What did the dove sing to Pope Gregory? Ancestral melody reconstruction in Gregorian chant using Bayesian phylogenetics.

An attractive goal in the study of Gregorian chant melodies is reconstructing unobserved melodies as they may have been transmitted along the history of chant, especially as early chant notation does not capture pitch exactly. We propose doing this computationally using Ancestral State Reconstruction (ASR) over phylogenetic trees. Bayesian phylogenetic trees have shown promise as a tool to study the evolution of chant melodies, by inferring a plausible topology of chant transmission. However, the inferred trees cannot be used as ASR inputs directly, because they are undirected, and their branch lengths conflate time and evolutionary rate. We therefore first apply Divergence Time Estimation (DTE) to separate them and represent the tree in a directed form on the time dimension. Using ASR, we then obtain reconstructions of melodies for each of the ancestral nodes, in addition to their distribution in time obtained from DTE, and thus we obtain a phylogeny of chant melody with a music-historical interpretation. We applied this method to the Christmas Vespers dataset, and compare the results against musicological knowledge and melodies reconstructed at Solesmes using methods of contemporary philology, which shows potential for reconstructing cultural transmission through time.