Measuring musics Notes on modes, motifs, and melodies

This dissertation develops computational methods to measure properties of musical traditions, with the aim of comparing them. It analyzes sheet music from a range of traditions, to which end two corpora of Western plainchant are introduced (Cantus Corpus and GregoBase Corpus). These corpora are used to confirm the melodic arch hypothesis, explore regularity in antiphon-differentia connections, and compose artificial chant using a recurrent neural language model. The central chant study, however, proposes a distributional approach to mode classification that can still determine mode fairly accurately even when all pitch information has been discarded. However, this seems to work best when the chants are segmented into ‘natural units’ corresponding to textual units such as syllables and words. Breaking down music into smaller units, or motifs, is the second theme in this dissertation. It is shown how rhythmic motifs can be used to effectively visualize rhythmic data, from music and animal vocalizations, in a rhythm triangle, an idea that is also extended to melodic data. The third theme concerns the shapes of melodies. The dissertation introduces Cosine Contours: a continuous representation for melodic contour, motivated by the observation that the principal components of melodic datasets approximate cosines. A second study on contour suggests that it should indeed be considered a continuous phenomenon, unlike several previous studies, as no evidence is found that contours cluster in distinct types. The dissertation ends with a case-study that applies a formal analysis to the ‘formal’ music of Arvo Pärt by reconstructing almost the entire score of ‘Summa’ using formal procedures.