Formal algorithms of tintinnabuli in Arvo Pärt's music (1/2)

The formal line of development in 20th century music points to the steady algorithmisation of imaginative processes, including sonic processes: Until recently, the utmost expression of the tendency to mathematically program musical form was seen in various twelve-tone techniques. In contemporary theoretical literature, this is considered structuralism in musical composition, and the concept of algorithm is associated with computer music.

In analysing Arvo Pärt's music, we are making a surprising discovery: In his original tintinnabuli-technique, the composer has invented mechanisms for processing diatonic (or polymodal) material, that in their essence function similarly to the serial technique of dodecaphony. However, the tintinnabuli technique is not connected with the serialisation of the parameters of sound: The essence of tintinnabuli lies in the algorithmisation of musical form that proceeds from formulaic thinking. Such a creative mode differs qualitatively from the serial technique. In tintinnabuli music, the formula could be defined as a minimized numerical program that incorporates the algorithm of development, but at the same time contains the summary of the musical work's pitch structure in its variety. Unlike, for example, Stockhausen's compositional formulas that are essentially bound up with serial technique, Pärt's programmed forms are founded on principally different numerical grounds – in diatonic or polymodal systems (the latter encompasses diatonic and one-and-half-tone scales, and, very rarely, also chromatic and diatonic scales). They embody a new comprehension of simplicity and postulate a new stylistic paradigm of aural simplicity and structural complexity.

In Pärt's compositional technique, the methods for working with melodic material, the logic of which is calculated with the help of the arithmetical progression, and with verbal text, all the parameters of which are most frequently used by the composer as a mathematical foundation for the construction of melodic voices (in other words, the text "dictates" numerical progressions), can be considered equally important. Both principles are applied in the composer's vocal as well as instrumental music. Unlike the arithmetical progression, the text allows of the "reading out" of more diverse and multilevelled numerical progressions that are projected into counterpoint, harmony (the vertical pitch structure), and the logic of form as a whole. To a large extent, this is exactly the source of the novelty of tintinnabuli.



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