In the current state of phonological research, embodied in e.g. laboratory phonology, much value is set on acoustic evidence for phonological analyses. Studies such as Sluijter (1995) and Sluijter and Van Heuven (1996) provide acoustic correlates for primary stress. In our study we are concerned with beat reduction and secondary stress shifts and we wonder whether or not the same acoustic correlates hold for secondary stress. Shattuck Hufnagel et al (1994) and Cooper and Eady (1986) do not find acoustic correlates of rhythmic stress at all. They claim that it is not entirely clear which acoustic correlates are appropriate to measure, since these correlates are dependent on the relative strength of the syllables of an utterance. The absolute values of a single syllable can hardly be compared without reference to their context and the intonation pattern of the complete phrase. Huss (1978) claims that some cases of perceived rhythmic stress shift may be perceptual rather than acoustic in nature. Grabe and Warren (1995) also suggest that stress shifts can only be perceived in rhythmic contexts. In isolation, the prominence patterns are unlikely to be judged reliably. In the remainder of this paper we try to find out if we can support one of these lines of reasoning. In other words, are we able to support our perceived rhythmic variability with a phonetic analysis? Therefore, we measured the duration, pitch, intensity, spectral balance and rhythmic timing of the relevant syllables as realized by subject P1.
Because Dutch is a quantity-sensitive language, the duration of the relevant syllable rhymes was considered. Onsets do not contribute to the weight of a syllable. In Figure 7, the duration analysis is shown for Type 2 data (left shifts). The four columns indicate, respectively, the duration of the rhyme of the first and second syllable in andante speech, and the duration of the first and second one in allegro speech. According to Sluijter (1995), duration is the main correlate of primary stress. As a starting point, we adopt her claim for our analysis of secondary stress. Our measurements would confirm our hypothesis and our auditive analysis, if the second column were higher than the first one and if the fourth column were lower than the third one. In that case, the subject would realize a word such as perfectionist as perfèctioníst in andante tempo and as pèrfectioníst in allegro tempo.
In the andante tempo, three out of six items show the dominant correspondence pattern and in the allegro tempo, four out of six items show the dominant markedness pattern. That is hardly a preference and it does not confirm our auditive analysis of the same data. Furthermore, if we consider the word pairs with different patterns, there is only one pair that has the ideal ratio: the patterns of amerikaan.
Figure 7. Duration (Left Shifts by Subject P1)
If duration does not enable us to confirm our auditive findings, maybe pitch is the main stress correlate for this speaker. However, pitch measurements reveal the same fuzzy result as the duration measurements. Again, only one pattern confirms the auditive analysis. This time it is not the item amerikaan, but the item perfectionist. Moreover, the differences in pitch in this item do not exceed the threshold of the 2.5%, which is the just noticeable difference for pitch. We also analyzed the mean intensity value of the relevant vowels without recognizable patterns between allegro and andante style. These results support the analyses of Sluijter (1995) and Sluijter and Van Heuven (1996), who also claim that the intensity parameter does not contribute much to the perception of stress.
Next, we considered the spectral balance. In order to rule out the influence of the other parameters, we monotonized the data for volume and pitch. Then we selected the relevant vowels and analyzed them as a cochleagram in PRAAT. The cochleagram simulates the way the tympanic membrane functions, in other words the way in which we perceive sounds. In Figure 8 we show two cochleagrams of the vowel [a] in the fourth syllable of, respectively, stúdietòelage 'study grant' (Type 1) in andante tempo and stúdietoelàge in allegro tempo. This item was taken from a pre-study. The allegro data show the expected increased perceived loudness in the higher frequencies, indicated by means of shades of gray; the darker gray the more perceived loudness.
Figure 8. Cochleagrams of  in studietoelage
The right cochleagram (stressed [a]) in Figure 8 shows increased perceived loudness in the regions of approximately 5 to 22 Bark in the allegro version of [a] in comparison with the left cochleagram (unstressed [a]). This confirms the results of the study of primary stress in Sluijter (1995). If we convert this perceptive, almost logarithmic, Bark scale into its linear counterpart, the Hertz scale, this area correlates with the frequency region of 3 to 10 kHz.
In order to measure perceived secondary stress, we will measure the relative loudness in the different frequency regions in Phon.47 According to Sluijter (1995) stressed vowels have increased loudness above 500 Hz compared to the same vowel in an unstressed position. This can be shown if we take a point in time from both cochleagrams in Figure 8 in which the F1 reaches its highest value (following Sluijter, 1995). In Figure 9 the values in Phon are depicted for these points and plotted against the Bark values in 25 steps.
igure 9. Loudness in Phon
The white line in Figure 9 indicates the pattern of the allegro stressed [a] in studietoelage and the black line indicates the pattern of the andante unstressed [a]. We see increased loudness in the region of 13 to 21 Bark, which correlates with the most sensitive region of our ear. The mean Phon value in Figure 9 between 5 and 21 Bark is 43.6 Phon for the andante unstressed [a] and 47.4 Phon for the allegro stressed [a]; a mean difference of 3.8 Phon.
Now, let us see whether or not we can find similar results for our subject P1. Figure 10 shows that the spectral balance confirms the leftward stress shift we perceived in the allegro realization of amerikaan. The first syllable vowel in allegro tempo is characterized by more loudness in the higher frequency regions than its andante counterpart. In the second syllable vowel it is just the other way around.
Figure 10. Spectral balance comparison of the first two vowels of amerikaan
Unfortunately, not all spectral balance data confirm our auditive analysis. For example, we claimed that the pitch analysis of the stress shift in perfectionist did confirm our auditive analysis. Therefore, we expected more loudness in the allegro realization of the first vowel and less loudness in the allegro realization of the second vowel, but it appeared that there is relatively more loudness in the andante realization of per. This result contradicts our auditive and our pitch analysis.
We have to conclude that the different phonetic analyses contradict each other. Sometimes the perceived stress shift is characterized by a longer duration of the stressed syllable; sometimes a relatively higher pitch characterizes it. The results of our spectral balance analysis show that the differences in loudness pattern with differences in duration. In our perceived stress shift in allegro perfectionist, pitch turned out to be the decisive correlate, whereas duration and spectral balance measurements indicated no shift at all. On the other hand, the perceived shift in allegro amerikaan was confirmed by the duration and spectral balance analyses together, whereas pitch measurements indicated the opposite pattern. For most perceived stress shifts, however, the acoustic correlates did not give any clue.
Finally, we will consider whether the perception of restructuring depends on rhythmic timing. Just as in music, speech can be divided into a melodic string and a rhythmic string as partly independent entities. With respect to speech, the melodic string seems to be more flexible than the rhythmic one. Imagine that the rhythm constitutes a kind of metronome pulse to which the melodic content has to be aligned. The listener expects prominent syllables to occur with beats. This behavior is formulated as the Equal Spacing Constraint: prominent vowel onsets are attracted to periodically spaced temporal locations (Couper-Kuhlen, 1993; Cummins & Port, 1998; Quené & Port, 2002; a.o.). Dependent on speech rate the number of intervening syllables between beats may differ. Suppose the beat interval is constant at 300 msec., there will be more linguistic material in between in allegro speech, e.g. the two syllables die and toe in stúdietoelàge, than in andante speech, e.g. only one syllable die in stúdietòelage.
If indeed the perception of secondary stress shifts depends on rhythmic timing, i.e. the beat interval between prominent syllables in andante and allegro speech is approximately equal, than we expect that the duration quotient of the interval between, for example, stu and toe in the andante realization of studietoelage and stu and la in the allegro realization approximates 1.
In our pre-study, the interval between the vowel onsets of the first and third syllable in studietoelage (andante) is 0.358 sec, whereas the interval between the first and the fourth syllable in the allegro realization of the same word is 0.328 sec. This means that the duration quotient is 1.091, which indeed approximates 1. In other words, this example supports the idea of the Equal Spacing Constraint.
Does the same result hold for our present data? We measured the beat intervals between all possible stress placement sites for all six subjects. Figure 11 depicts the duration quotients for subject 1. Figure 12 shows the beat intervals of the same data. It depicts as well the duration interval between the first and the third, as the first and fourth syllable for both speech rates. We expect restructuring for those data in which the line of the first to third syllable interval (andante (black line)) coincides with the line of the first to fourth syllable interval (allegro (white line)).
Figure 11. Quotient beat intervals of Subject P1
Figure 12. Beat intervals of Subject P1
The Figures 11 and 12 indicate that the relevant beat intervals of the items 1, 4 and 7, studietoelage 'study grant', kamervoorzitter 'chairman of the House of Parliament' and winkelopheffing 'closing down of a shop', respectively, coincide. In other words, we expect to hear restructuring in exactly these three items.
Unfortunately, our auditive analysis indicates only attested combinations of restructuring in items 2 and 6: wegwerpaansteker 'disposable lighter' and gemeente-inschrijving 'municipal registration', respectively. Obviously, rhythmic timing is not the decisive characteristic of perceived restructuring in allegro speech either.