Matematika v glasbi

magistrsko delo

Mateja Drnovšek (Author), Gregor Cigler (Mentor)

Abstract

Matematika v glasbi

Keywords

matematika v glasbi;Fibonaccijevo zaporedje;transpozicije in inverzije;linijski kontra ples;ljudski plesi;latinski kvadrati;različni partnerji - različna mesta;diedrska grupa;višinski razred;T/I grupa;delovanje grup;durovi in molovi trozvoki;PLR-transformacije;PLR-grupa;Neo-Riemannova teorija;tonska mreža;

Data

Language:	Slovenian
Year of publishing:	2017
Typology:	2.09 - Master's Thesis
Organization:	UL FMF - Faculty of Mathematics and Physics
Publisher:	[M. Drnovšek]
UDC:	519.6
COBISS:	18212697
Views:	3
Downloads:	4
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	English
Secondary title:	Mathematics in music
Secondary abstract:	In my master thesis I start with the history of mathematics in music. First, I introduce the harmonic relationships that were already known by the Ancient Greeks. Then, I describe Fibonacci numbers, Fibonacci sequence and the golden ratio and then I present the use of Fibonacci sequence with a piece of music. The golden ratio was also used in violin construction by Stradivarius. After that, I define transpositions and inversions and present their usage with the Bach's fugue. Then, I connect mathematics with dancing. First, I mention the contra dancing for which the best mathematical model is the dihedral group, and later, I continue with folk dances which can be mathematically described by using permutations, fixed points and compatible sequences. Next, I continue with the description of dihedral groups and pitch classes. Then, I define the group acting on sets and major and minor triads. After that, I continue with PLR-transformations and precisely define their effects and usage in graphs, torus and in Ludwig Van Beethoven's Ninth Simphony. Then I prove that the groups T/I and PLR are dual. Finally, I name some examples of usage of tone-network and PLR-transformations.
Secondary keywords:	mathematics in music;Fibonacci sequence;transposition and inversion;contra dancing;four couple folk dances;latin squares;different partners different places;dihedral group;pitch class;T/I - group;group acting;major and minor triads;PLR-transformations;PLR-group;Neo-Riemannian group;tone network;
Type (COBISS):	Master's thesis/paper
Study programme:	0
Embargo end date (OpenAIRE):	1970-01-01
Thesis comment:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Pages:	VI, 51 f.
ID:	10915180