Time series modelling in the analysis of Greek metrics

Quantitative character of Greek metrics is uncontested at the present state of research. Controversy concerns the rhythmical organisation of linguistic material. Many linguists claim that the sequence of short and long syllables is sufficient to generate the rhythm of text. For others, however, this condition seems insufficient. They argue that a special metrical stress, called ictus, was responsible for rhythmical organisation. Followers of this theory believe that in many cases ictus could coincide with the word stress. Followers and opponents of both theories do not restrain their argumentation to the linguistic material of Greek but often quote examples from Latin versification, based upon the Greek one. The discussion was summarised by A.J. Zajcev (ZAJCEV 1994:22–25). The texts of ancient theorists of grammar, versification and music are not of much help because of their terminological opacity (ALLEN 1973:275–276, ZAJCEV 1994:26–27). The significant fact is, however, that there are no explicit remarks on this issue in classical literature. (SICKING 1993:11).
Nowadays, the self-confidence of the opponents of ictus (KORZENIOWSKI 1998:34–39, LEONHARDT 1989:14, note 12) sharply contrasts with the timidity of attempts to reintroduce the notion of metrical stress into the theory of Greek versification, especially in the context of its oral performance (por. GLAU 1998:33: “Anders als in der Metrik spielt also in der Rhytmik die Akzentuierung bestimmter Töne eine wichtige Rolle”; declamations recorded on a CD supplementing this study leave no doubt that what the author means by “Akzentuierung”is precisely the dynamic metrical stress (ictus).
The first detailed question which arises is whether the rhythm can be generated solely by the sequence of short and long syllables, or whether it should be supported by the dynamic word stress. As has already been said, general research of rhythm confirms the presence of quantitative rhythm in classical Greek (ZAJCEV 1994:13). Sometimes this quantitative rhythm is reinforced by word stress e.g. in Delphic hymns from the 2nd c. B.C. (DEVINE & STEPHENS 1994:168–169). Some theorists consider this phenomenon an intentional figure of speech (SNELL 1982:6, note 11, ZAJCEV 1994:21), while others treat it as purely an accidental coincidence (SICKING 1993:64).
Cautious attempts to recognise the role of word stress in Greek versification are the only concession of the opponents of the ictus theory. There are, however, some general arguments speaking in its favour. Although Russian verse, for instance, can be represented as a sequence of short and long syllables (ZAJCEV 1994:6), its prosody is not based on quantity but on other suprasegmental features (ibid. 1994:15). More arguments in favour of the theory of ictus, using the notion of metrical sandhi, are presented by Kuryłowicz (KURYłOWICZ 1975). The existence of ictus can be also supported by the evidence coming from the relationships of metrics and colloquial speech (KURYłOWICZ 1987:219–234, DEVINE & STEPHENS 1994:102–120). From the theoretical point of view, ictus would be a transposition of word stress (KURYłOWICZ 1987:160, 1972:3–4).
Many other, detailed arguments are used in the discussion of dynamic stress in classical Greek poetry. But contrary to the opinions held by numerous contemporary linguists and philologists, both general and detailed claims have not provided us with a convincing solution of this problem. We argue that the application of statistical tools seems to give some new insights into the issue.

Statistical methods of sequential data analysis have been so far underestimated and rarely applied in the research of metrics. With regard to the specificity of linguistic material, they can be divided into two groups:

—probabilistic, i.e. based on qualitative (symbolic) sequences (e.g. metrical feet) (Xantos 2000);
—numerical, i.e. based upon discrete time series;

In the probabilistic approach, the most frequently used methods are Shannons's theory of information and the theory of Markov chains (tested by Markov himself on linguistic material). Naturally symbolic character of text makes this approach very effective in the analysis of linguistic data. Its disadvantage is a relatively limited number of states of a treated series: very practical in the analysis of phonemes or distinctive features (limited number of states), it becomes inoperative in the analysis of lexical units (theoretically unlimited in number).
As far as the numerical approach is concerned, spectral analysis (e.g. Azar & Kedem 1979) and time series analysis (in the time domain) are applied (e.g. Pawłowski 1998). In both cases, the real time is represented by the sequences of units of the series. In some sense, both approaches are synthesised in the ARIMA method of Box and Jenkins (Box & Jenkins 1976). The advantage of the numerical approach is the possibility of processing the series composed of a very great number of different units (e.g. lexical items), provided they are reduced to a relevant and measurable feature (e.g. the length of an item). The other advantage is the transparency of a model, due to the stationarity of time series generated from texts (in this case conditions of stationarity can be admitted a priori, even without preliminary empirical tests). Also so called seasonal models, described by Box and Jenkins, are very useful in the description of versification in the text.
In the present study, Greek metrics is analysed by means of the ARIMA method. The corpus composed of ca hundred ten-syllable samples of Homer's Iliad was coded as binary sequences, representing either short (0) and long (1) syllables or stressed (1) and unstressed (0) ones. In this way, we obtained parallel, numerical representations of all the samples and modelled them in the time domain. Then we compared the results obtained for quantitative and stress-based coding. The analysis of the autocorrelation (ACF) and partial autocorrelation (PACF) functions suggests that in the case of quantitative series (short vs long syllables) the underlying stochastic process is modelled by the moving-average model MA(4). In the case of accentual sequences, the best fit was obtained with the autoregressive AR(2) model. The goodness of fit was measured by means of the method of residuals —for each sample, we compared the percentage of the original variance explained by the model. The latter parameter is very important in the sequential analysis of text, because it can be considered a statistical, synthetic measure of orderedness in text.
The comparison of both types of series proves that:

both quantitative and stress-based sequences realise some underlying stochastic processes;
the depth of contextual relations equals ca 4 syllables in the case of quantitative series and exactly 2 syllables in the case of accentual series;
the average percentage of the original variance explained by the model is 47% in the case of quantitative series and it amounts to 60% for stress-based series;
This proves that the rhythm generated by Greek hexameter coded as a sequence of short and long syllables is weaker then the rhythm generated by the same samples, coded as sequences of stressed and unstressed syllables. If we admit that the rhythm is an inherent and universal feature of language prosody, affecting its aesthetic function but also facilitating the process of memorisation, (and this feature seems very important in Greek oral literature —cases of persons knowing the whole Iliad by heart are reported in the literature), the result obtained would prove that ictus is not an artefact (ictus fictus) invented by old-fashioned nineteenth century German philologists, but a real component underlying Greek prosody and metrics.
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