Elena Tokun. Formal Algorithms of Tintinnabuli

ELENA TOKUN | An excerpt from article “Formal algorithms of tintinnabuli in Arvo Pärt’s music”.
Moscow Conservatory Publishing House, 2011

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.

In the newest musicological literature dedicated to research on Arvo Pärt’s music, the application of the concept “tintinnabuli” appears to be rather broad. For this reason, it is by all means necessary to specify and generalize the concept’s possible meanings. In the most general sense, tintinnabuli is, first and foremost, Pärt’s philosophy of creation that is inextricably bound to the philosophical and theological tradition of the Orthodox faith. The spiritual foundations of the composer’s creation form all the levels in his system of tintinnabuli, which the composer himself has defined as “the flight into voluntary poverty”.* Through the concept oftintinnabuli, one can also define Pärt’s creative style from the works of 1976 onward. Its stylistic paradigm springs up from spiritual self-restraint and sonic asceticism, from the profound objectivity of music’s spirit and matter, taking form on the basis of strict algorithms.

More specific is an interpretation of tintinnabuli as Pärt’s original composition technique.

In the broad sense (of the concept of technique), tintinnabuli is a unique algorithmic system of composition aimed at the total reduction and the strictest organization of musical means. Simple and transparent in the auditory sensation, tintinnabuli music has a strong core: It is based on the number (autonomous series of numbers, or a text with all its parameters as the numerical structure), which determines the objectivity of the structure of the musical matter to the smallest detail.

Yet in a more narrow and practical sense, tintinnabuli is atechnique for the structuring of pitches in which two voices are connected on the basis of a set of strict contrapuntal rules. The main components of the texture consist in the rationally constructed, mostly scalar melodic voice and the tintinnabuli voice that is sculpted on a central triad. The names of these two voices, the M-voice and T-voice in abbreviated form, are used by the composer himself. Finally, in the narrowest and most musically inherent sense, tintinnabuli refers to the voice that is built up on the three pitches of a central triad.

To conclude: as a compositional system, tintinnabuli represents a novel unity of counterpoint, harmony, and form in the music at the turn of the 20th and 21st centuries, in which the simplicity of a sound’s aural parameters as well as the clarity and strictness of sounding music commingle with the numerical programming of musical material. Arvo Pärt himself has said of his works: “The construction is definite, the colour is not”.** If the initial solution of a numerical formula is correct, one can declare the content of atintinnabuli composition to be materialized and able to endure the “test of strength” in any timbral embodiment.

* Arvo Pärt. Tintinnabuli – Flucht in die Freiwillige Armut. – Sowjetische Musik im Licht der Perestroika, hg. v. Hermann Danuser. Laaber 1990, p. 269.
** Klangwelten der Langsamkeit und Stille: Der estnische Komponist Arvo Pärt im Gespräch mit Klaus Georg Koch und Michael Mönninger. – Berliner Zeitung, 2. März, 1997.

Elena Tokun defended her PhD thesis “Arvo Pärt. Tintinnabuli: composition technique and style” at the P.I. Tschaikovsky Moscow State Conservatory in 2010. The present text is an excerpt from her article “Formal algorithms of tintinnabuli in Arvo Pärt’s music”, published in the collection “In memory of Yevgeny Vladimirovich Nazaikinsky” (Moscow Conservatory Publishing House, 2011)