Algo Pärt: An Algorithmic Reconstruction of Arvo Pärt's Summa

Abstract

Arvo Pärt is one of the most popular contemporary composers, known for his highly original tintinnabuli style. Works in this style are typically composed according to precise procedures and have even been described as algorithmic compositions. To understand how algorithmic Pärt's music exactly is, this paper presents an analysis by synthesis: it proposes an algorithm that almost completely reconstructs the score of Summa, his "most strictly constructed and most encrypted work," according to Pärt himself in 1994. The piece is analyzed and then formalized using so-called tintinnabuli processes. An implementation of the resulting algorithm generates a musical score matching Summa in over 93% of the notes. Due to interdependencies between the voices, only half of the mistakes (3.5%) need to be corrected to reproduce the original score faithfully. This study shows that Summa is a largely algorithmic composition and offers new perspectives on the music of Arvo Pärt.

Figures (15)

• Figure 1: Excerpt of Für Alina (mm. 2--7). This piano piece was Arvo Pärt's first work in his tintinnabuli style. The right hand plays a melodic voice (m-voice) that mostly moves stepwise, and which is freely composed. The left hand has the tintinnabuli voice (t-voice), that is restricted to notes from the B-minor triad. The relation between the two voices is shown on the right: the t-voice plays the highest triad note below the m-voice, but one octave lower.
• Figure 2: Tintinnabuli positions for an A minor triad. Solid notes show the A minor scale as a melodic voice, and open notes show tintinnabuli voices in the five different positions introduced by Hillier1997. His terminology is shown above the staff, the numbering used in \ref{['sec:synthesis']} below it.
• Figure 3: The melodic structure of Fratres is a series of variations of a six-bar theme, of which the first two are shown. The theme leaves and then approaches a pitch center, moving one step further for three consecutive bars. The next three bars repeat the first three but played backward. This results in four types of melodic movement, or modes, that are often used by Pärt to compose m-voices. The first staff also shows the parallel m-voice and the t-voice as small notes.
• Figure 4: Four melodic modes commonly used by Arvo Pärt to construct m-voices: two ways to move away from a central pitch, and two to approach it Hillier1997. All of these are found in Fratres, as shown in figure \ref{['fig:fratres']}.
• Figure 5: The opening measures of Summa, a setting of the Credo. The piece consists of 16 three-bar sections containing 7, 9 and 7 syllables. The voice distribution is mirrored in every section: sa--satb--tb. The alto and bass have the m-voices, the soprano and tenor the corresponding t-voices. If one skips the small, slurred 'ornaments', the m-voices walk up and down an E natural minor scale, while the t-voices are constrained to the E minor triad.