2.1 Data: The Christmas Eve vespers and the solesmes edition

The dataset of Christmas Eve vespers, used in [16], is so far the best that we have available with a set of fully transcribed directly comparable melodies from a diverse selection of 14 sources: two secular French, three Cistercian, three Benedictine, one Augustinian, a secular source from the Low Countries, and a set of later secular sources from Bohemia. The dataset was originally collected in order to study relationships between late medieval Bohemian sources with the data including transcribed melodies available in the Hymnologica database (http://hymnologica.cz/jistebnice), and we combined this data with all further melodies available for Vig. Nat. Domini vespers from the Cantus Index interface, in order to cover a broader European context. Because the repertoire in office sources is not entirely consistent across sources and our system aligns melodies directly, we had to select a subset of chants contained in as many sources as possible, and then reduce the set of sources to those that contained as many of these chants as possible. The resulting dataset contained 14 sources, with fully transcribed melodies for the following Cantus IDs: 001737 (Orietur sicut sol, antiphon), 002000 (Cum esset desponsata, antiphon for the Magnificat), 003511 (Judaea et Jerusalem, antiphon), 004195 (Bethleem non es minima, antiphon), 007040a (Constantes estote videbitis, responsory verse), and 007040 (Judaea et Jerusalem, responsory). The responsory Judaea et Jerusalem has previously been misreported as Cantus ID 605019, which refers to a shorter version of the reponsory which uses the text “Cras egrediemini...” as a verse instead of respond, while 007040 uses “Constantes estote...” as the verse (Cantus ID 007040a). A full overview is given in Supplementary Table S1 in S1 File.

We originally intended to use the CantusCorpus dataset [30] of Office melodies. However, the authors of the Cantus Database preferred transcribing entire sources, so while there are more than 13000 fully transcribed antiphons in CantusCorpus v0.2 [31], the vast majority comes from less than 20 sources. This is further compounded by the surprising diversity of office repertoire. Thus, in the entirety of CantusCorpus, it is only possible to find 10 different sources that have transcribed melodies for the 5 antiphons. Hence, we decided to use the Christmas dataset, with its advantage of having been collected specifically in order to make the comparison between different sources possible.

For each of the 14 sources, we briefly report its century of origin, its provenance, and which ecclesiastical institution it belonged to (Supplementary Section S2 in S1 File).

The three major dimensions of external similarity between chant sources, in terms of how similar the segments of culture represented in these sources are expected to be, are geography, chronology, and cursus, i.e., space, time, and the liturgical context within which the books were used. It is not entirely clear in chant scholarship how strongly each of these factors should influence chant melodies (the exception where cursus is clearly expected to dominate other factors is that of the Cistercian order, which mandated that all monasteries must have identical liturgical books [37, p. 99]), but these organizing principles should be observed in the resulting tree.

Solesmes editions are found in the Gregobase corpus (https://gregobase.selapa.net), from where we collected the melodies corresponding to our inference dataset. However, only the responsory Judaea et Jerusalem, its verse Constantes estote videbitis, and the antiphons Judaea et Jerusalem, Orietur sicut sol, and Cum esset desponsata are available.

2.2 Methods

We extended an earlier procedure [16] that aimed to reconstruct the unrooted phylogenetic tree of sources by adding three additional steps: Model selection for the root using Bayes factors, divergence time estimation on the fixed rooted tree selected in the previous step, ancestral melody reconstruction using the resulting timetree, and finally comparison of the maximum a posteriori melodies with those reconstructed in the Solesmes edition of chant (Supplementary Figure S3 in S1 File).

A Bayesian phylogeny [39] of chant melodies was carried out following the approach by [16] using mrbayes_volpiano [16,40] (available at https://github.com/gaballench/mrbayes_volpiano). In short, the method uses the Mk evolutionary model [41] for an arbitrary number of discrete states to calculate the branch lengths in units of expected numbers of substitutions per site, which is in essence an evolutionary distance, and co-estimates the tree topology using the phylogenetic likelihood function [42]. The resulting tree is unrooted and has limited interpretation in terms of cultural transmission, because it is not clear how time flows along the tree (as opposed to rooted phylogenetic trees). Also, branch lengths in unrooted trees are measured in units that conflate evolutionary rate and time [43]. We identify rate and time using divergence time estimation methods [44] (see below) to measure evolutionary rate and its heterogeneity along the tree, and also to use time as the unit of branch lengths [14]. At that point we chose a single tree on which to carry out further analysis, and then calculated a maximum clade credibility tree as a summary tree from the posterior distribution of topologies, for which we used treeannotator [45]. Tree formatting was carried out with phyx [46].

2.2.2 Divergence time estimation (DTE).

Once we have selected a rooted tree we can use Bayesian DTE on the fixed topology in order to separate evolutionary rate r from time in branch lengths [51]. The Bayesian model in general form (Equation 1) uses time calibration densities on either the nodes or the tips in order to generate the joint time prior using the calibration densities (Supplementary Table S4 in S1 File) and the tree process. Separation of rate and time requires also a clock model which describes the branch-specific evolutionary rates. The model parameters include parameters of the tree process, the clock model, and the evolutionary model. Then, the model estimates the PP densities for all of the model parameters conditional to the melody alignment data D.

(1)

It is possible to extend the Bayesian model by specifying the tree prior using a fossilised birth-death model parametrised using speciation, extinction, and sampling proportion (equation 1 in [52]). These parameters are often difficult to model from previous knowledge, but it is possible to use “uninformative” or flat priors for them [53].

DTE was carried out in mrbayes_volpiano using the Mk model with inverse-gamma rates [41]. The rooted tree topology was fixed. The clock model was set to independent gamma rates [54] and an Exponential(2) prior used for the variance, whereas an Exponential(5) prior was used for the clock rate. The FBD parameter priors were set to uniform(0,10) for the speciation rate, and Beta(1,1) for both the extinction and fossilisation rates. Please note that these rates are not necessarily normalized proportions and need not to be constrained to the interval [0,1], and are instead in units of number of speciation or extinction events per unit of time. Calibration densities were specified as in Supplementary Table S4 in S1 File. Parallel-tempering MCMC [55] was used with eight chains, one cold and seven hot, with a temperature of 0.001. MCMC sampling was carried out with 10.000.000 generations, sampling every 1.000. Posterior summarisation used a burn-in of 10%. All parameters attained effective sample size (ESS) > 500, indicating an appropriate sampling of the parameter posterior distributions. Time tree plotting (Fig 1) was carried out in figtree [56].

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Fig 1. A) Model selection for the position of the root.

Bar height represents posterior model probability, each bar is a topology resulting from rooting at a given branch in the maximum credibility tree. Rooted trees labeled tree0 through tree24. B) Divergence Time Estimation. The horizontal axis is time in years (A.D.). The blue horizontal bars at internal nodes represent the 95% highest posterior density intervals for divergence times. The color of the branches corresponds to evolutionary rate. Tips (colored squares) correspond to sources from the Christmas dataset, identified by their sigla. Their region of origin is encoded by a rondel corresponding to the current country governing said location, their cursus by the image (secular – church building, Benedictine – black monk, Cistercian – white monk, Augustinian – heart). The root separates a distinctly French and Cistercian clade (the order was founded in France) from sources east of the Rhine, following [3]. The grey internal nodes with asterisks are not in the majority consensus tree, highlighting topological uncertainty. Finally, a depiction of the Gregorian legend of the dove dictating melodies to Gregory I. from the Registrum Gregorii (Trier, Stadtbibliothek, Hs. 171/1626) is centered at the time of his papacy (590-604 AD).

https://doi.org/10.1371/journal.pone.0350014.g001

3.1 Evolution of melodies in a temporal scale: DTE

3.2 Estimating ancestral melodies: AMR

Given that the root position found via model selection separates the tree into east Frankish “Germanic” (node 20) vs. west Frankish “Romanic” (node 16) melodies [3,4], we focus on comparing the melodies inferred for the roots of these two clades. The “Germanic” chant dialect has been characterized by its preference for minor thirds d-f, a-c instead of seconds e-f, a-b (incl. a-b flat) [4], with the insight that it is a general German preference for re-fa over re-mi or mi-fa. A melody in a “Germanic” source exhibiting none this preference merits scrutiny [4, p. 95] (Fig 2).

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Fig 2. A) Comparing the results of Ancestral State Reconstruction for the nodes corresponding to the common ancestors of the East Frankish (“Germanic”, node 20) and West Frankish (“French”, node 16) melodic dialects.

Each pitch is assigned a background color to make differences in melodies easier to spot. In previous literature on the topic (Peter Wagner’s book “Gregorianische Formenlehre”, 1911), the “Germanic” dialect was supposed to be characterized by its preference of fa over the “French” dialect’s preference for mi, which corresponds to the “Germanic” dialect preferring the tone f over e and c over b (natural, also termed “h” in German nomenclature, as well as flat), which given the prevalence of stepwise motion often translates to preferring thirds d-f and a-c over seconds d-e, e-f, and a-b(h), b(h)-c. While the sources were “sorted” into these two main melodic dialects by the phylogeny, this preference seems to very weak in the inferred ancestral melodies for these two dialects: while in 7 positions the East Frankish dialect does exhibit this preference (green frames), in 3 positions this is the other way around (red frames), and most importantly, there are many places where the East vs. West Frankish preferences could have been expressed but is not (some examples in blue). B) Analysis of the reconstructed melodies for the inferred root (node 15 of the DTE tree), the common ancestor of the later Cistercian sources (node 19 of the DTE tree), and the Solesmes version of the melodies. The log probability of observing the Solesmes melody at the Cistercian node is higher for each of the five melodies (the antiphon Bethleem non es minima is not in the Solesmes editions) except for the responsory Judaea et Jerusalem. Under each of the melody comparisons, we color-code the positions where Solesmes agrees with the root and not with the Cistercians (purple), positions where Solesmes agrees with the Cistercians rather than the root (teal), and positions where both inferred melodies agree but the Solesmes edition differs (light green), against the MAP estimates of the melodies obtained from ASR. Most of the differences are between the Solesmes edition and both of the inferred medieval melodies: thus one can observe where the Solesmes editorial process prioritized other criteria than fidelity to the earliest possible sources.

https://doi.org/10.1371/journal.pone.0350014.g002

This is observed in the inferred melodies to a limited extent. For five out of six Cantus IDs in the dataset, at least one such position where node 20 preferred what is in [3,4] considered Germanic. At the same time, four melodies also have positions where the “Romanic” clade root MAP estimate has “Germanic” features. Out of a total of 77 manually identified “opportunities” for the melodies to differ in their treatment of re-fa thirds, the “Germanic” option is only chosen by node 20 melody 5 more times than by the node 16 melody. This may partly be an artifact of mode. Most of the Christmas melodies are in mode 8, while the most characteristic examples in [3] and [4] are in mode 1. However, the literature does also indicate that the melodic dialect doesn’t at all manifest at every opportunity, and that one might easily find the “Germanic” preference in sources west of the Rhine and vice versa [4, pp.95–98]. Therefore, while ASR results are not as clear a success as accurately predicting the timing of the Cistercian reformation, it does again conform to existing expectation.

3.3 Comparing AMR to the Solesmes editions

The posterior log-probabilities of observing the Solesmes melodies at individual nodes are shown in Supplementary Figure S5 in S1 File. At least for the Christmas Eve vespers, the model indicates the editors of Solesmes have preferred melodies of the west Frankish style (nodes 16–19), most prominently those of the Cistercian order (nodes 18 and 19). The melodic features of later secular Bohemian sources (nodes 24–26) are the least preferred models overall, which is mostly influenced by the longer responsory Judaea et Jerusalem (judjer2) and the Magnificat antiphon Cum esset desponsata (cumesset), not so much by the psalm antiphon Orietur sicut sol (orisic) or the responsory verse Constantes estote (consest).

This complements what we know about the process, as well as expectation of the time [1, pp.5–6]. The Solesmes editorial process did not, for unexplained reasons, consider German sources [4, p.113]. Furthermore, the second and third criteria – legitimate tradition and needs of contemporary liturgy, which included the skill sets and habits of early 20th century singers [62,63] – would gravitate towards a later aesthetic of chant that is closer to the world of tonality, and the Cistercian reform is a significant stepping stone in this respect [38].

4.1. Cistercians sources

There are three sources in the Christmas dataset of Cistercian provenance: A-Wn 1799**, D-KNd 1611, and CDN-Hsmu M2149.L4. The Cistercian order is known to have maintained very strict discipline in copying liturgical books. This is already seen in the topology inferred in [16], where these sources are grouped closely together, and this is replicated in our topology as well. However, additionally, the DTE step of our pipeline provides an explicit time for the common ancestor of Cistercian sources: the median falls on the year 1145, which coincides with the reform of the antiphonary initiated by St. Bernard of Clairvaux in 1147 or prior [64]. Drafts of the Bernardine liturgy are found in the 12A-B Westmalle Antiphonary, dating from 1140–1143 [38]. The 95% credibility interval covers 1075–1210.

4.2 The position of A-VOR Cod. 259 I

The source A-VOR Cod. 259 I merits attention. It is a source from the late 14th century that was brought to Vienna and later the Augustinian monastery in Vorau when the Chapter house at Vyšehrad (Prague) was fleeing the Hussite wars of 1420–1434, as evidenced by the inscription on its f.1r. This inscription, which describes the history of the manuscript, is written over a rubbed-out earlier melody (Gaude et laetare, Cantus ID 002922, which is often the first antiphon in numerous sources of Bohemian provenance), which is how the new owners found space for the inscription on the first page. Why is this source not grouped closer with either the Augustinian CZ-Pn I D 20, or the similarly late 14th century CZ-Pu XV A 10? In 1496, the manuscript underwent significant revisions according to the Salzburg diocese rite [65]. A look at its digitized folios 69r-71v reveals the presence of possible palimpsests (instances of an older layer scratched out: see https://www.cantusplanus.at/common/rism.php?rism=A-VOR259_1). Some are clearly visible (the doxology at the top of f.71r), and some are just suspicion (traces of rhombic shapes that resemble bleedthrough in the last two staffs on f.69r but do not have corresponding rhombes on f.69v or the neighboring f.68v, which incidentally also has modifications in its bottom half). Furthermore, the antiphon “Gaude et laetare”, overwritten on f.1r by the inscription with the source’s history, is used again on f.70r for Christmas Eve vespers, but with a different melody than what was on f.1r – another reason to suspect that the melodies for Christmas Eve vespers may have been changed later in the 15th century. Of course, codicological expertise is needed to resolve the extent to which this was done; however, this shows how the inferred phylogeny can, aside from providing verifiable predictions such as the Cistercian common ancestor date, also point towards specific problems requiring further musicological study.

If we do accept the later origin of A-VOR Cod. 259 melodies, the branch leading down to node 24 that exhibits the highest evolutionary rate can be symptomatic of two phenomena: one geographic, the Bohemian Reformation, and one chronological – the transition into the late middle ages. The fact that the A-VOR melodies were modified outside of the lands controlled by the Hussites (or, later, Utraquists) lends, in our view, more credence to the chronological explanation (which then leads to unexplored questions about chant melody between the late middle ages and the Editio Medicaea of 1604), but weighing these two interpretations is not possible with the Christmas dataset.

The case study of A-VOR Cod. 259/I shows that this method also brings value in reexamining assumptions about the input data, and thus can also serve as a “quality control” tool. Its improved interpretability further makes it more accessible for musicologists without a significant technical background.

4.3 The Solesmes edition and AMR

We now use our estimated model of chant evolution to study the modern chant restoration movement through the properties of the melodies from the group of 20th- and 21st-century editions of chant produced primarily by the Benedictine monks of the Solesmes Abbey. The Solesmes editions are the central output of the chant restoration movement, led by the Benedictine monks of Solesmes since the latter half of the 19th century [66]. Their core output is the official new edition of Gregorian chant – originally under the auspices of the Editio Vaticana, led by Dom. Pothier and an editorial council, based on the document Motu Proprio of Nov 22nd, 1903, of pope Pius X; later editorial activity has been carried out by the monks of Solesmes themselves.

The main contribution of this edition was, in line with the philological thinking of the time, to recover as much as possible the “original” melodies of Gregorian chant, trying to recover – in principle – what the dove had whispered into Gregory I.’s ear. Thus, in the context of ASR, it is enticing to use the Solesmes editions as the “best effort” reconstruction of the melodies that should correspond to the root of our tree, and thus different ways of building the pipeline could theoretically be evaluated by how similar their predicted root melodies are to the Solesmes edition – thus matching this ongoing “best effort” reconstruction using philological methods. However, reconstructing the earliest melodies of chant was not the only priority of Editio Vaticana: another was to do this while retaining “legitimate tradition” from later times, and third, to serve the needs of the day. From the Motu Proprio of Pius X.: “The Gregorian melodies are to be restored in their completeness and true nature, according to the testimony of the more ancient manuscripts, taking into consideration not only the legitimate tradition of intervening centuries, but also the common practices of present-day liturgy.” Transl. from [66, p.xxi]. The clashes between these priorities, as manifested in the resultant melodies, were subject to heated exchanges at the time [62,63,67]. and the process involved diverse influences such as anticlericalism or business interests of print unions [68]. This can be observed also in the melodies directly when we compare them with the inferred medieval melodies in Fig 2.

The melodies thus cannot be used to directly evaluate how well the root melody is reconstructed by ASR. Instead, observations can be made about the results of the Solesmes efforts: what was the extent to which these were “archaeological”, and what influence did “legitimate tradition” and “common practices of present-day liturgy” have? Here we borrow the term that Peter Wagner applied in his polemic with the critics of Editio Vaticana [63], while we do not necessarily agree with its original disparaging nature, it is not chosen without merit to represent that particular methodological approach. How does this recent layer of chant tradition relate to the medieval sources? These results serve to show how the inferred phylogeny can be used to provide insights complementary to philological methods, and perhaps also how the editorial practices of Solesmes evolved throughout the 20th and 21st centuries.