Variações sobre o Tresillo: subdivisões aplicadas à bateria por meio de superimposição rítmica

Abstract

Inspired by the rhythmic modulations that occur in the music of Vijay Iyer and Tigran Hamasyam, a procedure was elaborated for the analysis and application of the modulation associated with the alteration of the subdivisions of the notes of a clave, mainly through rhythmic superimposition. This procedure is called Modulation through the Alteration of the Subdivisions of the Clave (MASC). The main objective of this research is to apply the MASC to the tresillo (a clave present in both African and American music) in the context of baião, in order to obtain and analyze alternative rhythmic variations to those traditionally known. The methodology is based on a bibliographic review on the subject, with an emphasis on approaching concepts that are little used in Western musical conception, such as those used in the analysis of African rhythms. Together with the deepening of studies on rhythmic superimposition, temporal modulation and analogue transformation, this set of concepts served as the basis for the elaboration of the MASC. From it, the songs “Mystic Brew”, “Pt1 Collapse” and “Pt2 Alternative Universe” were analyzed. Then, with the aim of applying the MASC to the tresillo in the context of baião, two recordings were made: “O Ovo”, by Hermeto Pascoal, and “Asa Branca”, by Luiz Gonzaga. The analysis of these songs showed that the application of the MASC, although based on the idea of tuplets in order to facilitate its execution, generates results that are closer to a polyrhythm. In theory, the subdivision of the clave notes into tuplets should present differences in the duration of the subdivisions (better discussed in chapter 4). On the other hand, the polyrhythm must generate differences in the synchronization with the clave notes. In order to find out if these differences are within the limit of human perception, that is, between 50 and 100 ms (London, 2004), a mathematical model is proposed. That shows the theoretical values of the time intervals in the modulations applied to the tresillo, both by tuplets and polyrhythms. Finally, the differences between the measured values in the execution of the modulations and those calculated with the theoretical models were compared. The results show that the differences in duration of the tuplet applied to the notes of the clave, measured at 180 bpm for the 2+2+1 modulation and 90 bpm for the 4+4+3 and 5+5+4 modulations, are below the limits of human perception. It was also confirmed that the application of the MASC on the tresillo results in subdivisions with smaller differences in relation to the polyrhythmic model than in relation to the tuplet model.