An Analysis of the 4th Movement of György Ligeti’s Musica Ricercata based on Information Theory and Number Partitioning

Autores/as

  • Adolfo Maia Jr. Universidade Estadual de Campinas. Núcleo Interdisciplinar de Comunicação Sonora
  • Igor Leão Maia Universidade Federal de Minas Gerais. Escola de Música

DOI:

https://doi.org/10.11606/rm.v21i1.188845

Palabras clave:

György Ligeti, Musica ricercata, Information theory, Music analysis, Number partitioning

Resumen

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.

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Biografía del autor/a

  • Adolfo Maia Jr., Universidade Estadual de Campinas. Núcleo Interdisciplinar de Comunicação Sonora

    Adolfo Maia Jr. is a retired professor from the University of Campinas (UNICAMP). He holds a Dr. Sc. in Theoretical Physics. He was invited researcher at the University of Oxford (Theoretical Physics), Brown University (Astrophysics and Cosmology) and University of Plymouth (Computer Music). He is currently invited researcher at the Interdisciplinary Nucleus for Sound Communications (NICS/UNICAMP).

  • Igor Leão Maia, Universidade Federal de Minas Gerais. Escola de Música

    Igor L. Maia is a composer and conductor, Assistant Professor at the Federal University of Minas Gerais (UFMG), Brazil. He holds a PhD in Musical Composition from King's College London, a Master's from the University of Campinas and a Bachelor's in Music Composition from the Royal Conservatory of The Hague. He participated in several festivals and concerts in Europe, Argentina, Brazil, United States and Japan, and was also awarded important national and international awards. As a conductor, he performed in Germany, Brazil, Spain, Holland and the United Kingdom. His music is published by Babel Scores (France) and Donemus (Netherlands).

Referencias

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Publicado

2021-07-27

Cómo citar

An Analysis of the 4th Movement of György Ligeti’s Musica Ricercata based on Information Theory and Number Partitioning. (2021). Revista Música, 21(1), 343-368. https://doi.org/10.11606/rm.v21i1.188845