Matematika v glasbi

Povzetek

Ključne besede

Podatki

Jezik:	Slovenski jezik
Leto izida:	2017
Tipologija:	2.09 - Magistrsko delo
Organizacija:	UL FMF - Fakulteta za matematiko in fiziko
Založnik:	[M. Drnovšek]
UDK:	519.6
COBISS:	18212697
Št. ogledov:	3
Št. prenosov:	4
Ocena:	0 (0 glasov)
Metapodatki:

Ostali podatki

Sekundarni jezik:	Angleški jezik
Sekundarni naslov:	Mathematics in music
Sekundarni povzetek:	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.
Sekundarne ključne besede:	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;
Vrsta dela (COBISS):	Magistrsko delo/naloga
Študijski program:	0
Konec prepovedi (OpenAIRE):	1970-01-01
Komentar na gradivo:	Univ. v Ljubljani, Fak. za matematiko in fiziko, Oddelek za matematiko, Pedagoška matematika
Strani:	VI, 51 f.
ID:	10915180