Open AccessAn Analysis of the 4th Movement of György Ligeti’s Musica Ricercata based on Information Theory and Number Partitioning
Author(s) -
Adolfo Maia,
Igor Leão Maia
Publication year - 2021
Publication title -
revista música
Language(s) - English
Resource type - Journals
eISSN - 2238-7625
pISSN - 0103-5525
DOI - 10.11606/rm.v21i1.188845
Subject(s) - rhythm , notation , information theory , mathematics , divergence (linguistics) , entropy (arrow of time) , integer (computer science) , combinatorics , computer science , statistics , arithmetic , linguistics , physics , philosophy , quantum mechanics , acoustics , programming language
In this paper we present a mathematically oriented analysis of the 4th Movement of György Ligeti’s Musica Ricercata (MR). The pitch analysis is based on Theory of Information and rhythm is analyzed through the Theory of Partitions of integer numbers. After a brief historical review of Musica Ricercata and its structure we make an analysis of the pitch distribution along the whole MR4 score, as well the Left and Right hand separately, through Theory of Information. We calculate two Information measures, namely, the Shannon’s Entropy and the Kullback-Leibler Divergence for the three cases. In the second part, about rhythm, we introduce a simple notation for coding rhythm patterns in terms of partitions of an integer number. We show that, with few exceptions, Ligeti used the partitions of number 6 to get rhythm variations on the Right hand against the ostinato on the Left one. In addition, we show the usefulness of the so called Hasse Diagram as a pre-compositional device to generate rhythm patterns.