Quantitative Interpretation of Time Delay Plots

stress. In comparison to the plots produced by popular global rhythm measures described in Chapter 3, time-delay plots have the advantage to be directly inter-pretable along similar rhythm-related dimensions as have been detected in typolog-ical analyses. Of course, they have the advantage over phonologtypolog-ical analyses that they are not limited to categorical classification. Instead, they are able to show very fine-grained timing differences on a continual scale.

Our exploratory study can go further, however — that lack of acoustic marking of lexical boundaries by an increase in duration in French is well-known — this lack certainly stands in sharp contrast to the common notion of French being “iambic”, since iambic lengthening usually would require a pronounced lengthening effect.

Still, it is possible that word boundaries are still marked in French and our graph simply did not highlight the correct type of transition. Therefore, we alter the plot and instead of highlighting transitions to word final syllables, those from word fi-nal syllables to presumably unstressed syllables are plotted. The resulting graph is shown in Figure4.6. Here, we clearly see that a lengthening effect does take place

— albeit relative to the following very short beat in the upcoming foot. Thus, the intuitive impression of French both having final lengthening at word boundaries and the empirical finding that is does hardly show word final lengthening are both true. A pronounced lengthening does not take place within the foot or group but relative to the upcoming one. It is interesting that the remaining transitions are con-centrated left of the diagonal. This indicates a general tendency of lengthening in French propagating throughout the foot and is limited by lexical boundaries.

transi-Figure 4.6: The plot shows French timing relations between transitions from word final beats to subsequent ones, marked in blue (+), transitions to other beats marked in green (o), transitions to phrase final beats marked in red (x).

tion types show highly significant differences between consecutive durations for the three transition types (F = 223;df = 2;p <0.0001) while for French, there are no clear differences between the groups’ variances (F = 1.44;df = 2, p= 0.24(n.s)) (cf.

Table4.2).

English

Transition Type Mean (z) Variance to phrase final 1.02 0.78

to stressed 0.79 0.7 to unstressed -0.39 1.72

French

to phrase final 0.4 1.5 to stressed 0.19 0.36 to unstressed 0.24 0.42

Table 4.2: The table shows the mean difference and variance between consecutive durations beatduri+ 1−beatduri(z-scores) for the various transition types in our two example languages.

In order to get a better understanding concerning the nature of the differences between the various transition types per language, we calculate the mean values for each “transition type” (to stressed, to unstressed, to final) on both dimensions thus identifying the most typical transition for each language. Then we calculate the Eu-cledian distance between the different types of transition for each language and see whether our visual classifications are confirmed. Eucledian distance is calculated between two points in a two-dimensional spaceP = (px, py) andQ = (qx, qy)with the help of Equation4.1:

Distance=^q(p_x−p_x)²+ (p_y−q_y)² (4.1) It is important to keep in mind that Eucledian distance is identical to the distance we would measure with the help of a ruler. It has of course no perceptual relevance, i.e. the difference in relative timing may look quite different on a perceptual scale.

Still, we can show the relevance of this metric for a typological timing distinction.

The Eucledian distances between the three transition types are calculated for a num-ber of languages contained in the BonnTempo database (Dellwo et al.(2004)), some

of which have been classified as stress timed (English, German), others as syllable timed (French, Italian) while Polish timing has been notoriously hard to describe, its accentual lengthening being extremely subtle (Klessa(2006)). Results are shown in Figure4.7, where it is also evident that there exist clear distinctions between the various languages, albeit in different dimensions. While prototypically stress timed English shows the highest distances between transitions to stressed and those to unstressed, German behaves similarly but less strongly. French shows much less difference between transitions to stressed and those to unstressed, but also a small distance between stressed, unstressed and final transitions. The difference between transitions to stressed and unstressed beats is very similar in French and Italian, both having been claimed to be syllable timed, while final lengthening in Italian has more in common with stress timed languages. Polish behaves completely differ-ent by showing hardly any effect of accdiffer-entual lengthening, but a final lengthening slightly stronger than French. In total, this simple comparison delivers much direct information about language specific timing that goes beyond a binary classification of syllable and stress timing.

Figure 4.7: The graph shows the Eucledian Distance between the transition typesunstressed—stressed, unstressed—finalandstressed—finalfor our two example languages. It is evident, that there are dis-tinctive differences for each language.

However, the Eucledian distances plotted above are mean values that do not capture the variability contained in the data or whether the distinction between the various transition types is systematic and stable enough to generalize. If a

system-atic relationship between relative timing and transition type exists, it could be used by a listener as a perceptual cue when processing the acoustic input. In order to test whether such a systematic relationship exists in the data, a K-Nearest Neighbor (KNN) classification³withk = 5was performed for our two prototypical languages, English and French. The KNN-classifier was used because it also builds on Eucle-dian distances and thus provides a method that can be straightforwardly linked to the visual interpretation of the time-delay plots. Thus, the KNN classifier here pri-marily serves as an evaluation of the visual interpretation method—mainly for this reason, no model optimization e.g. by cross-validation was performed. The material used for classification was again taken from the BonnTempo database (roughly 2400 transitions per language) and it was tested whether the different transition types

“to unstressed beat”, “to stressed beat” and “to final beat” could be distinguished.

From the material in the database,66% was randomly chosen for training and33%

was used for testing. The hypothesis was, that such a classification would work for English which puts each transition in very different categories, while a classifica-tion would prove to be much more difficult for the French data. The results confirm this hypothesis quite clearly: While the classifier reaches 73% overall accuracy for English, it performs a lot worse for French with overall 63% accuracy. When regard-ing the different classes that were to be predicted, the results become even clearer.

While the prediction is clearly above chance level (calculated based on the relative amounts of transitions in the data) in all three transition categories for English, and extremely successful in classifying the transitions to stressed beats, it performs a lot worse for French. Here, the classifier performs slightly better than chance but the improvement rate is clearly below the results for English, especially with respect to the transitions to beats categorized as stressed. The high accuracy for transitions to unstressed beats is the result of the large amount of such transitions in the data itself. An overview of the results is given in Figure4.8.

Of course, our visual interpretation already indicated that we should not con-clude from these results that French has not pattern at all — we can merely deduce that so far, that French does not have a timing pattern organized similar as English

— with pronounced timing differences between a local unstressed and upcoming stressed or final syllable. Based on our visual interpretation in Figure4.6, another

3See e.g.Dasarathy(1991) for an in-depth description of the approach

Figure 4.8: The KNN classification based on beat duration transitions was able to predict the various transition types in English well above chance level, in French the classification fails — especially for the transitions to stressed beats. The black horizontal bars indicate the chance level for each transition type based on the distribution in the original data.

KNN classification based on the same data and under the same conditions was per-formed to find out whether poststress shortening rather than stress lengthening can be detected by the classifier. Indeed, the classifier performed better in detecting poststress syllables based on their tendency to be short than in detecting stressed syllables based on their tendency to be long. Still, it only reached an accuracy of 40%(chance level: 27%) It therefore seems that finding instances of shortened sylla-bles alone is insufficient to describe any systematic regularity in French rhythm. In consequence, another attempt to find a clear pattern in French timing is performed with respect to the distinction between deceleration and acceleration. Figure 2.19 gave the impression that French contains many sequences which are moderately decreasing and occasional sequences of long followed by short sequences. Thus, timing appears to be more smooth in French, except certain “dips” which seem to be restarts of a foot. On the contrary, the English data seems to contain more se-quences showing a steep rather than moderate increase in duration. In order to con-firm this impression, a simple count is performed for both languages, calculating the number plots for the four different quadrants depicted in Figure 4.3, thus filtering out predominant timing relations for both languages. The results of this count re-veals that both English and French show a distribution deviating from an expected equal spreading across all four quadrants (χ²;df = 3;p < 0.05). Furthermore, they

show an interesting difference in this distribution, namely a predominance for long-long and long-short- sequences in French, while English is slightly dominated by short-long-sequences (cf. Figure4.9). The comparatively large number of long-long sequences in French may add to the impression of French having less alternations and a general tendency towards deceleration. Both languages favour short-short-sequences the least.

Figure 4.9: The Figure depicts the different concentrations of sequences in the different relative tim-ing quadrants. The left (grey) number indicates the percentage of timtim-ing relations in English, the right (blue) one for French. The count indicates a slight predominance of French to favour sequences of long or long-short sequences, while English slightly favours short-long sequences.