Nariá Ribeiro

FCSH, NOVA University of Lisbon, Portugal;


The idea of writing musical rhythms that no longer follow the stratification of beat and meter finds resonance in post-tonal music. However, although composers pointed out the necessity to overcome traditional notions of rhythm and this trace can in fact be observed in the 20th and 21st century repertoire, the field of music theory has not yet devoted itself extensively on this topic. In this presentation, we investigate the construction of non beat-based rhythms (NBR) in Xenakis’ string quartet Tetras. By NBR we mean the absence of underlying sensation of pulse, normally perceived if rhythms elicit a regular accentuation. Beat therefore is defined not merely as a notational tool but as a perceptual phenomenon.

Although Xenakis did not talk directly about NBR in his writings, he wanted to do away with all of the inherited rules of composition in order to create new ones. In a way similar to Varèse’s liberation of sound (1966), Xenakis wrote about the investigation of more deeply seated properties of space, freed from the tutelage of time. Metrical organization may be a way to constraint space exploration, as the spatialization of music required new forms to organize durations without beat. There are some elements of Xenakis’ construction of rhythms in Tetras that dialogue with NBR: a) glissandi and tremolo exploration; b) irregular distribution of durations with geometric notation; c) fast passages in equal durations with irregular melodic contour; d) polyrhythms and e) non-aligned polyphony. As observed by Barthel-Calvet, there is a dialectics between regularity and irregularity reflected by the various types of formalizations: stochastic, sieve and permutations. Harley discusses sonic and parametrical entities such as glissandi, which he thinks contributes to “hinder rhythmic perception”, although he adds: “a more generalized conception of rhythmic structures needs to be formulated in order to account for the range of materials used by Xenakis”. Besides, there are the Brownian movements, a transposition of a natural phenomenon into a compositional tool that appears in many works, including Tetras. Therefore, we identify which passages include NBR and why; describe what are the compositional tools used to achieve these rhythms; and differentiate them in terms of how they are perceived in order to establish a preliminary typology. To judge beat perception, we will work with the piece’s both score and audio, creating graphic representations that reflect hearing when necessary. The analysis considers every beat level in the metrical grid, as this score is written mostly in traditional notation, with the support of some perceptual preferences and thresholds described in the literature: preferred tempo, tempo limits and just-noticeable difference. We will also use a broad concept of accentuation, as multiple factors in music can be responsible to create regularities or disturb them. In some cases, the notion of tempo will have to be replaced by density, when there is no perceptual measure unit to serve as reference.

Keywords: Non beat-based rhythms; Xenakis; modern music.


Nariá Ribeiro is a Brazilian pianist, music educator and composer. She holds a master’s degree in music from Federal University of Rio de Janeiro (BR). She is currently a doctoral student in musicology at Nova University in Lisbon (PT). In 2022 the Foundation for Science and Technology (PT) granted her with a doctoral scholarship. She published the articles: “O conceito de métrica incomum com pulso obscuro de Allen Winold” in the Anais do 15º Colóquio de Pesquisa do PPGM-UFRJ and “Phonograph effects, modernism and sound art: a reading (listening) of O som é um texto desmutado – b-Aluria (Gabriela Nobre)” in the Musimid journal. Her main research interests are 20th and 21st centuries’ music, non beat-based rhythm and piano pedagogy. She recorded several works by Brazilian composers such as Tatiana Lima Castro, Philippe Meyohas, Matheus Souza, Caeso e Gabriel Katona. In 2022, she released her first digital album, MUDA, by Brazilian experimental label Música Insólita.