Aldo Clementi musicus mathematicus

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Paolo Emilio Carapezza


Like that of Liszt and Stravinsky, the composers by whom he was attracted in his adolescence and early youth, Aldo dementi’s (Catania 1925-Rome 2011) musical production went through various phases, greatly changing on the surface and in appearance, though not in depth and substance. He himself suggests a division into five phases: 1. Preliminary (1944-1955), juvenile and apprenticeship works. 2. Structural (1956-1961). 3. Informal material (1961-1964). 4. Non-formal optical (1966-1970). 5. Polydiatonic (1970-2011): groups of letters indicating musical notes (for example: B-A-C H), or canti dati (modal or tonal - monodic or polyphonic - compositions of the western tradition, from the Stele of Sicilus to Stravinsky), but most often segments of melodic lines inferred from them. But - in the polyphonic counterpoint that derives from it - they are simultaneously intoned in the different voices in different tonalities: hence their superimposition restores the chromatic dodecaphonic total. Clementi himself proclaims the constitutional continuity of this development. The substance of his music consists in the direct transposition of a figurative project into a sonorous structure. Geometrie di musica: the title of the 2001 book by Gianluigi Mattietti refers first of all, as the subtitle says, to The <poly> diatonic period of Aldo Clementi, but it perfectly defines his whole musical production, all pervaded by dense polyphonic counterpoints. For Clementi construction is a goal, not a means to articulate discourse: indeed, he was even to do without discourse in his three central creative periods; and when in the fifth and latest one he has returned to it, he has enslaved it entirely to construction : he draws fragments from it, to be used as raw material, i.e. the diatonic subjects, of his dodecaphonic counterpoints. After the different phenomenology of the eruptions of sound matter of Varèse and Stravinsky, dementi’s music represents a further peak of pure construction in the sonorous space. His counterpoint however, like Webern’s, is limpid, subtly articulated, and dominated by reason: but here construction reigns supreme, and the composer in accordance with his requirements uses discursive melodic segments as raw material, as bricks (“modules” he says, and he describes them as mosaic tiles). “The idea of a construction achieved with the dovetailing of mirror-like images is also at the base of the figurative research of Escher, hinging on the concept of division of the plane, through repeated figures, mirror-like and congruent” (Mattietti). Indeed, dementi’s music is “disciplina quae de numeris loquitur” (discipline that speaks of numbers), according to the definition by Cassiodorus, rather than “scientia bene modulandi” (art of singing well), according to the definition by Augustine; and it is, more precisely, paraphrasing the famous definition by Leibniz, “exercitium arithmeticae manifestum coscientis se numerare animi” (evident arithmetical exercise of the mind aware of counting). Three compositions of dementi’s polydiatonic period are here thoroughly considered: two canons for string quartet, the very simple four-voiced Canone on a fragment by Platti (1997) and the very complex eight-voiced Tributo (1988) on “Happy birthday to you!”; and a de-collage, Blues and Blues 2, “fantasies on fragments by Thelonious Monk”, for piano (2001).


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Carapezza, P. E. (2018). Aldo Clementi musicus mathematicus. Interdisciplinary Studies in Musicology, (12), 57-72. Pobrano z


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