Bas Cornelissen

Bas Cornelissen, Willem Zuidema, John Ashley Burgoyne et al.

How to describe the shape of a melodic phrase? Scholars have often relied on typologies with a small set of contour types. We question their adequacy: we find no evidence that phrase contours cluster into discrete types, neither in German or Chinese folksongs, nor in Gregorian chant. The test for clustering we propose applies the dist-dip test of multimodality after a UMAP dimensionality reduction. The test correctly identifies clustering in a synthetic dataset, but not in actual phrase contours. These results raise problems for discrete typologies. In particular, type frequencies may be unreliable, as we see with Huron's typology. We also show how a recent finding of four contour shapes may be an artefact of the analysis. Our findings suggest that melodic contour is best seen as a continuous phenomenon.

Bas Cornelissen

This paper develops a framework for conceptualizing, visualizing, and measuring regularities in rhythmic data. I propose to think about rhythmic data in terms of interval segments: fixed-length groups of consecutive intervals, which can be decomposed into a duration and a pattern (the ratios between the intervals). This simple conceptual framework unifies three rhythmic visualization methods and yields a fourth: the pattern-duration plot. When paired with a cluster transition network, it intuitively reveals regularities in both synthetic and real-world rhythmic data. Moreover, the framework generalizes two common measures of rhythmic structure: rhythm ratios and the normalized pairwise variability index (nPVI). In particular, nPVI can be reconstructed as the average distance from isochrony, and I propose a more general measure of anisochrony to replace it. Finally, the novel concept of quantality may shed light on wider debates regarding small-integer-ratio rhythms.

Bas Cornelissen

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.