Metrical position has long interested scholars of Greek hexameter poetry. In his Encheiridion dia Metrôn (“Handbook on Meter”), Hephaestion of Alexandria (2nd c. CE) referred to positions within meter as χώραι (“places; positions,” cf. LSJ s.v. χώρα 3) and used the term to describe places in the line that contain various types of metrical “feet” (πόδες, cf. [LSJ] s.v. πούς 4), such as the dactyl (‒ ⏑ ⏑) and spondee (‒ ‒), as well as the “final” (τῆς τελευταίας, 7.1) position that may contain syllabic diversity, such as catalexis.[1] Aristides Quintilianus (circa 4th c. CE) likewise used χώρα to describe metrical position in his Peri Musikês (“On Music”), including the “first places” (ταῖς πρώταις χώραις, 1.24.27) of feet in the line (cf. [van Ophuijsen 1987, 82] [Winnington-Ingram 1963]). But it was not until the early 20th century that scholars interested in the statistical analysis of meter systematized notation for all possible positions of linguistic phenomena in the hexameter line; of these efforts, [O’Neill 1942] has gained the most currency.[2] Later, [Giangrande 1959] and others Latinized the terminus technicus from χώρα to sedes (“seat; place”), and now the term is ubiquitous in philological studies of metrical position.

With this greater precision, scholars have examined various forms of repetition in hexameter according to their metrical position. These studies largely focus on articulating metrical tendencies, such as colometric patterns [Porter 1951], [Barnes 1986] and the primacy of caesurae (τομαί) at certain sedes [Fränkel 1926], [Beekes 1972]. [3] In particular, [O’Neill 1942] discovered what he called the “localization” of “word-types,” that is, the “concentration of occurrences (of specific metrical shapes) in but a few of the possible positions” (114). Following O’Neill, [Porter 1951] argued that such tendencies established “patterns of expectancy” or norms in the mind of poet and audience, and philologists have begun to explore the potential intertextual, stylistic, cognitive, and literary effects of these patterns, for example, in [Giangrande 1967], [White 1986], [Hagel 1994], [Kahane 1994], [Martin 2000], [Forstall and Scheirer 2012], [Schein 2015, 93–116], and [Forstall and Scheirer 2019]. [4]

These studies have provided useful data and promising applications, but their potential has been somewhat constrained by limitations in scope, objects of analysis, and at times computational media. O’Neill treated only a relatively small number of lines, though his survey has been expanded and the data verified by [Porter 1951], [McDonough 1966], [Hagel 2004], and [Forstall and Scheirer 2012]. A lack of aggregate statistics on repeated words by sedes has restricted intertextual readings to the examination of infrequent words, hapax, or dis legomena, for example in [McLennan 1977]. [5] Even inquiries into anomalous behavior such as breaks in Hermann’s Bridge (that is, avoidance of word end between the biceps [two short elements] of the fourth foot [Martin 2000], [Schein 2015]) have been confined to a few authors or passages, due to a lack of available data. Existing digital tools for identifying repetitions in hexameter poetry — for example, the Thesaurus Linguae Graecae [TLG] or Perseus Project under PhiloLogic [PhiloLogic], for searching corpora by word list, lemma, or text string; the [Chicago Homer], for repeated phrases; and [Tesserae], for intertexts by n‑gram matching [Forstall et al. 2015] — do not take into account metrical position. Future work on metrical position in Greek hexameter needs new methods and access to data in order to identify repetitive phenomena in meter more accurately and completely. [6] With such information, scholars can then better discern their linguistic causes and potential poetic effects.

In this article, we introduce SEDES, a software system for identifying, quantifying, and visualizing metrical position in ancient Greek hexameter poetry. Like intertextualist studies of metrical position, SEDES at present focuses on the repetition of words — more specifically, of lemmata. Our present purpose is to describe the design of the SEDES system and demonstrate a sample of its utility. [7] Engineering the system required bringing together existing resources in the processing of Greek poetry, as well as the creation of new processes, measurements, tests, and visualizations, all of which aid researchers of Greek literature and otherwise in the processing of poetic texts for computer and literary analysis and, more generally, provide a method that benefits the quantitative analysis of repetitive language in meter. In what follows, we show how SEDES generates these data, before giving examples of its application to Greek hexameter poetics, in particular the fields of oral formularity and intertextuality.

The core function of SEDES is to assign a numeric value — an expectancy score — to every word in a work of verse. The expectancy of a word is a quantification, in a sense we will define later, of how frequently that word’s lemma appears at a given sedes in a corpus of works. After computing expectancy scores, SEDES provides ways of visualizing and interacting with them. The SEDES system is composed of a pipeline of programs, each of which performs a portion of the processing task. See Figure 1.

The input to the pipeline is a set of XML documents marked up according to the TEI Guidelines [TEI]. The selection of documents defines the corpus relative to which expectancy scores are computed. In developing SEDES, we have used 12 TEI texts from the Perseus Project [Perseus], totaling about 73,000 lines, with a minimum length of 479 lines and a maximum of 21,356. See Table 1 for a listing of texts, which span more than a millennium and comprise a variety of styles. We often define the corpus as all 12 works, but the system makes it possible to work with only a subset, in order to include or exclude certain authors or eras, for example.

Though similar techniques could be applied to other forms of verse, SEDES is specially adapted to hexameter. In hexameter, vowels are distinguished by length. A line consists of six feet, which each may be either a long syllable followed by another long syllable (a spondee, denoted “– –”), or a long syllable followed by two short syllables (a dactyl, “– ⏑ ⏑”). The metrical shape of a word — its pattern of long and short syllables — limits the places (sedes) in a line it may appear. (Though there is some flexibility: a word may, subject to certain rules, sometimes be reinterpreted to have a different metrical shape than it would otherwise have, in order to fit the meter.) Even given the range of permissible “slots” for each word, most words tend to appear at some sedes more often than others. It is this non-uniform distribution of word placements that SEDES is designed to analyze.

The first program in the SEDES pipeline, tei2csv, assigns a lemma and a sedes to every word in the corpus. (We consider multiple instances of the same word separately — the same word in different lines may appear at different sedes, for example.) Later parts of the pipeline will operate, not on the original words of the text directly, but on the “lemma–sedes pairs” to which they are mapped by tei2csv. Concretely, tei2csv does the following three steps of segmentation, lemmatization, and scansion for every document in the corpus:

The output of tei2csv is a collection of CSV files, one for each TEI file in the corpus. The CSV files map every instance of every word in the corpus to the lemma and sedes of that instance, what we call a lemma–sedes pair. The next program in the pipeline, called expectancy, takes these CSV files as input and does the statistics necessary to compute expectancy scores:

The output of the expectancy program is another CSV file that maps every observed combination of lemma and sedes to a numeric expectancy score. The final program in the pipeline, tei2html, takes as input the expectancy CSV file and the TEI of any single work — which may or may not be part of the corpus that was used to define expectancy — and produces an output visualization of the work:

We will describe the above steps in detail in the subsections that follow. But first, we will walk through an example of applying the SEDES processing pipeline to book 1, line 1 of the Odyssey [Perseus – Odyssey] from start to finish.

In the source TEI file, the line looks like this: [8]

<l>a)/ndra moi e)/nnepe, mou=sa, polu/tropon, o(\s ma/la polla\</l>
                     

The <l> and </l> XML tags delimit a line. The text between the tags is Beta Code [TLGBetaCode], a method of representing written ancient Greek using ASCII characters: “a” represents the letter alpha; “)”, “/”, “\”, and “=” are various diacritics; and so on. The tei2csv program isolates the line from the XML markup and decodes the Beta Code to yield a line of verse represented in Unicode:

ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ
                     

(“Tell me, Muse, about the versatile man, who very many…”) The program then scans the line metrically, marking each syllable as long (notated “–”) or short (notated “⏑”). A long syllable counts for 1 position and a short syllable counts for 0.5. The scansion of the example line is:

ἄν	δρα	μοι	ἔν	νε	πε,	μοῦ	σα,	πο	λύ	τρο	πον,	ὃς	μά	λα	πο	λλὰ
–	⏑	⏑	–	⏑	⏑	–	⏑	⏑	–	⏑	⏑	–	⏑	⏑	–	–
1	2	2.5	3	4	4.5	5	6	6.5	7	8	8.5	9	10	10.5	11	12
                     
				

The sedes of a word is the sedes of its first syllable. In this example, ἄνδρα is at sedes 1, μοι is at sedes 2.5, and so on. Separately from scansion, every word in the line is mapped to its lemma. Here, the word ἄνδρα maps to the lemma ἀνήρ, μοι maps to ἐγώ, and so on for the rest of the words. The output of this process is a lemma and a sedes for each word: a lemma–sedes pair. The calculation of sedes and the finding of a lemma are independent operations: it is the syllables of the original words of the line, not their derived lemmata, that determine sedes.

The tei2csv program emits a CSV file with one row per input word, representing the word’s lemma, sedes, and other metadata.

Expectancy is a function of lemma and sedes jointly: it measures, for each lemma, how that lemma is distributed over the possible sedes, in the context of the overall corpus. Having run tei2csv on the Odyssey, we run it again on the other works of the corpus to obtain the necessary context, in the form of a collection of CSV files that give a lemma and a sedes for every word. The expectancy program takes all these files as input, analyzes the statistical distribution of sedes for each lemma, and outputs another CSV file that maps lemma–sedes pairs to their expectancy scores, using mathematical formulas we will define below. An excerpt of the output of the expectancy program is shown below. The x column counts the number of occurrences of a lemma–sedes pair throughout the corpus, and z shows the expectancy of that pair. From this sample output, we see that the expectancy of the lemma ἀνήρ (“man”) at sedes 1 is +1.11, that of ἐγώ (“I”) at sedes 2 is −0.13, and so on.

Finally, the tei2html program takes as input the TEI file of the Odyssey along with the expectancy CSV file. tei2html renders a human-readable HTML representation of the text, optionally highlighting each word according to its expectancy. One visualization style is shown below, with words shaded according to their expectancy: low expectancy is dark and high expectancy is light. Other styles will be explored in the section on visualization.

ἄνδρα μοι ἔννεπε, μοῦσα, πολύτροπον, ὃς μάλα πολλὰ

The programs that constitute SEDES are written in Python 3. Running SEDES from start to finish on every work in our corpus (12 TEI files, 73,000 lines, and 490,000 words) on a 2019 MacBook Pro takes about one minute. About 45% of the time is spent on segmentation, lemmatization, and scansion; 9% on expectancy computation; and 46% on generating visualization output.

Scansion is an operation on individual lines, and lemmatization is an operation on individual words. SEDES begins by breaking a TEI document into lines, and its lines into words.

Segmentation into lines is fairly straightforward. Lines are delimited by either the l element, which encloses lines; or the lb element, which separates them: [9]

Having isolated a line, we decode its text contents from Beta Code to Unicode. We extract words from the line by splitting on sequences of non-letter, non-diacritic characters. For this purpose, the apostrophe character (’), used to mark elision in words like ἀλλ’, is considered to be a letter character. Some TEI documents use apostrophes to mark quotations, which complicates word extraction by giving the character a second meaning as punctuation. When we discovered uses like this, we amended it in the source document using quotation markup.

SEDES needs a way of defining which words count as “the same” for the purpose of computing distributions over sedes. Our instrument for deciding which words are considered equivalent is the lemma. [10] In lexicography, a lemma is the dictionary headword with which all its morphological variants are associated. Ancient Greek is a highly inflected language, one in which words take on many forms according to their grammatical function. The lemma unifies the many related forms of a word and bundles them under one label. For example, the genitive singular word ἀοιδῆς and the dative plural ἀοιδαῖς both have the same lemma, ἀοιδή (“song”); the two words therefore fall into the same bucket for the purpose of computing statistics. (Note, however, that lemma assignment does not affect the scansion procedure that will be described in the next section; scansion uses the words of the original text, pre-lemmatization.) As a semantic matter, lemma corresponds to lexeme, an item of meaning removed from a language’s inflectional rules; we may think of a lemma as a representative of a lexeme, standing for a group of related words. [11]

Mapping a word to its lemma is not trivial [Heslin 2019, 391]. But strictly speaking, we do not care about a word’s lemma per se. All we care about is when two words have the same lemma. In mathematical terms, equality of lemmata is an equivalence relation that partitions the universe of words into equivalence classes: all words that have the same lemma are in the same class, and no two words in the same class have different lemmata. [12] As long as a lemmatization algorithm is consistent, it may as well output abstract tokens like “x1234” as literal Greek words. [13] This is to say that the consequence of a word being lemmatized incorrectly is that the word ends up in a different class than it should: it is missing from its “true” class and is instead grouped with some other class of words (or a class by itself). Whether such an error makes a meaningful difference in the statistics depends on how many times the word occurs, and the sizes of the other lemma classes. In SEDES, we use the backoff Greek lemmatizer [14] of the Classical Language Toolkit [CLTK]. The backoff lemmatizer employs a chain of sub-lemmatizers (which are various forms of dictionary lookup and regular expression transformations [Burns 2018], [Burns 2020, 161–62]), trying each in turn until one returns a result. If no lemma is found by any of these techniques, the last-resort fallback is to use the word itself as the lemma. The fallback occurs for about 2% of words in the corpus (7% of unique words). A random sample of 100 lines suggests a 98.6% accuracy rate: we identified 10 misattributed lemmata among the 721 words in Iliad 13.563–662.

We augment the CLTK lemmatizer with a preprocessing step that attempts variations on accent marks: if the initial lemmatization fails, the lemmatizer applies one of a small set of accent transformations, namely, changing a grave accent to an acute accent, or removing an acute accent.[15] The pre-transformation step makes a few thousand words lemmatizable that would not be otherwise. We further have the lemmatizer first consult a hardcoded list of our own, manually determined lemmata, which we use this list for words that are common in our corpus but for which automatic lemmatization fails.

The computation of expectancy requires a word’s lemma and sedes. In the previous step we found the lemma; now we tackle the sedes. Sedes is a byproduct of scansion, which, in the context of Greek hexameter, means determining the metrical value (long or short) of every syllable in a line.[16] Once a scansion is settled, the sedes of a word is determined by the metrical values of the words preceding it in the line. For automatic scansion, we use the Python hexameter module [Ranker 2012]. Here we will briefly describe how the algorithm works.

The first step is to isolate syllables by looking for vowels and diphthongs. Each lexical syllable is assigned a preliminary metrical value according to language rules that are specific to Greek. An example of these rules is that, unless modified by other rules, the vowels “ε” and “ο” are short, “η” and “ω” are long, and other vowels are (for now) undetermined. At this point in the analysis, a syllable may be classified as definitely long, definitely short, or one of a few other values that govern how the syllable may be resolved into long or short in the next step.

Resolution of preliminary metrical values into final metrical values is accomplished using a finite automaton. A finite automaton is a computational state machine that represents (or recognizes) a restricted set of inputs — in our case, the set of properly formed lines of Greek hexameter. The automaton matches lines of hexameter the same way that a regular expression matches a subset of strings. The automaton encodes various rules of the poetic form: for example, that a line contains six feet total; that the first half of a foot must be a long syllable; and that the second half of every foot but the last may be either one long syllable or two short syllables. Each transition in the automaton is marked with both the preliminary metrical values that permit the transition to be taken, and the final metrical value the syllable is to be assigned, when that transition is taken. In general, there is more than one way of fitting a line into the schema of hexameter. For example, one might change a short syllable to a long early in the line, making compensating adjustments to following syllables in order to maintain the same total length. This fact is reflected in the automaton by there being multiple paths from start to finish when there are multiple feasible scansions. Not all scansions are equally good, however. The automaton’s output is biased towards parsimony by weights attached to state transitions, which penalize metrical value assignments that require uncommon metrical rules. The associated final metrical values of the path with lowest weight becomes the scansion of the line.

Occasionally, the automatic scansion algorithm yields either no paths through the automaton, or two or more paths of equal weight. We scanned these problematic lines by hand and added them to a list of scansion overrides, which take precedence over automatic scansions. There are 1,526 entries in the list of overrides, about 2.1% of the lines in the corpus. Manually scanning lines whose automatic scansion is undefined or ambiguous requires human expertise in the form of meter being analyzed. The CSV output of tei2csv records the source of the scansion in the scanned column — either manual or auto. The num_scansions column counts the number of equally weighted automatic scansions found, usually 1.

Once every syllable in a line has been assigned its metrical value, it is straightforward to determine the sedes of each word. Start at the beginning of the line and sedes 1. Advance the sedes by 1 for a long syllable, and by 0.5 for a short syllable. The sedes of a word is the sedes of its first syllable. The sedes of words in a line are not all necessarily distinct. For example, in Iliad 1.241 [Perseus – Iliad], σύμπαντας· τότε δ’ οὔ τι δυνήσεαι ἀχνύμενός περ, the two adjacent words δ’ and οὔ share sedes 5, because they are pronounced as one word.

To evaluate the accuracy of the automatic scansion algorithm, we randomly sampled 1,200 lines from the entire corpus and manually checked their automatic scansion. 1,195 lines (99.6%) were scanned correctly.

We now come to the central question: how expected is each word, given its lemma and the sedes at which it appears? Following [Porter 1951], we call the measure of expectedness “expectancy.” Expectancy is not a property of lemma only or of sedes only, but of both considered jointly. For each lemma–sedes pair, we ask: given the distribution of this lemma in the corpus, is this sedes usual or unusual?

Our metric of expectancy is the z‑score, which measures distance from the mean of a distribution in units of the standard deviation [Hoover 2013, 520–21], [Allen 1988, 6–7]. The formula for the z‑score of an observed value x is z = (x - μ)/σ where μ is the mean of a population and σ is its standard deviation. A z‑score of +1.5, for example, describes a value that is 1.5 standard deviations greater than the mean. Values greater than the mean have positive scores, and values less than the mean have negative scores. We count how many times a certain lemma appears at a certain sedes, and the z‑score expresses whether that count is greater or less than would be expected, given the counts at that and other sedes.

In our definition of expectancy, different lemmata do not interact. [17] The expectancy of a lemma at a particular sedes depends only on the distribution of that lemma. For example, in our corpus, the lemma βοῦς (“cow”) appears 448 times, while χέλυς (“tortoise”) appears only 8 times. It is more “expected,” then, in some sense, for any given word to be βοῦς than to be χέλυς. But we are not interested in comparing βοῦς versus χέλυς; rather we weigh βοῦς against other instances of βοῦς, and χέλυς against other instances of χέλυς.

To establish corpus-wide distributions of lemmata and sedes, we repeat the three previous steps — segmentation, lemmatization, and scansion — for every work in the corpus, using the tei2csv program to create a collection of work-specific CSV files with a lemma and sedes for every word. Then a separate program, called expectancy, takes as input the whole collection, computes the expectancy of every unique lemma–sedes pair across the entire corpus, and writes a table of computed expectancy values to another CSV file. This table will be used in the next step to produce a visualization for a single work.

The expectancy program begins by counting the number of occurrences of each unique lemma–sedes pair. Then, for each lemma, it examines the lemma’s distribution over the possible sedes. Before applying the z‑score formula to the table of sedes counts, we weight each count by itself. For instance, the weighted mean of the distribution of counts [1, 2, 2, 15] is not (1 + 2 + 2 + 15) / 4 = 5, but rather (1×1 + 2×2 + 2×2 + 15×15) / (1 + 2 + 2 + 15) = 11.7. This is because the counts represent 20 total words, not 4; since the majority of words appear at a sedes having a count of 15, a representative count should be closer to 15 than it is to 1 or 2. We similarly weight the standard deviation calculation. To be precise, we use the following formulas for the weighted mean and standard deviation of a vector of sedes frequency counts [c1, …, cn]:

$$\begin{align*} \mu &= \frac{\sum_{i=1}^n c_i \times c_i}{\sum_{i=1}^n c_i} \\ \sigma &= \sqrt{\frac{\sum_{i=1}^n c_i \times (c_i - \mu)^2}{\sum_{i=1}^n c_i}}. \end{align*}$$

The output of the expectancy program is a CSV file that maps lemma–sedes pairs to their respective z‑scores.

The z‑score formula is not defined for distributions whose standard deviation is zero. Such a situation arises when the frequency counts for a lemma are exactly equal in every sedes where it appears. Examples are ἑκηβόλος (“far-shooter”), which occurs 42 times but always in sedes 6.5, and Κίλλα (the astyonym “Killa”), which occurs 4 times total, twice each in sedes 1 and 11). Important special cases of this general phenomenon are words that appear only once or twice in the corpus, such as the hapax legomenon ἑλώρια (Iliad 1.4, lemma ἑλώριον). Expectancy is also undefined for lemmata that never appear in the corpus — those whose table of frequency counts is everywhere zero. This last situation may occur only when when the work under consideration is not part of the corpus that defines expectancy: if it had been, all its lemmata would necessarily have a nonzero count in at least one sedes. For the purposes of visualization, we treat undefined z‑scores as if they were zero; i.e., neither more nor less frequent than expected. Figure 2 shows the distribution of z‑scores for every word in the entirety of our corpus.

Even disregarding lemmata, it is not the case that all sedes are equally likely to be the site of the start of a word. A simple demonstration of this fact is that every line of hexameter contains a word at sedes 1 (the first word), but whether there is a word at sedes 2 depends on the how long the first word is. Figure 3 shows the distribution over sedes for the works in our corpus. One might reasonably suggest applying a correction to the expectancy formulas to adjust for an assumed a priori distribution over sedes. We have chosen not to do so, reasoning that a word’s appearing at an uncommon sedes is itself a sign of unexpectedness.

Further exploration and justification of the utility of z‑scores as a measure of expectancy appears below in the section “Interpretation of z‑scores.” We now show how expectancy scores feed into the final step of the pipeline, namely visualizing numeric expectancy data.

The data files emitted by the previous steps lend themselves to various forms of analysis. Our specific goal is to produce a readable visualization of the source text, with every word highlighted according to its expectancy.[18] Such a visualization enables a human reader to quickly visually peruse and identify words whose expectancy is much different than expected, aided by the context of the surrounding text. Words thus identified may be worthy of further investigation.

The processing pipeline terminates in the tei2html program, which takes as input a TEI text and the table of lemma–sedes expectancy scores output by the expectancy program, and produces a visualization that uses HTML, CSS, and JavaScript. Like tei2csv, tei2html isolates words from its TEI input and assigns each one a lemma and sedes. It looks up the expectancy scores of the lemma–sedes pairs, and emits an HTML document where every word is annotated with its expectancy and other metadata.

The HTML document provides an interactive selection of visualization styles. A simple and effective way to depict expectancy is to shade the color of words on a scale from dark to light.[19] In this style, words with higher expectancy fade into the background, and those with lower expectancy are visually emphasized (Figure 4).

A variation of this style is a diverging color gradient, which, rather than emphasizing the difference between negative and positive, emphasizes distance from the mean. In this style, z‑scores close to zero are visually diminished, while those that are large positive or large negative are highlighted in saturated and contrasting colors. Here, negative z‑scores are red and positive z‑scores are blue (Figure 5).

Words vary in their length and visual density; of two words shaded identically, the longer word may be visually more prominent, simply because up more space. In an attempt to mitigate this potential bias, we have provided alternative styles that attach filled circles of uniform size to words, where the circles are shaded rather than the text (Figure 6). Here, as well, the gradient may be sequential or diverging.

The visualization has an “align to sedes grid” option that vertically aligns words according to their sedes (Figure 7).[20] This option may be combined with any visualization style.

The HTML output provides a panel for selecting visualization options and displaying additional information (Figure 8). Clicking on a word shows its metrical shape, lemma, sedes, and expectancy, as well as the distribution of the lemma over sedes and the resulting z‑scores.

The essential aspect we hope to capture with SEDES is how expected, in some human sense, a lemma is at a particular metrical position. There are many possible ways to quantify expectancy (e.g., frequency charts à la [O’Neill 1942]); the one we have chosen is the z‑score. The z‑score is an adaptive measure that does not assume a specific prior distribution of counts over sedes. Because the z‑score is normalized to the standard deviation of a distribution, it provides a common basis of comparison for all lemmata, whether frequent or rare. Let us take two examples to explore the meaning of the z‑score and how it is affected by the underlying sedes distribution. The two lemmata we will look at both occur over 50 times, but with markedly different distributions.

First, consider the lemma μορφή (“shape; beauty”). It overwhelmingly appears at sedes 11, and only rarely occurs at four other sedes. Sedes 11 is assigned a z‑score of +0.33, whose nearness to zero indicates that it is expected, or unmarked, at this sedes.[21] In contrast, the rarely occurring sedes are assigned large negative z‑scores, less than −3.00, which indicate a low degree of expectancy.

Next, consider the lemma δένδρεον (“tree”). Its distribution is less skewed. It occurs with roughly equal frequency at sedes 3, 7, and 9; still more often at sedes 1, but not overwhelmingly so. This lemma is more likely to appear at sedes 1 than at any other single sedes — but sedes 1 accounts for fewer than half of total instances. In this distribution, a count of 11 is closer to “typical” than a count of 19. The evenly distributed sedes accordingly get negative z‑scores that are relatively close to zero. The sedes with a larger count gets a positive z‑score, farther from zero.

The extreme z‑scores — those that are most negative and most positive — naturally stand out as being worthy of attention. The most negative scores are the rare outliers, the sedes at which a lemma appears much less frequently than usual. The first example above illustrates such a situation. A large negative score is a hint (though not a guarantee) that something unexpected is happening compositionally: perhaps a common word is used in an uncommon way, or as part of an uncommon poetic structure. In the other direction, the most positive z‑scores show where a lemma appears more frequently than usual. Note an apparent contradiction: in order for a lemma to be more than expected at a certain sedes, it must appear there a large number of times — does that not make the lemma actually expected at that sedes? But there is no contradiction, really: large positive z‑scores arise only with counts that are larger than the mean, but which are outweighed by the sum of smaller counts at other sedes. The second example above is such a case. In contrast to the rare outliers signified by large negative z‑scores, large positive z‑scores represent occurrences that occur frequently yet are still unusual in the larger context of the lemma. The diverging color scale visualization options bring out both phenomena.

It is important not to confuse z‑scores with pure frequency counts. A low z‑score does not mean that a lemma itself is uncommon. Just the opposite: it means that a particular sedes is an uncommon one for the given lemma. Intuitively, a lemma’s appearance at one sedes can only count as unusual if there are sufficiently many instances of the lemma at other sedes to establish what “usual” is. Large negative z‑scores are only possible with frequently occurring lemmata. To reach a z‑score as low as −2, there must be at least 5 total instances of a lemma; for −5 there must be at least 26; and for −10 there must be at least 101. (Compare to the empirical distribution of z‑scores in Figure 2.)

It may happen that the demands of poetic form affect word placement and therefore the distribution of sedes. For instance, some lines in a poem may be more or less formulaic than others, and therefore be more or less constrained in their composition. Suppose that in a special subset of lines (invocations, say), a certain lemma falls at a sedes at which it does not commonly appear in other, non-invocation lines. The relatively low frequency of the lemma at its place in an invocation is, then, partially a reflection of the relative rarity of invocation lines. In the subset of lines that are invocations, the lemma may in fact be perfectly expected at a sedes that is unusual in the wider context of the poem. It is possible to imagine specializations of sedes expectancy that take into account additional factors, such as the functional or literary purpose of the lines in which words appear. Doing so, however, requires presupposing criteria by which a work is to be subdivided. Our present purpose is different: to use sedes as a tool to discover where the placement of words has been affected, whether by formula or by any other cause.

We have engineered SEDES to be useful for diverse types of analysis and, by making the code available as free software, to be adaptable to the interests of future researchers of metrical position in Greek hexameter, by itself or in tandem with other digital humanities tools. Most readily, it is designed to compute and visualize the frequency of lemmata. Users can explore the corpus with the visualization (either online or by downloading the program), look for dark shading among the sea of gray, and click for statistics on the lemma. Or, after downloading the program, they can create the CSV file of underlying data and organize it in a spreadsheet according to their own interests, for example by ordering rows by lemma and z‑scores. Once the user finds a word in an unexpected position, they then can interpret its literary significance (see, e.g., [Sansom 2021, 454–60]). As a sample of its functionality in relation to established ways of interpreting Greek hexameter, in what follows we briefly gesture towards the integration of sedes analysis with two prominent interpretative modes: formularity and intertextuality.

SEDES adds granular, novel information to our understanding of formulaic regularity. In oral-poetic theory and Homeric philology, the formula serves as one of the most basic and useful units of composition, though the quality and nature of the formula in epic diction is highly contested.[22] As defined by [Parry 1930, 80], a formula is “a group of words which is regularly employed under the same metrical conditions to express a given essential idea” ([Parry 1971, 272]; cf. [Parry 1928, 16] “une expression qui est régulièrement employée, dans les mêmes conditions métriques, pour exprimer une certaine idée essentielle”). Despite its focus on single and not groups of words, SEDES helps to identify unexpected behavior in constituent words of the group, behavior that should inform our conception of formulaic regularity. Take the phrase πατρίδα γαῖαν, “(to one’s) fatherland.” Using a collated lemma search in the [TLG] or a phrase search in the [Chicago Homer], we find that the phrase πατρίδα γαῖαν occurs 21 times in the Iliad, with 19 instances positioned at line end (after the “bucolic diaeresis” at sedes 9–12).[23] Iliad 15.499 is typical:

There is variance in the preceding elements: most often the phrase is introduced with the preposition φίλην ἐς (“to the beloved (fatherland)”), though three instances at line end lack preceding φίλην ἐς (Iliad 7.335, 13.645, and 15.706). Although the phrase πατρίδα γαῖαν is highly regular and predictable in other respects, two exceptional instances in the Iliad shift its metrical position away from line end:

In the two exceptions, by collating the paired lemmata search or phrase search with the SEDES visualization, we see that there is also a change in the expectancy of the phrase’s constituent parts, πατρίς and γαῖα. Sedes 9 is a natural place for the lemma πατρίς, whether or not part of a formula. While γαῖα remains relatively expected in each position, in sedes 3 and 7 πατρίς is placed unexpectedly (Figure 9).

When comparing the instances of the phrase at Iliad 15.505 and 24.557 with the 19 others at line end, there is a difference in formularity. If you were to ask which instances of the formula πατρίδα γαῖαν are most “formulaic,” it seems reasonable to claim that the 19 instances of the phrase at line end are more “formulaic” than the two that occur elsewhere, due to their regularity in that position of the line. This in itself suggests that not all instances of even a single formula are equally expected in a given metrical position. But we could have seen this shift of phrase even without SEDES, using, for example, the repeated phrase tool of the Chicago Homer or a proximity search for the two lemmata in the Thesaurus Linguae Graecae. What SEDES allows us to see for the first time is that the placement of the phrase at sedes 3 and 7 not only deviates from normal metrical placement for the phrase, it places the word πατρίς, in particular, in a less expected place. In other words, while the phrase is “formulaic” in all instances, it is less so in Iliad 15.505 and 24.557, where it is out of place and where its constituent words, especially πατρίς, stray from their typical positions.

This new information about the differing metrical behavior of constituents of formulae has at least three effects. First, it nuances the notion of the “flexibility” of formulaic language [Hainsworth 1968]. SEDES shows that words within a phrase may behave in different ways qua words, even if they remain contiguous within the phrase and the phrase is not otherwise “expanded” or “contracted.” Future work on epic formularity can adapt and incorporate SEDES to fit different models of concepts central to the idea of the formula. If scholars of epic language who are committed to the empirical investigation of formularity are to define the quality and nature of this fundamental component of epic composition, the sedes expectancy of constituent elements of formulae — individual words — should factor into notions associated with formularity, such as typicality, regularity, expectation, economy, and flexibility.

Second, unexpected constituents of a formula may interact with other literary features of a text. Scholars have shown how the meaning of individual elements of formulae, such as an epithet, can become more or less salient at different moments in the text [Elmer 2015], [Visser 1988], [Bakker and Fabbricotti 1991]. Sedes expectancy may also do something similar when one or more elements of a formula occurs in an unexpected position. Of the two instances above, the more statistically marked instance of πατρίδα is at Iliad 24.557, in which it occurs at a sedes (3) that is more than two standard deviations away from the mean (z = −2.37). In the context of book 24, the unexpected placement of πατρίς (“of one’s father[land]”) concords with the book’s emphatically paternal semantics, several of which align with the sedes of πατρίδα. The final book of the Iliad features a clandestine visit by Priam, the king of Troy, to Achilles’ tent through divine aid. Priam appears suddenly at Achilles’ camp and kisses Achilles’ hands (24.477–9), astounding Achilles and his companions (θάμβος…θάμβησεν…θάμβησαν Iliad 24.482–4), and utters his first words of petition: “remember your father” (μνῆσαι πατρὸς σοῖο Iliad 24.486). As [Edwards 1991, 10] states, “Priam’s first words are a culmination of (the Iliad’s) theme (of father–son relationships).” In this sudden, incipient statement, πατρός occupies sedes 3, a less expected position for the lemma πατήρ (z = −1.24) and the same unexpected sedes as πατρίδα (γαῖα) later. It is notable that of the twenty instances of words with the root πατρ- in Iliad 24, only this πατρὸς, the errant πατρίδα (γαῖαν) of 24.557, and one final instance (24.592) occur in sedes 3. The last time that Achilles addresses Patroklos, whose name etymologizes as “glory (kleos) of the father (patr-),” the name of his dead companion occurs in sedes 3 (μή μοι Πάτροκλε σκυδμαινέμεν, Iliad 24.592) for the only time in the vocative case — a case particularly marked for Patroklos, as the narrator famously speaks it in apostrophe eight times [Allen-Hornblower 2020]. Moreover, as a phrasal search in [Chicago Homer] shows, the lines immediately surrounding the shifted πατρίδα γαῖα are suffused with paternal referentiality, including an interformulaic reference to the fatherly petitions of Chrysês in book 1 (δέξαι ἄποινα Iliad 24.555 ≈ δέχθαι ἄποινα 1.23) and the often parental formula, ζώειν καὶ ὁρᾶν φάος ἠελίοιο, spoken by Thetis about Achilles twice (18.61, 442; cf. 24.562) and by the Trojan leader Anchises after pleading for his “flourishing progeny” (θαλερὸν γόνον) in the Homeric Hymn to Aphrodite (104–5).[24] Sedes expectancy draws our attention to potential cross-effects of the unexpectedly placed πατρίς, related words in the same sedes, and paternal thematics in the passage.

Third, the fact that otherwise “formulaic” phrases, lines, or passages may contain words that are unexpectedly placed can reveal craft where before the reader may have assumed strict regularity. We see this especially at work in passages that are repeated verbatim in two or more places. Take, for example, Ajax’s speech to the Achaians in Iliad 15.560–64, three lines of which are repeated from book 5 (15.562–64 = 5.530–32). We may visualize sedes expectancy and repeated phrases together using SEDES and notation from the [Chicago Homer] (Iliad 15.560–64):

It is immediately apparent that within the passage’s formulae there is variation in the expectancy of individual words. Some phrases contain words that are especially expected in their given sedes, such as the pronoun and epithets (phrases 1–4) on line 560. We see greater disparity beginning on line 561, where, although they occur elsewhere in repeated phrases, words such as ἀνέρες (“men”) and αἰδῶ (“shame”) are less expected. Perhaps what is most interesting is that the lines (passage 10) repeated verbatim from book 5 contain several unexpected placements of words at sedes 4 (αἰδεῖσθε, ἀνδρῶν, and οὔτ᾽). Here, sedes expectancy joins other remarkable stylistic features, such as the pragmatic focus on the participles αἰδομένων and φευγόντων which begin both their lines and sentences opposed rhetorically in antithesis (fighting vs. fleeing). Rhetoric affects word order which, with SEDES, we can now see shifts words from their more typical positions and can result in “stacking” of unexpectedly placed words along particular sedes. SEDES also reveals that formulaic analysis with frequency data is insufficient in articulating the regular or erratic composition of constituent features of this otherwise repetitious material of epic diction, as is especially apparent in longer passages repeated verbatim.

There are likely more ways that sedes expectancy can alter our understanding of epic formularity, the identification and study of which will occupy future research with SEDES. For example, it is clear from the brief look at sedes expectancy and formulae above, in particular the regularity of πατρίδα γαῖα at line end, that formulae too have sedes expectations of their own. Adaptation of SEDES code and methodology could assist in articulating these expectations quantitatively, a function that could then better identify moments when even formulae subvert expectation.

SEDES allows scholars to better locate and qualify intertextual relationships between different passages based on the sedes expectation of lemmata. While the utility of sedes expectancy to intertextuality is argued more extensively in [Sansom 2021], below is a synopsis of the significance of sedes expectancy to words that appear in the same or different sedes in two texts (Figure 10).

Passages that feature the same lemma in the same sedes have different interpretations given the expectancy of the lemma. If a word is expected in a particular position, such as πατρίδα in sedes 9 (z = +0.51 in the Archaic corpus, cf. above), its appearance there in two or more passages should not in and of itself suggest intentional reference or allusion. Rather, it is likely to be the result of typical compositional practice for hexameter poetry, what [Conte 1986] calls modello-codice (“generic model”). But if a word occurs in the same unexpected sedes in both passages, it is more likely to be a direct reference, what [Conte 1986] calls modello-esemplare (“individual model”). An example of this can be found in the highly unexpected placement of the lemma σελήνη (“moon”), which occurs only twice at sedes 6.5 (x = 2, Σx = 157, z = −8.80 in the whole corpus): in the Shield of Achilles passage in both Iliad 18.484 and Quintus of Smyrna’s Fall of Troy 5.8. SEDES provides readers of Greek hexameter the quantitative information necessary for better distinguishing between generic and individual types of intertextuality when regarding the shared metrical position of words.

In the past, scholars would often disregard the possibility of an intertextual relationship if a word occured in different sedes. Sedes expectancy, however, provides a way to identify new intertexts even in cases when there is a difference in sedes. When a word occurs in different sedes that are both relatively unexpected, in both instances the unexpected sedes reflects a break in the pattern of expectancy and thus merits further attention. For example, the name of the goddess Ἀφροδίτη occurs at sedes 6 in Iliad 9.389 (οὐδ’ εἰ χρυσείῃ Ἀφροδίτῃ κάλλος ἐρίζοι) and at sedes 2 in Od. 20.73 (εὖτ’ Ἀφροδίτη δῖα προσέστιχε μακρὸν Ὄλυμπον), both of which have z‑scores of −10.0 in the whole corpus, which are among the lowest of any lemma–sedes pair; the other 99% of the time Ἀφροδίτη occurs exclusively at sedes 10 (x = 200, Σx = 202, z = +0.10).[25] Despite their different sedes, both instances thwart expectations. This fact should cause the researcher to investigate the two further, at which point other collective features emerge: shared language such as the “works of Athena” (ἔργα δ᾽ Ἀθηναίη) in adjacent lines (Iliad 9.390, Od. 20.72) or their presence in character speech by notoriously versatile speakers, Achilles and Penelope; cf. [Martin 1989]. Conversely, in cases in which the expectancy of the word is high in both sedes, or mixed high and low, there is perhaps less reason to suppose intertextuality by sedes is a helpful mode of interpretation. Such statistical data combining word and meter could inform future quantitative intertextuality such as that of [Tesserae] and as described in [Forstall and Scheirer 2019]. By focusing interpretive efforts on statistically marked instances of words, SEDES gives readers of hexameter an additional tool with which to investigate repetitive phenomena in Greek epic such as formulae and intertexts.

SEDES reached its current state through a long process of evolution and iterative development. It originated as a tool to investigate sonic patterns in poetry, by identifying lines with similar tonal patterns, counting letter n-grams, and quantifying alliteration. It later became specialized for the purpose of finding the metrical positions of all occurrences of forms of a lemma, which enabled analysis of the kind we have described in this article, albeit of only one lemma at a time. At that point, we were using texts sourced from the Thesaurus Linguae Graecae [TLG] and Diogenes [Diogenes] as a tool for lemma lookup. A concrete vision began to take shape of what we wanted to accomplish with SEDES: to compute metrical positions and other statistical information about every word in a large corpus, in an automated fashion. The difficulty of automating Diogenes lookups, and a general preference for freely available data sources, caused us to switch our source of texts from the Thesaurus Linguae Graecae to Perseus, and to begin developing programs around the direct processing of source TEI files. Automating all the steps of the processing pipeline made it feasible to start producing visualizations of an entire work at a time.

The decision to switch to Perseus texts was an important one, enabling us to take control over the entire processing pipeline. Moreover, open-access texts facilitate reproducibility of statistical results, and lower the barriers to participation by people who are not specialists in classical studies. Regardless of the source of texts, a project of this nature requires paying substantial attention to textual and data-format issues.

SEDES was developed in the context of a set of texts we wished to analyze and does not automatically generalize to other Greek hexameter texts. Analyzing texts outside the set we have considered will likely require manual tweaking of the processing programs, as well as adding to the tables of manual lemmatizations and scansions for words and lines that resist automatic processing. When we expanded the corpus from six to twelve texts, to incorporate Hellenistic and Imperial Greek works, we had to make adjustments to the TEI parser to account for previously unseen markup variations. [26] A beneficial side effect of this work has been the discovery and correction of various errors in the source texts.

SEDES provides groundwork for future corpus-level analysis of Greek hexametrical poetry, including by combining textual features (lemma, sedes, and metrical shape) in different ways and by expanding to additional features. More generally, it provides a framework for the analysis of metrical position in metrical language, by which the researcher assembles a corpus, analytical pipeline, and visualization of basic statistics for further development of the program, model, concept, and interpretation and appreciation of the text. Due to the limited size of the Greek hexameter corpus, the method results more from the slow work of philology using basic statistics than from the capacious abilities of machine learning. In some respects, this methodology reflects the disciplinary background of the authors. Yet the benefits of such an interest in poetic language within a limited corpus have focused our attention on a particular approach to lemmatized word frequencies correlated with metrical position. This attention to metrical position, a long-standing interest in classical philology, demonstrates a new route for future studies that seek strong correlations between linguistic phenomena and other formal features of Greek poetry.

SEDES source code and documentation are available at https://github.com/sasansom/sedes. The project home page, with sample visualization outputs, is https://sasansom.github.io/sedes/.

We express gratitude to Patrick Burns, author of CLTK’s Greek lemmatization; Kyle P. Johnson of CLTK; Hope Ranker, author of the hexameter scansion module; Lisa Cerrato of the Perseus project; David Mimno; Rachel Greenstadt; Annie Lamar; Simeon Ehrlich; Stanford’s Center for Spatial and Textual Analysis (CESTA); and the Digital Humanities Quarterly reviewers.