Structures I”, Urmas Sisask using
mathematics and astronomy to compose his choir piece “Gloria Patri” and also some
mathematical methods that could be used to describe music.