Poetic meter in the Middle High German (MHG) tradition has always been a contentious and complex subject, as it requires a nuanced knowledge of MHG literature, a strong understanding of MHG linguistics, particularly phonology, and knowledge of the musical practices of the period¹. Most work thus far has not been able to master all of these areas². While this paper does not attempt to fully unite these diverse fields, it does seek to take careful consideration of each in developing a computational model to better understand how medieval German poets crafted their words into meter, and in turn aid us in our own reading of the text. The increased popularity of machine learning algorithms and their application to textual data presents a particularly fruitful opportunity in a domain that has plagued MHG scholarship for years. Instead of a deductive approach, i.e., beginning with the assumption of trochaic alternation as fundamental, supervised learning allows for a large-scale inductive approach, supplying the algorithm with a wealth of specific examples from which general principles can be discerned. Crucially, the goal of any such model is not to establish an absolute truth about a historical language; the goal is to automatically reproduce the annotation decisions of scholars on a large scale. Annotating the entire MHG epic corpus would allow us to better understand any rules that do exist as well as the challenges any particular text poses. Automatic annotation would also support a large scale analysis on how specific metrical values and meter types are invoked in different contexts. Scholars often discuss how changes in meter, metrical values, or specific cadences are triggered in specific scenes, but can we measure this complexity? MHG meter provides for fascinating flexibility in emphasis, but did authors have preferences for different metrical values? Are certain texts or passages intentionally crafted to be more difficult to scan? This paper seeks to answer these questions and others through a large scale analysis of automatically scanned poetry.

While late twentieth century scholarship neglected meter primarily due to theoretical disagreements and a lack of manuscript evidence, Christoph März recently re-framed MHG scholarship on meter in his article “Metrik, eine Wissenschaft zwischen Zählen und Schwärmen,” in which he attempts to revive a meter-based formal perspective (März, 1999). According to März, form has two important functions and opportunities: it reminds us, and it allows for comparison (März, 1999, p. 325). Both of these observations provide motivation for the following analysis. Poetic meter acts not only to support the memory of a performer or composer, but also affects the audience, prompting this comparative reception. März writes:

This act of remembering serves as an opportunity to identify connections between songs and texts (both formally and semantically), and compare texts, as März would have it. This comparison, when recognized by a performer or audience, can generate and add meaning to a poem or song. Especially in the MHG tradition, a connection between form and content has always been presumed. Yet März is also interested in lower level connections and references within genres. März asks whether these abstracted metrical schemata “transport” specific ideas, and if so, how they are created (März, 1999, p. 325). Klaus Kohrs asked a similar question decades earlier. Kohrs explains in Saussurian terms how meter itself can add signification to language, which it does not inherently carry: “With the metrical, that is even “quasi-musical” formation of language as a symbolic and sonoric phenomenon the side of the signifié is quasi sublimated, i.e., sensical and semantic references become virulent, which the “natural” language does not have and does not need to have” (Kohrs, 1969, p. 605). Hugo Kuhn presents the idea similarly in relation to music and melody, but emphasizes its “Gebrauchsfunktion” (use function), i.e., the use cases for these artworks, as folksongs, religious uses, for the court, knights, etc. (Kuhn, 1969, p. 38). This point is taken up by Thomas Cramer, questioning what the actual Gebrauchsfunktion for these artworks was, and whether our ideas of them are correct according to the sources (Kuhn, 1969, p. 39). But März crucially reshapes this question, instead of asking what meaning or function poetic meter may contain, he notes that meter is always determined relatively (März, 1999, p. 325). As Paul Zumthor and Ferdinand de Saussure have claimed about words and sound, there is no meaning in the base element itself, only in context and pattern. But for both words and poetic meter, this context must be extended beyond the contained object of a line of poetry to the body of referential objects.

The aim of this paper is to disambiguate these relative relationships. This project does not intend to argue that any particular metrical theory is without fault, nor that specific metrical values even exist as such, but rather that implementing any framework inevitably teases out relative differences within a corpus. Heusler decries the nineteenth century philologists for altering the text and making a statistical analysis of MHG metrics impossible, and for this reason he gives no statistics in his MHG study of meter (Heusler, 1956, p. 4). Yet the focus here is not concrete, in terms of absolute numbers or statistics, but rather in establishing relative relationships between texts, which, when aggregated over a whole text or corpus, will not drown out clear characteristics³.

The distribution of Latin into distinct regional dialects had profound linguistic and literary implications for all of Europe. One notable consequence was on poetry with quantitative meter. Even before the Middle Ages, the syllable length of classical Latin had been nearly forgotten in the vernacular⁴. Latin poetry had used quantitative meter, in which syllable length is the organizing principle. Syllable length was a phonologically distinctive feature to Latin speakers. However, the emerging dialects differed from Latin in that stress became a phonologically important feature, and thus so-called qualitative meter (“rhythmic poetry”) predominated in the Romance languages. Reconciling these linguistic differences, MHG meter relied on both stress and syllable length. This hybrid metrical form poses unique challenges to scanning poetry and allowed for a diverse development in genre and style (Heusler, 1956, pp. 74–75). Yet this freedom raises one of the main questions and theoretical problems in MHG research on meter: not necessarily Heusler's question of “How am I to measure it?,” but rather what: in a system of “measured syllable verse with free syllable counts”—what is it that we can count, or should count? (Heusler, 1956, pp. 9, 13) “What is countable in the verse?” (März, 1999, pp. 323–324) We could count syllables, but it is not clear if the poets did this naturally themselves, despite what the Meistersänger⁵ would like us to believe. Herbert Bögl describes MHG verse in his Abriss der mittelhochdeutschen Metrik: mit einem Übungsteil: MHG “presents in an abstract language of symbols the sequence of syllables in a verse and weighs them taking into account their length and stress” (Bögl, 2006, p. 9). It is this “taking into account” that presents a difficult computational problem for analysis MHG meter, in that strict rules for length and stress cannot always be employed.

To illustrate this shift from a quantitative classical meter to a qualitative post-classical vernacular meter, we first consider the quantitative epic poetry of Latin and Greek. Each line consists of six feet, each foot typically a dactyl (a long syllable followed by two short syllables) or spondee (two long syllables). A syllable is considered long if it has a long vowel or diphthong, or ends in two consonants (Hayes, 1989). All other syllables are short. The first line of Virgil's Aeneid serves as example:⁶

A widely cited poem displaying the shift from quantitative to qualitative rhythmic poetry in the Latin tradition is Bishop Auspicius of Toul's late fifth century letter to Arbogast, the Count of Trier, imitating the iambic dimeter⁸ already made famous by Ambrose⁹. The letter begins:

The first hemistich¹¹ — ⌣ ⌣ — ⌣ — ⌣ ⌣ shows that a quantitative scansion would be ill-fitted to the rest of the verse, and that a strictly iambic scansion is preferred with a paroxytone¹² in the cadence. Much Latin poetry followed suit, and the medieval Codex buranus famously bears witness to the intermingling of Latin and MHG rhythmic verse, clearly demonstrating that they were drawing from the same rhythmical schemata. Germanic verse, on the other hand, did not originally follow the quantitative meter of antiquity, preferring organization according to alliteration and stress. In fact, Heusler calls alliteration the “Hausmarke” (house brand) of the Germanic language family (Heusler, 1956, pp. 92–93). In addition to alliteration, a further marker of Germanic verse is the Langzeile (long line), traditionally consisting of two Kurzzeilen (short lines), an Anvers (first half of the line) and Abvers (second half of the line) (Heusler, 1956, p. 100). While this tradition began earlier, a classic example of Germanic alliterative verse is the ninth century Bavarian Muspilli:

This alliterative verse dominated throughout most of OHG and continued strong in the Nordic traditions. Around the same time that the Muspilli was written in the southeast, in the west Otfrid von Weißenburg in Alsace was beginning to incorporate characteristics of Old French poetry into his ninth century Old High German (OHG) verse. Otfrid's decision to incorporate end rhyme (referred to as a strictly Romance language influence by Heusler) is the first attested instance of Germanic poetry's break from the alliterative tradition. Thus Otfrid is generally considered the starting point for a study of modern German verse¹⁴. Otfrid's Evangelienbuch became the model for this new Germanic verse, though he retained the Langzeile from the older Germanic tradition. Otfrid established many of the new metrical possibilities in cadence (monosyllabic full, bisyllabic ringing, and trisyllabic ringing) witnessed in the MHG period (Heusler, 1956, p. 13). Much of the influence on Otfrid's style came from various writings on religion, heroic stories, and charms recorded at the time¹⁵. Heusler argues that this freedom in verse came primarily from the church, specifically church songs. Heusler writes: “song more easily takes advantage of the prosodic freedom” (Heusler, 1956, p. 32). Concerning rhyme, for nearly 300 years there was only pair rhyme in the AABB form, occasionally AAA, until around 1150 (Heusler, 1956, p. 12). Otfrid's rhyme began as pure monosyllabic rhyme, and later developed into multi-syllable assonance and other types (Heusler, 1956, p. 20). As the importance of rhyme grew, it became necessary for the rhyming syllable to also carry accent (Heusler, 1956, p. 24,3 1). This new rhyme and accent provided an alternative means to tie verses together, but also ushered in new freedoms of measuring verse, as rhyme required syllables to relate to one another, something emphasized by the contemporary musicologists (Heusler, 1956, p. 9). The form of the Ambrosian hymn is the closest metrically to Otfrid. The greatest difference lies within the construction of the line, where the syllable count is not certain, and divided lifts¹⁶ are abundant (Heusler, 1956, p. 35).

Otfrid's founding of the Germanic rhythmic verse was what Heusler calls a “Germanicizing” of the Romance iambic verse: free filling of verses with syllables, anacrusis, and more varied cadences (Heusler, 1956, p. 36). Heusler charts out the development of Germanic verse and its influence from the Romance tradition, particularly in that the mixing of alliterative and pair-rhyme verse led to the early Germanic free filling of feet. Yet metrical conventions did exist in Otfrid's verse. The last foot was still strictly monosyllabic and verses could range from four to ten syllables, but were more often somewhere in between (Heusler, 1956, p. 43). OHG verse often had feet with more syllables than MHG because OHG words simply had more medial syllables¹⁷. In contrast to MHG verse, OHG verse was more consistent with syllable length and duration (Heusler, 1956, p. 56). In this sense, OHG verse was a “mediator” between Latin and alliterative verse (Heusler, 1956, p. 63). With Otfrid, the German pair-rhyme Vierheber (four stresses per line) began to take shape:

The most comprehensive and still referenced study of German meter is Andreas Heusler's three volume Deutsche Versgeschichte. Heusler's theory has been criticized incessantly over the years, but persists as the accepted theory for MHG meter today. März claims that as reluctant as we are to use Heusler's theories, we use them because there is simply no better alternative (März, 1999, p. 318). While attempts have been made to supplement or critique Heusler's work, especially the existence of the fundamental “Takt” (measure, as in music), it has proven difficult for alternative theories to escape temporal restraints. If there is no “Takt,” is there no foot, or stress alternation? (März, 1999, p. 319) As März observes, many of the alternative theories do not differ significantly from Heusler's, only Franz Saran's “Schallanalyse” (acoustic analysis) is suggested by März as a plausible alternative to better incorporate the actual voice of the verse (März, 1999, pp. 321–322).

What follows is a description of MHG epic meter in the Heusler tradition, with supplement from other, mostly pedagogical, resources. The Heusler theoretical framework is then employed to construct a supervised machine learning model of scansion²⁰.

The predominating pattern in all MHG verse is an alternation between stressed and unstressed syllables (Tervooren, 1979). MHG epic verse employs trochaic tetrameter: each line has four feet, and each foot is a trochee; this is known as the Vierheber for the four lifts (stressed syllables) in a line. Phonologically, a trochee consists of two syllables; the first syllable is stressed, and the second is unstressed. For example, the English word “better” is a trochee, but the word “alive” is not. The famous Longfellow epic poem The Song of Hiawatha is written in trochaic tetrameter, and the first line serves to illustrate this rhythm:

Similarly, the prototypical MHG epic verse foot is two syllables in length, a stressed syllable followed by an unstressed syllable. However, feet can also be filled by one or three syllables (Domanowski et al., 2009). If a foot is filled by one syllable, the syllable must be phonologically heavy (containing a long vowel or ending in a consonant). If the foot is filled by three syllables, either the first two or the last two syllables are often phonologically light²².

It is in these atypical feet that the influence of quantitative meter, where syllable length is a key factor, becomes evident in MHG verse. The foot in a Vierheber must be slightly redefined to account for this. Phonologically, syllable length is measured in morae, a unit of time such that a short syllable has one mora and a long syllable has two morae (Fox, 2000)²³. A foot in MHG meter is more precisely defined as having two morae, not necessarily two syllables²⁴. Indeed the mora, not the syllable, has been called the fundamental unit of MHG verse, although the mora functions differently in this poetic tradition than in its phonological definition (Tervooren, 1979, p. 1). If a foot has only one syllable, the syllable must be heavy because a heavy syllable is two morae and the MHG foot requires two morae. A light syllable cannot be the only syllable in a foot, since it cannot be two morae. If a foot has three syllables, two are often light because half morae are most often light syllables (the first half mora of a pair must always be light), together forming one mora²⁵. The other syllable is analyzed as one mora, yielding the required two morae in the foot. To summarize, a syllable can have one of three length values: mora, half mora, or double mora. A half mora must be phonologically light, and a double mora must be phonologically heavy. Phonological length is otherwise irrelevant and any syllable can be one mora (Heusler, 1956, p. 111).

In addition to length, as a function of morae, syllables are also assigned stress. There are three stress values: primary, secondary, and unstressed. Primary stress is assigned to the first or only stressed syllable in a word. Secondary stress is assigned to any following stressed syllable(s) in that word. All other syllables are unstressed²⁶.

The final mora of the final foot of a line is omitted by convention²⁷. This is construed as a pause, analogous to a rest in music, and receives its own symbol in the scansion ^, even though there is no corresponding word or syllable²⁸. A short, word-final syllable may also be elided before a word beginning with a vowel. Finally, MHG epic verse permits up to three syllables in anacrusis (or pickup notes, a series of syllables at the beginning of a line that do not count in the meter). Phonologically, these syllables may or may not carry lexical or syntactic stress, but metrically, they are always scanned as unstressed morae.

The above features yield eight possible metrical values for any syllable:

Line 1 of Hartmann von Aue's Der arme Heinrich is prototypical. Each foot consists of a stressed syllable followed by an unstressed syllable. There is a one-syllable anacrusis:²⁹

Line 6 also begins with one syllable in anacrusis. The second foot has a stressed mora consisting of two syllables, each one a half mora. The third foot has one syllable; a diphthong allows it to be scanned as long. The final foot has a mora with secondary stress, since the preceding syllable is stressed and in the same word:

Line 34 has no anacrusis, and in the second foot two half mora syllables form the unstressed mora:

Line 8 shows an elided syllable in the second foot:

There are two prevailing treatments of meter in the literature concerned with computational poetic text analysis. One approach takes a known meter and assigns syllables to stress patterns based on such parameters (Hartman, 1996). The second approach assumes nothing of the meter, and seeks to determine it by marking syllables and identifying patterns (Plamondon, 2006; McAleese, 2007; Greene et al., 2010; Agirrezabal et al., 2013; Navarro, 2015). This project draws more on the latter. Previous scholarship has also focused on relatively simple systems of meter and adopted rule-based, statistical, or unsupervised approaches. The hybrid nature of MHG meter, and other complex systems developing out of classical antiquity, makes it difficult to scan poetry using these methodologies, and thus supervised learning presents itself as an attractive method. After initial results of this project were published in Estes and Hench (2016), similar studies were undertaken for English in Agirrezabal et al. (2016), Spanish in Navarro (2017), and Portuguese in Mittmann (2016) with the results here serving as the benchmark.

Because supervised learning is a novel approach to poetic meter, annotated metrical data do not exist for MHG or most other languages. Following the Heusler scansion system outlined above, syllables of MHG epic poetry were annotated into the eight categories of metrical value. The annotated data consist of 450 lines from Hartmann von Aue's Der arme Heinrich, 200 lines from Wolfram von Eschenbach's Parzival, and 100 lines from Wirnt von Grafenberg's Wigalois³⁴. An additional 10% (75 lines of Hartmann von Aue's Iwein) was annotated to be held-out for testing, yielding a total of 825 annotated lines. Summary statistics for all annotated data are reproduced in Table 1.

Syllabification was performed prior to annotation according to the system detailed in Hench (2017), i.e., following the Sonority Sequencing Principle (SSP) with correction from the Legality Principle (LP). Annotation was carried out by the authors, who are both trained in MHG scansion³⁵. In the case that a line exhibits multiple permissible scansions, priority is given to the scansion that best preserves the alternation of stressed and unstressed syllables. If a decision still cannot be made, then stress is determined according to semantic importance. An additional consideration is the syntactic stress of a particular line. Clearly, such evaluations allow some room for interpretation. Nevertheless, on a sample of 100 lines from the annotated data (739 syllables), the Cohen's kappa coefficient for the inter-annotator agreement is 0.962 (confusion matrix given in Table 2). The greatest disagreement for the human annotators was among unstressed and stressed morae, and between unstressed morae and unstressed half morae, implying both some stress and some value disagreement.

We present a new workflow, illustrated in Figure 1, for the automated scansion of poetic meter (MHG and other). The process begins with the syllabification of texts³⁶. Because the syllable is the base unit for many poetic traditions, it is what needs to be annotated. After syllabification is the metrical annotation, requiring experts in scansion and the texts themselves³⁷. After annotation, features must be developed and extracted to help the model understand what part of a verse is important in assigning metrical values. Many of the most important features are phonological. After these features are identified, an algorithm must be developed for obtaining and annotating these features before they, along with the syllables themselves, are sent to the model. After feature identification and extraction, there is a process of development and validating the model, in order to choose the most suitable parameters for the task. The model then makes predictions for each syllable based on the features and parameters supplied. The model also yields marginal probabilities for all predictions for any given syllable, i.e., each syllable comes with a list of probabilities for each of the possible metrical values. Simply taking the most probable sequence for any given line can be very accurate³⁸.

For epic poetry, and the model described here, the predictions must be further processed through specific constraints, as the model will not impose strict rules unless instructed to do so³⁹. If the predicted sequence passes each constraint, it is considered the final scansion. If not, the line is sent for further processing. The following tests check for impossible scansions in MHG epic meter:

If the line fails any of the above tests, it is sent for further processing, where, depending on the phonology of the syllables and the rules above, all phonologically possible metrical values as well as the calculated marginal probabilities are combined into every possible sequence for all the syllables in the line. Illegal combinations according to the tests above are ruled out of the set, and the set is then ranked by overall probability. The most probable, legal scansion is then selected. Thus, errors in the model stem primarily from incorrect identification of the language's natural stress, as all certain metrical patterning errors are sorted out. The model itself is intended to account for this natural stress by taking advantage of the information provided to it through the annotated data. The constraints help the model further cut out possibilities that conform to the natural stress, but not the metrical environment (which is relatively weakly learned by the model), yielding an ultimately highly accurate model.

Two baseline models were developed⁴¹: an n-gram model⁴² cascading into regular expressions and a Brill transformation-based model on top of the n-gram model, both using syllables as units, though not explicitly accepting features beyond the syllables and tags themselves. The n-gram model consists of cascading trigram, bigram, unigram, and regular expressions models, i.e., first a value is predicted based on the previous two values, if possible; otherwise it is predicted based on the previous one value, and if the first two models fail, it is predicted solely based on the value probability for the syllable itself. If the syllable did not appear in the training data, and it cannot be predicted by the first three models, it resorts to regular expressions. Based on MHG scansion theory and observations while annotating, syllables with long vowels were assigned to double mora, short syllables to unstressed mora, and the remaining syllables to mora with primary stress⁴³. The n-gram model was implemented with default settings, and is a very naïve most-frequent-tag approach. This model helps to illustrate the variation between appropriate metrical values for the same syllable.

The Brill model⁴⁴, first assigns the most common label for a given syllable and previous syllable's metrical value from the n-gram model described above and then generates rules to improve the initial estimate of the n-gram model according to the training data. It then iterates over these rules, correcting labels until F-score no longer increases. The Brill model was implemented with a maximum of 200 rules. This approach is very similar to Dimpel's enumeration of hierarchical rules for MHG scansion.

To compare to the baseline, efforts were focused on constructing a Conditional Random Field (CRF) model⁴⁵. The decision to implement a CRF model was predicated on the interpretability of CRF modeling and understanding the primary features for MHG scansion⁴⁶. In the model, each syllable contains the features for the syllable itself, but also those of every syllable in the line, marked by index. The features and their motivations are:

Position within line: the last mora of a line is always stressed (except in masculine bisyllabic cadences), and double morae occur most often in the third foot. If there is anacrusis, these syllables will be unstressed morae.

The model was tuned only on the cross-validated development data and the best performing model was chosen. The resulting best model uses an L1 coefficient of 1.3 and L2 coefficient of 0.001. No further changes to the model itself were made after the model features and parameters were selected⁴⁷. However, the additional rules described above were enforced in order to increase the F-score for epic meter specifically.

The n-gram model found little success even with additional training data, ending with an F-score of only 0.602 (95% CI [0.583, 0.623]). The transformation-based Brill model improved quickly upon the n-gram model, but plateaued at an F-score of 0.810 (95% CI [0.796, 0.838]). Figure 2 shows the increase in F-score with an increase in the number of annotated lines for all models, suggesting that marginal returns to annotation begin to diminish significantly after around 400 lines, or, in the case of MHG, about 3,000 syllables. The final results of the CRF model are given in Table 3 in descending order of frequency in the data, along with a final held-out test set of 75 lines from Hartmann von Aue's Iwein. The preferred CRF model achieves an F-score of 0.925 (95% CI [0.911, 0.939]) on the cross-validated development data and 0.909 on the held-out testing data⁴⁸. Supervised learning thus proves to also be an economical option for languages with complex meter.

The top ten highest scoring features of the CRF model and rules of the Brill model are given in Table 4. It is evident that the CRF model takes advantage of the phonological features provided, an advantage over the baseline models. Top CRF features (1) and (5) suggest any heavy syllable is likely stressed, and often a stressed mora. The CRF model also discerned cadence from the line patterning, exhibited in top CRF features (2) and (4), noting that except for the rather uncommon occurence of a cadence with a divided lift in the last foot (masculine bisyllabic cadence), the last syllable is always a stressed mora. Elision appears frequently in the top CRF features (3) and (6). Anacrusis is recognized in top CRF features (7) following the prototypical patterning:

Where there are eight syllables, if seven syllables down the line is the last syllable of the line (EOL), and alternation is regular, that focal syllable will be unstressed in anacrusis. Top CRF features (8), (9), and (10) each consider words and word boundaries, specifically that double morae often occur at the beginning of a multi-syllabic word, and often that word is bisyllabic, with the second syllable ending in “en,” such as “mae-ren” or “rî-ten.” Top CRF feature (10) notes that unstressed half morae often occur after the first syllable of multi-syllabic words (half morae are only stressed when beginning a word).

The Brill model adopts a more general rule for alternation in top Brill feature (1). Notably, the Brill model takes greater advantage of word boundaries in (1) and (2), while these features rank lower in the CRF model. The Brill model inevitably also notes the influence of specific words or prefixes. The unstressed prefix “ge” ranks as a top five rule for the Brill model. If “ist” is two syllables down the line, the current syllable's assignment is changed from stressed to unstressed, or if “ein,” “ich,” or “er” is two syllables away, the original half mora assignment is changed to an elision.

The scores from both models confirm extant MHG metrical theory (as it was employed for the annotation), but suggest new methods of approach for students of MHG meter. Instead of first marking stress, as suggested by Minimalmetrik (Tervooren, 1979) and the pedagogically oriented website Mittelhochdeutsche Metrik Online (Domanowski et al., 2009), it may be useful for students to first determine the cadence and anacrusis by counting the number of syllables in the line, and looking for heavy syllables at the end of the line. Stress can then be marked in the remaining syllables and metrical values can be assigned based on phonological features. This method may be particularly useful for non-native German speakers, who may have less feeling for the natural stress of German. These results and insights support our feature decisions and our implementation of a CRF model.

Investigating the errors and challenges of a supervised model presents the opportunity for the greatest new insights into the field and the advantage over an unsupervised approach. The confusion matrix for the CRF model in Table 5 shows the errors made in the prediction of the held-out data. The model has the most trouble predicting both stressed and unstressed half morae, particularly the latter. This situation is mirrored in the human inter-annotator agreement matrix, demonstrating, as may be expected, that the machine learning model makes similar errors to the human annotators. The unstressed mora and half mora confusion, common in both human and machine annotation, is understandable, as these two are the most phonologically ambiguous metrical values in MHG meter. Double morae, stressed half morae, and elisions all have the phonological restrictions listed above, and stressed morae are evidently less confused with double morae, likely due to clear alternation in the surrounding environment. Unstressed morae and half morae have hardly any restrictions (only that they are likely not heavy syllables). This then generates further stress confusion between unstressed morae and stressed morae seen in both the computer model and human annotation.

If an algorithm can be trained to scan MHG meter similar to how a human does, it may be interesting to see what is considered difficult for the algorithm. This can be computed by averaging the marginal probabilities calculated by the CRF model. The lower the average probability for a line, the less confident the model is about its provided scansion, and vice versa. With the model, this can be computed for any text (annotated or not), but let us first look at the model text used extensively for annotation and instruction, Hartmann's Der arme Heinrich. Unsurprisingly, the easiest lines for the model to scan are lines that hold true to the trochaic tetrameter patterning, inclusive of the common one syllable anacrusis:

In these examples we also see very distinct prosodic stress patterning. “sus,” “ouch,” “mîn,” “ber,” “ge,” “ten,” “ge,” “dez,” “ein,” “ter,” “ge,” “ret” are all common unstressed MHG syllabes both in poetry and prose, while “trouc,” “mich,” “tum,” “wân,” “frum,” “sô,” “sun,” “hin,” “rit,” “sô,” “lêr,” “was” are all either semantically significant, or heavy, stressed syllables. Moreover, the stress of all multi-syllabic words is clear: “gefrumten,” “gesundez,” “gelêret,” and “verschaffen” have unstressed prefixes, while the rest follow the typical word-initial stress. Any MHG scholar would notice the clear trochaic quality of these lines, and few would disagree with the typical trochaic scansion. One must also wonder how the poets understood and wrote these lines. Were they particularly easy to craft? Do they carry less importance in the story? Or are these lines particularly true (and just not informative?), because the poet did not need extra effort to fit the truth into a legal line of MHG poetry? Rhyme and rhythm together can be restrictive or prescriptive forces acting on a medieval poet. They can force poets to write a verse slightly different than the original thought in order to fill or fit the meter, or complement the rhyme. Thus the selected words were not only selected for sematic suitability, but for formal effect. They may not communicate the full truth (Mertens, 2005, p. 194) (Cramer, 1998, p. 180).

The computer model has difficulties with foreign words, outlier line lengths, and uncommon prosodic and metrical patternings. Belows are the lines about which the model was least confident, even though it correctly scanned (7), (9), and (10).:

While the Latin in example 6 does not pose any problem for a human scanner trained as a medievalist, the model cannot identify the long syllable in speculātor, and having learned MHG, it would never presume a stressed syllable on the third syllable of a multi-syllabic word⁶¹. The marginal probabilities in Table 6 are striking compared even to the other difficult lines, as the model is unsure about nearly every syllable⁶². The other troubling cases are more relatable. In example 7, we are confronted with the minimum number of syllables that a MHG epic verse is permitted to contain, one which the model nearly guesses correctly. Adding to the difficulty is that each word is monosyllabic, and as documented above, the model prefers bisyllabic words as double morae. The double morae are also only two characters (or phonemes) in length, an adverb and a preposition. Table 7 shows that the model is not confident about any of the assignments except for the very last syllable, which as a monosyllabic ultima, is likely a stressed mora.

Example 8 with it's marginal probabilities in Table 8 appears as classic trochaic tetrameter following the form of an easy prediction for the model, yet the natural stress of the bisyllabic “alle” prevents this scansion, forcing “mir” to be in a stressed position in the preferred scansion. The model is least confident about the three syllables it in fact scans incorrectly, (“mir al-le”) but evidently believes the alternation to be the stronger choice than a midline, monosyllabic double mora followed by a divided lift, which itself is a rare occurrence.

While the model correctly predicts example 9 (see marginal probabilities in Table 9), it has little confidence in the middle of the line. A two syllable anacrusis is not uncommon, though not frequent, and the two light, open syllables “de” as a stressed syllable and “ne” as a final stressed syllable further add to confusion. Although to give the model the benefit of the doubt, “salerne” is a proper noun.

The model also correctly predicts example 10 (see it's marginal probabilities in Table 10), though again MHG prosody would not suggest “dem” or “ouch” as double morae. The duration of the line is typical and the marginal probabilities confirm this. It is particularly striking in this example that the model is very uncertain about the beginning of the line. While “dem” is clearly a rare double mora, in this position it would even be considered a rare stress, and would typically be scanned as part of the anacrusis. In contrast to the beginning of the line, the model has great confidence in the end of the line, where “ze” would commonly be unstressed (often even elided or in a divided lift), and the heavy syllables “niht” and “wol” are assigned the remaining stresses.

Example 11 shows another outlier in terms of line length (10 syllables, see it's marginal probabilities in Table 11). Whether or not we accept “fremeden” as three syllables or two (“fremden” is attested in manuscript A) the line begins with a two syllable anacrusis (notably, only one word), and ends in a three syllable word, the first syllable of which is unstressed. Once again, the syllables about which the model is least certain are also those incorrectly scanned. Yet the model evidently believes a double mora for “tôt” and a divided lift are less likely than retaining alternation. The masculine bisyllabic cadence, particularly difficult to scan on first read, is correctly identified.

These marginal probabilities additionally allow us to calculate the difficulty of scanning any given MHG Vierheber text as a whole (and even specific sections of any text). Although we are determining difficulty for the model, we have shown above that the model appears to approximate a human annotator. Thus, difficulty for the model may be reasonably inferred to represent difficulty for a human annotator. This can be computed by taking the average of each syllable's maximum marginal probability over the syllables in a line. In this sense, each syllable has a marginal probability for each possible metrical value⁶³. The examples illustrate that the typical trochaic tetrameter causes problems for neither the model nor the human scanner, while unexpected double morae and longer anacrusis are cause to stop and think, particularly when syllables with relatively few phonemes, or monosyllabic words, are properly assigned double mora value. To sort the epic Vierheber texts in the Mittelhochdeutsche Begriffsdatenbank (MHDBDB)⁶⁴ corpus by difficulty of the meter, the median and mean marginal probabilities for all lines in each text are calculated (Table 12). While Konrad von Würzburg and the anonymous author of Reinfried von Braunschweig utilize the ringing cadence frequently, Ulrich von Liechtenstein does not, yet both do so consistently and in a predictable manner that distinguishes them from the rest of the texts. The major use of simple trochaic tetrameter, or double morae only in the penultimate foot, likely further pushed texts toward the top of the list (evidenced by the model's ease in predicting strictly trochaic verse). An odd mix of texts appear at the bottom of Table 12. Both Ulrich von Türlin's Willehalm, or Arabel, and Wolfram's Willehalm evidently employ more difficult metrical schemata, as does Der Stricker's Daniel von dem blühenden Tal, perhaps a consequence of his unique Strickerkadenz. Particularly interesting is the difficulty of scanning Der Welsche Gast. Because Thomasîn was not writing in his native language, his native language being Italian, perhaps he more often confuses stress in MHG and thus creates difficulties for the model despite a very simple trochaic patterning. While this ranking is interesting for scholars and those teaching MHG meter, it cannot be fully validated as such a measure has not yet been considered in the scholarship. Nevertheless, assuming preference for trochaic tetrameter in easier meters this ranking is roughly accurate.

Both the analysis above and the following analyses assume a high degree of reliability in the model to accurately scan poetry from different authors than those in the train and test sets. This certainly harbors potential bias. The training and testing data authors were chosen for their generality and the degree to which it is believed they were imitated by other authors in the corpus. While additional data from each author were not annotated, these authors all followed the same principles and framework as outlined in Heusler's theory. The features given to the model were decisive for all authors of MHG epic poetry. However, it is certainly possible other authors viewed word stress differently due to geographic or other differences. Future work should validate the model's performance on a variety of MHG epic poetry texts.

Perhaps the most interesting aspect of MHG verse is the beschwerte Hebung, or double mora. Double morae allow for a syllable to carry twice the metrical weight (and likely thus twice the duration) of a normal syllable. The use of double morae is often considered to be an important stylistic choice in indicating semantically, or contextually, important words in a verse: “only then did the monosyllabic foot become a “declamatory machinery”; it exhilaratingly disrupted the up and down pacing and increasingly yielded the natural stress of the language” (Heusler, 1956, p. 118). Since a double mora occupies an entire foot, the following syllable is necessarily stressed, since it is the beginning of the next foot. Hence the disruption of the otherwise naturally occuring alternation. Heusler also notes that double morae were quite common in early MHG epics such as Heinrich von Veldeke's Eneide, and even had an “altertümlich” (“antiquated”), effect in later works containing many double morae, such as Hartmann's Erec and Gregorius (Heusler, 1956, p. 101).

The trend began to move away from this “Germanic” characteristic toward adopting a more strict trochaic style from the French tradition, seen in Rudolf von Ems' Alexander and nearly eliminated by Ulrich von Liechtenstein and Konrad von Würzburg, who aim for almost exclusively strict stress alternation (Heusler, 1956, pp. 101, 118). Heusler understands Konrad as the endpoint, after whom German verse began to be written more freely once again. Table 13 confirms most of these observations. Of these texts, the five most common double morae are: “rîche” (“rich,” “powerful”), “waere” (“would be”), “maere” (“story”), “ere” (“honor”), “mêre” (“more”) (closely followed by “sêre” (“very”)). All double morae must be heavy phonologically, but it is interesting that all of the most frequently occurring double morae have front vowels, and all but rîche have an open syllable (the velar fricative “ch” is construed as ambisyllabic in MHG). Another phonological similarity among them is that each begins with a sonorant consonant (/m/, /n/, /w/, /j/, /l/, /r/)⁶⁵, and all, except for “rîche,” end in “re.” Sonorant consonants are voiced consonants with continuous airflow faciliated by minimal obstruction in the vocal tract. This is in contrast with obstruent consonants, such as stops (e.g., /p,b/) or fricatives (e.g., /f,v/), in which a greater occlusion in the oral cavity occurs. Furthermore, sonorants are typically louder than obstruents. In preferring sonorant consonants in double mora syllables, MHG poets clearly aimed for the greatest resounding word to place in the double morae position, perhaps pointing to a greater significance of the vocal performance tradition in MHG epic verse than has previously been acknowledged. Since open syllables allow for an unobstructed flow of air from the mouth, they may be preferred for notes of extended length (or melismatic syllables), especially considering the relative dearth of open, heavy syllable words in MHG. Table 14 shows the most common double mora for each text. It is evident that double morae contribute heavily to the characterization of a given text, which can come as no surprise given that double morae would present themselves most prominently in memory. These are also concepts that are often studied for their respective text, such as “ere,” “maere,” and “rîche.”

Heusler was particularly interested in the variety of ways a foot could be filled with metrical values. To measure Heusler's diversity of “Versfüllung” (filling of the verse) in its entirety, we adopt a popular measure of diversity originally developed in the context of information theory and widely used in environmental science, namely Shannon entropy (Shannon, 1948-07). Shannon entropy fits this application well, considering that Shannon's original problem dealt with string prediction given a set of characters. The entropy measure quantifies the degree of certainty in predicting a random character from a string dataset, given a finite number of characters. Similarly, a useful measure of “Versfüllung” entails the degree of certainty in predicting a specific foot or line. To this end, we calculate the Shannon entropy for a complete foot (excluding anacrusis and the last foot) and for the entire line, sampling 1,000 feet with replacement from each text. The results are shown in Table 15. The earlier, more “Germanic” texts display a wider diversity in metrical patterning, while Ulrich von Liechtenstein and Konrad von Würzburg aim toward monotonous trochees. We also see all the works attributed to Hartmann von Aue in the top ten for diversity. Save Parzival and Der Welsche Gast, the top ten contains the works most often discussed by scholars.

This paper has presented a new approach to a very old problem for medieval German scholarship. Investigating the meter of this tradition poses unique challenges to literary scholars, philologists, and computational linguists alike. By constructing a supervised model of the meter, this paper demonstrates the benefits of a quantitative corpus-wide analysis enabling us to characterize its idiosyncrasies and suggest improvements to the current pedagogical approach. Moreover, this approach has proven generalizable to other traditions, having been taken up by scholars working on other languages with the results presented here as baseline⁶⁶. A promising extension of this work would be a comparative analysis, particularly in the medieval context, as it is well-known that these traditions were influenced by their contemporaries.

All authors listed have made a substantial, direct and intellectual contribution to the work, and approved it for publication.