(untitled) (Orfeu, 2022)
Translation of the seminal article A Formal Theory of Generalized Tonal Functions by David Lewin, published in 1982, which foreshadows some ideas later developed in Generalized Musical Intervals and Transformations (LEWIN, 1987) and which would give rise to transformational theory and neo-Riemanian theory. The author builds, through mathematical formalization, a structure called the Riemann System, which generalizes certain concepts pertinent to the theory of tonal music, such as harmonic function and melodic function. Transformations that relate Riemann Systems to each other are also conceptualized, embracing and extending the scope of traditional Riemannian transformations. Such transformations can be interpreted as corresponding to other familiar theoretical notions, such as transposition, inversion, “taking the relative”, the “taking the mediant”, among others. Some short analyzes of excerpts from Wagner, Brahms, Stravinsky and Beethoven are elaborated in order to show the relevance of the theory developed for musical analysis.