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Symmetry: Culture and Science
Volume 32, Number 2, pages 265-268 (2021)
 https://doi.org/10.26830/symmetry_2021_2_265

SYMMETRY OF RESONANCE IN ALMEIDA PRADO’S CARTAS CELESTES I

Manuel Gaulhiac*

* IReMus (Institut de Recherche en Musicologie), Institut Jean le Rond d’Alembert - équipe LAM (Lutheries - Acoustique - Musique), Sorbonne Université, Paris, France
E-mail: gamaievsky@gmail.com

Abstract: In this article we highlight through an original acoustic approach the symmetrical role of the upper and lower harmonic series in the “transtonal” system of the Brazilian composer Almeida Prado. We focus on the chords catalog unifying the cycle of the first six Cartas Celestes for piano. The composer states that he chose these chords for their resonant properties, appealing to intuition, and not through a scientific or systematic approach. According to him, the upper and lower harmonic series play a major role as they form the basis of his “writing of resonance,” in equal parts. We confront his words with acoustic reality by analyzing chords catalog recordings using two audio descriptors – upper harmonicity and lower harmonicity – which measure their resemblance to the upper and lower harmonic spectra. We thus map the catalog in the space of descriptors, which reveals an absolutely non-trivial symmetry. This symmetry confirms the equivalent role of the upper and lower harmonic series in the constitution of the chord catalog, and therefore in the inspiration of Almeida Prado.

Keywords: harmony, resonance, transtonal writing, upper and lower harmonic series.

References:
Parncutt, R. (1998) Harmony: A Psychoacoustical Approach. Berlin: Springer Science & Business Media, 212 pp. https://doi.org/10.1007/978-3-642-74831-8

Prado, A. (1985) Cartas celestes: uma uranografia sonora geradora de novos processos composicionais (Tese doutorado). Campinas: Instituto de Artes, Universidade Estadual de Campinas, 586 pp. http://repositorio.unicamp.br/handle/REPOSIP/284332

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