Gregorian melody, modality, and memory: Segmenting chant with Bayesian nonparametrics

The idea that Gregorian melodies are constructed from some vocabulary of segments has long been a part of chant scholarship. This so-called ``centonisation'' theory has received much musicological criticism, but frequent re-use of certain melodic segments has been observed in chant melodies, and the intractable number of possible segmentations allowed the option that some undiscovered segmentation exists that will yet prove the value of centonisation. Recent empirical results have shown that segmentations can, in fact, outperform music-theoretical features in mode classification. We operationalise the fact that Gregorian chant was memorised, and find an optimal unsupervised segmentation of chant melody using nested hierarchical Pitman-Yor language models. The segmentation we find achieves a new state-of-the-art performance in mode classification. Modelling a monk memorising the melodies from one liturgical manuscript, we then find empirical evidence for the link between mode classification and memory efficiency, and observe more formulaic areas at the beginnings and ends of melodies corresponding to the practical role of modality in performance. However, the resulting segmentations themselves indicate that even such a memory-optimal segmentation is not what is understood as centonisation.