Structure and usage do not explain each other: an analysis of German word-initial clusters

2.1 German word-initial clusters

Descriptions of German agree that up to three consonants can be found in word-initial position (Hall 1992; Kohler 1990; Meinhold and Stock 1980; Wiese 1988). Viewed from a cross-linguistic perspective, present-day German thus allows for a moderate degree of phonotactic complexity (see a classification in Maddieson 2013). However, the precise list of such clusters differs between descriptions.

For the present work, we used a list originally collected for the analysis in Orzechowska and Wiese (2015), who compiled a set of 56 clusters from an extensive corpus of newspaper texts (Leipziger Wortschatz-Portal, see Section 2.3 for a detailed description), as evidenced in Table 1. This inventory is thus more comprehensive than lists given in the published accounts mentioned above. The resulting inventory includes clusters found in assimilated loans, rare words and proper nouns. Examples of such clusters include /pn/ in Pneu, /sm/ in Smog, /fʝ/ in Fjord and /ʃk/ in Schkopau.

The rationale behind the inclusion of such items is the intention to study the usage of present-day German on a broad empirical basis, rather than to base the choice of clusters on a preconceived notion of what constitutes “German” in a historical or norm-based sense, or what in fact constitutes a fully-fledged cluster (e.g., see the treatment of /s/C and /ʃ/C sequences in Goad 2011; Goad and Rose 2004; Yavaş et al. 2008). As a result, the analysis starts with the above inventory of 56 word-initial clusters, among which 48 are bisegmental (CC) and 8 are trisegmental (CCC). Except for treating the affricates /pf ts/ as monosegmental, we take no stand here on the structure of such clusters in terms of, for instance, extrasyllabicity or sub-syllabic categories: it is quite possible that the clusters are diverse in this respect.

2.2 Feature-based analysis of clusters

Based on an in-depth description of phonetic and phonological features of clusters in Table 1, Orzechowska and Wiese (2015) identified a number of new phonotactic constraints for the cluster set in German. The goal was to find an empirically grounded method of ranking CCs and CCCs in terms of these constraints. The authors proposed a method involving an analysis of sub-segmental properties of consonants within clusters, leading to a set of 15 constraints (called parameters).^[1] This set was grouped into four broad dimensions pertaining to Complexity, Place of articulation, Manner of articulation as well as Voicing. Table 2 provides a complete list of the parameters. Each parameter is instantiated by a range of patterns (with further details given in Appendices B and C). The parameters were based on features used in the classification of consonants by the International Phonetic Association (2007). While there are many alternative featural descriptions (e.g., see Hall 2001; McCarthy 1988), such a list of articulatory phonetic features ensures a theory-neutral description of consonants and their clustering, as much as this seems feasible.

The dimension of Complexity is represented by three parameters, two of them reflecting phonotactic universals. Size specifies the number of consonants in a string and is related to the basic CV syllable as proposed in Greenberg (1978). In German, the parameter has two possible patterns; clusters composed of two and three segments (e.g., /kl/: CC; /ʃpʁ/: CCC). Compositionality, related to Greenberg’s (1978) principle of ‘resolvability’, states that clusters are decomposable into shorter constituents with independent existence. Thus a CCC (e.g., /ʃpʁ/) is fully compositional if it is formed of two CCs (/ʃp/ and /pʁ/) and three individual consonants, all of which are attested in the phonological system of the language. The third parameter, Identity avoidance, refers to the occurrence of identical segments in a cluster and is an instance of the Obligatory Contour Principle (Yip 1988). For Compositionality and Identity avoidance, only one value is available as all clusters in German are composed of existing (i.e., fully compositional) and non-identical consonants (i.e., avoid identity).

Within the Place of articulation (POA) dimension, the Distance parameter captures the place distinctions in the IPA description of consonants and their ordering from bilabial to glottal. The distance equal to one holds between consecutive places on the scale: bilabial – labio-dental – alveolar – post-alveolar – palatal – velar – uvular. For example, the distance between /p/ and /l/ in /pl/ has the value of 2, while the smallest and the largest distances of 0 and 6 are assigned to clusters such as /sn/ and /bʁ/, respectively. The parameter is related to phonotactic models using place distances (e.g., Dziubalska-Kołaczyk 2019). The remaining parameters specify either the number of segments with a particular feature (labial, coronal, dorsal) or the feature’s position in a cluster (initial, final). For instance, the /skʁ/ cluster is assigned the following values: labial = 0, coronal = 1, dorsal = 2 for parameters 5 through 7; initial C = coronal and final C = dorsal for parameters 8 and 9.

Similarly, the Manner of articulation (MOA) parameters called Increase in opening and Distance evaluate clusters with respect to degrees of articulatory opening between adjacent consonants and the manner distinctions on the following scale: plosive – affricate – fricative – nasal – liquid. These parameters have an obvious relation to sonority-based principles such as the Sonority Sequencing Generalization (e.g., Selkirk 1984) or the Dispersion Principle (Clements 1990). Thus the parameters determine, for example, a cluster’s rise or fall in sonority as well as its sonority distance (e.g., /kl/: increase, distance 4; /ʃp/: decrease, distance 2). All CCCs in German combine the two articulatory gestures, while their distance is a mean of the constituent distances (e.g., /spl/: mixed, distance (2 + 4)/2 = 3). The last manner parameter counts the number of Obstruent C in a sequence (e.g., /skl/: 2; /tm/: 1). The calculations are performed separately for CCs and CCCs to adequately embrace the proportion of obstruents and sonorants in a cluster.

Finally, the Voicing dimension covers the position of voiced and voiceless segments in a cluster. More specifically, Initial C and Final C specify the feature at cluster margins (e.g., /fʝ/: voiceless initial C and voiced final C), while Agreement states the voicing profile throughout a cluster (e.g., /fʝ/: no agreement). A detailed exposition and justification of the 15 parameters in Table 2 is offered in Orzechowska and Wiese (2015).

Given the parameters, the first step of the analysis involves tagging each cluster with the pattern it represents. Next, the number of clusters that adhere to a particular pattern is calculated. The numbers are then transformed into percentages that are calculated over the total number of clusters in the dataset. The percentages express the degree to which a given parameter holds in the inventory of clusters under scrutiny, revealing whether it represents a common (preferred) or rare (dispreferred) pattern.^[2]

Let us illustrate the computation procedure on the example of /fʝ/.^[3] The cluster is composed of two consonants and is therefore labeled ‘2’ on parameter (1) Size. The cluster inventory embraces 48 CC types, which corresponds to 86 % (=48 × 100/54) of all clusters under investigation. Thus, /fʝ/, similarly to each 2-member cluster, is assigned a percentage score equal to 0.86. Moreover, since 46 types (82 %) start with a voiceless consonant and 46 types end with a voiced one, /fʝ/ scores 0.82 on two parameters: (13) Voicing in initial C and (14) Voicing in final C. However, as a sequence of two fricatives, /fʝ/ displays the manner distance equal to 0 (parameter (10) Manner of articulation distance), which is represented by only 4 cluster types (=4 × 100/54 = 7 %) in the inventory, scoring 0.07. On this basis, we can state that in word-initial position German displays strong preferences for shorter clusters (86 %), whose constituents consonants differ in voicing (82 %) but disfavors plateaus (7 %).

As was mentioned earlier, parameters (2) Compositionality and (3) Identity avoidance are represented by a single pattern. Since all clusters in German are fully compositional and do not contain identical segments, each cluster is assigned a score equal to 1 (100 %). These parameters are included neither in Appendices B and C nor in the statistical analyses.

Summated individual percentage scores for a cluster constitute the composite feature score (Σ). Such a score assigned to all clusters reflects the degree to which the criteria in Table 2 are met. Next, the arithmetic mean (x̄) is calculated over this sum in order to arrive at an overall evaluation of clusters. Composite features scores derived for the present dataset range between 38 % (for the lowest-scoring /skv/) and 56 % (for the highest-scoring /ʃʁ/), with a median of 48 %. These values make it possible to estimate the relative preferability of clusters. For instance, as for /fʝ/, the composite score Σ equals 5.58 (x̄ = 43), which suggests that /fʝ/ represents a cluster in the mid-range of cluster preferability. Averaging over the values found for parameters (1–15) reveals the degree to which the German clusters in Table 1 follow the proposed set of parameters. The composite feature scores and the means are given in the final two columns of Appendix C.

Along with the composite feature score, the analyses to follow also look at individual constituent parameters that contribute to Σ. For this purpose, we consider two types of statistical analyses.

First, we provide a set of correlations between different frequency measures and selected parameters that are associated with the structural composition of clusters, namely Size, Increase in opening and Composite feature score. Size (CC, CCC) is an obvious structural property of clusters: starting with the work by Jakobson (1962), it has been assumed that the markedness of clusters increases with the number of adjacent consonants, where a single consonant constitutes the unmarked case. Increase in opening characterizes the type of articulatory constriction from the first to the last consonant in an initial cluster (i.e., increase, decrease, plateau, mixed). Increase in opening is thus a close approximation to the concept of sonority. The Composite feature score Σ expresses the overall degree of cluster preferability in terms of a summation of all structural feature patterns.

Next, following this analysis, we investigate the relevance of selected parameters suited for regression with a view to determining whether, and to what extent, various place, manner and voice properties are related to cluster frequency in German. To reach this goal, we use the wide range of preferences presented in Table 2 and values given in Appendix B (with the exception of Compositionality and Identity avoidance).

2.3 Frequency measures

For measuring frequencies of linguistic items, a number of alternatives are available. First, types can be distinguished from tokens. Word types refer to individual words starting with a particular cluster, while word tokens represent the number of occurrences of such words in a corpus. Secondly, frequencies can be taken at face value or can be transformed logarithmically.

Most importantly, present-day corpora allow for large-scale counts. Even with a wide-ranging list of German clusters, it is possible to establish frequency counts. The frequencies to be used here were derived from the Leipziger Wortschatz-Portal database (www.wortschatz.uni-leipzig.de). This corpus of newspaper texts of present-day German comprised, at the time of access, 172 million tokens representing 1.65 million of word types. Words were transcribed automatically by the Festival software. Items containing word-onset clusters were extracted manually. Entries with very low token frequencies (<100) were excluded after visual examination because they were usually caused by spelling variants, spelling errors or misparsings by the software. This cut-off point also resulted in eliminating some rare but potential clusters such as /pt/ in Ptah and Ptashnikov.

On the basis of this corpus, the frequency counts listed in (1) were at our disposal. Raw token frequencies in the corpus ranged from 47 to 1.9 million occurrences (with those below 100 excluded). Raw type frequencies were defined by the number of word types per cluster, and ranged from 1 to 1 261. Logarithmic transformations of both token and type frequencies (base 10) change the exponential and highly skewed scales into nearly linear ones. In addition, we used rank orders for raw types and tokens. Overall, the following six frequency measures are employed in the present study.

(1) Frequency counts for clusters

1. token frequencies

   1. raw

   2. logarithmic

   3. rank order

1. type frequencies

   1. raw

   2. logarithmic

   3. rank order

A detailed account of all type and token frequencies for clusters in Table 1 as used in the analyses below is provided in Appendix A.

3.1 Analysis 1: correlating preferences and usage

This section reports the results of correlating the three structural preferences and frequency counts introduced above. As the optimal arrangement and selection of frequency data for statistical analysis are difficult to determine a priori, the six different frequency counts listed in (1) were considered. For each correlation (Pearson correlation coefficients), significance levels were computed. The summary of the results is presented in Table 3 (sample size n = 56 clusters, significance level 5 %).

As can be observed, correlation coefficients are always low, and predominantly non-significant (n.s.). A single statistically significant result is marked with an asterisk ‘*’ (the shaded cell). The widely spread non-existence of a correlation is also illustrated as a scatter plot in Figure 1, which shows, as one of many examples, the relationship between the Composite feature scores and Logarithmic token frequency (r = 0.1335) from Table 3.

Figure 1:

Scatter plot for the composite feature score (y-axis) and logarithmic token frequency (x-axis).

Results in Table 3 demonstrate that only one out of fifteen correlations turns out to be weak (r = 0.2268) but just significant, namely that between Logarithmic type frequency and Size. At present, we do not offer an interpretation for this single case.

We also computed correlations between two measures of usage, Raw token frequencies and Raw type frequencies. The results are presented as a scatter plot in Figure 2. In contrast to the previous results comparing usage and structure, this correlation is highly significant (r = 0.810, p-value = 0).

Figure 2:

Scatter plot for frequency measures; raw types (y-axis) and raw tokens (x-axis).

This finding demonstrates that, within usage, measures are not independent of each other. In other words, types and tokens are largely correlated. The one obvious outlier to be seen in the right-hand bottom of Figure 2 is /tsv/. The cluster has high token frequency due to token-frequent zwei ‘two’ (1 002 205 occurrences of zwei out of all 1 968 112 /tsv/ occurrences), but it is found in only 235 word types. This disproportion contrasts with the vast majority of clusters as they display a monotonic increase in both types and tokens. This is also true for the top-most cluster /ʃt/, which has the highest type and token frequencies (1 261 word types, 1 802 222 word occurrences).

3.2 Analysis 2: regression analysis of structures and usage

In order to investigate the relationship between a wider range of structural and phonological parameters and various frequency measures in a different manner, we also performed a linear regression analysis using the R software (v. 4.1.0) (R Core Team 2020 online) and the lmtest package (Hothorn et al. 2021). The key question here was whether frequency can be estimated from the contribution of phonetic/phonological properties. Thus, Raw type frequency, Raw token frequency, Logarithmic type frequency and Logarithmic token frequency served as dependent variables. Independent variables were the feature-based parameters presented in Table 2. A complete list of variables along with their levels (numerical or categorical) is given in Appendix B. Again, parameters (2) and (3) from Table 2 are not included in the regression models as they do not distinguish between clusters at all.

At the outset, we performed dummy coding to change each categorical variable into a dichotomous variable. Next, we tested a number of models. The best models for types and tokens were selected on the basis of stepwise regression (function: step) using the Akaike Information Criterion (AIC). These best models were obtained for logarithmic tokens and types, which are presented in Tables 4 and 5, respectively. Since models including raw frequencies yielded worse results in terms of higher AIC values, they will not be discussed in the sections to follow.

In both tables, tests of significance give strong premises to infer the significance of two variables: MOA distance and Voicing agreement between adjacent consonants. These models – as best fitted to the data – also include the following variables: the presence of a coronal consonant, place of articulation of the final consonant in a cluster, voicing of the first and the last consonant in a cluster. In other words, more than half of the thirteen structural parameters did not contribute to the regression models, and of those included, only a few are statistically significant.

The results for token and type frequency measures largely coincide. First, average frequency values are higher for larger MOA distances. More specifically, logarithmic frequencies for both types and tokens increase along with an increase in MOA distance. An increase in the sonority distance equal to 1 (i.e., along the scale ranging from 0 to 5) corresponds with an increase of 0.84 in log freq for types and of 0.94 in log freq for tokens. This finding demonstrates that clusters displaying the largest sonority distances are most frequent. Such a group of clusters is represented by plosive + liquid sequences such as /pl bl kl gl/, whose logarithmic frequencies are found in the range between 2.27 and 2.63 for types (with an overall scale 0–3.1), and between 5.39 and 5.66 for tokens (scale 1.67–6.29); see Appendix A.

Second, voice agreement has a negative effect on both dependent variables. Partial and total agreement lower logarithmic frequencies of types and tokens, although the effect is stronger for total agreement (a higher estimate value). This pattern is primarily represented by clusters such as /s/+stop, /ʃ/+stop and C₁C₂ represented by a sequence of a voiced obstruent followed by a liquid or a nasal. The results suggest that clusters displaying no voice agreement, represented by the voiceless + voiced pattern, are positively correlated with the frequency measures, i.e., they have higher log-freq values (Appendices B and C).

As for type frequency, several other variables constitute borderline cases in terms of the statistical significance levels, namely, voicing and place of articulation properties. For instance, an increase in the number of coronal segments in a cluster corresponds with an increase in logarithmic frequency (p-value = 0.05844). A similar effect can be reported for the presence of a dorsal consonant (p-value = 0.05564) and a voiceless consonant (p-value = −0.05635) cluster-finally. In the first case, further conclusions can be drawn. In particular, the presence of a dorsal segment cluster-finally is relevant for type frequency, however, in the absence of a dorsal, there is no difference whether the position is occupied by a labial or a coronal. This observation is related mainly to the presence of /ʁ/ in prevocalic position. In order to determine the relationship between the ‘borderline’ place and voice variables and frequency, further studies and analyses would be required.