TEXTUAL ACCENT AND MENSURAL RHYTHM IN SIXTEENTH-CENTURY SETTINGS OF THE "PATER NOSTER"
By Joshua J. Veltman
IMPLICATIONS REALIZED: AN ANALYSIS OF THE MUSICAL PRACTICE
3.1 Methodology. When one attempts to gain perspective on a potentially difficult or complex issue, the question of methodology inevitably arises. A method often adopted in musicological writing is the presentation of well-chosen examples in illustration of a certain point or in support of a certain argument. The example method can be appropriate and effective, but may leave itself open to the skeptic's suspicion that an analyst's bias, whether conscious or not, has systematically elevated supporting examples and suppressed counter-examples.
Many statistical methods are designed to address suspicions of that nature. While unscrupulous use of statistics can become a heinous form of deception, their proper use is intended to avoid bias and to impart clarity. In that spirit, I have chosen to employ statistical methods in this study.
The common saying about not seeing the forest for the trees (and vice versa) provides a good analogy for this methodology. Through an assessment of all the music in a specified sample rather than of selected examples from the repertoire as a whole, we will attempt to gain a view of the "forest," or more correctly, of a patch of the forest. This necessarily means that the distinctive features of individual "trees" will recede into the distance, though of course together they still compose the forest. During the process, it may become tempting to perform increasingly fine-grained statistical assessments, making more and more exceptions and allowances for various aspects of the music. A certain amount of fine-tuning is appropriate and necessary, but the further one travels down that path, the closer one gets to an instance-by instance analysis of the trees. The following analyses attempt to strike a balance between statistical panopia on the one hand and analytic myopia on the other. The discussions which follow are intended as an analysis of the commonly-shared style of the works in the sample, rather than of the motets per se or of the stylistic differences among motets and composers.
3.2 The motet sample. A number of issues arise regarding the selection of an appropriate musical sample. The sampled music should be representative of the kind of music the theorists were writing about. Earlier we saw that the three composers in the sample fall into Stoquerus' "younger generation" category. Similarly, we have already established the applicability to Latin-texted works of the theory discussed in the previous chapter. Given the subject of interest here, text is clearly a focal criterion. In order to maintain a common thread throughout the works in the sample, a single, fairly wordy text was chosen that had been set numerous times by different composers (see the "Pater noster" text in Chapter 1). From among all the "Pater noster" settings available, seven works were chosen on the basis of chronological, generic, and stylistic suitability, and on the basis of the fact that each composer had set the text more than once (in order to increase the sample size). Figure 13 identifies the sampled motets.
1) Adrian Willaert. 6 voices. Motecta VI vocum liber primus (Venice:
2) Adrian Willaert. 4 voices. Mottetorum IV vocum liber secundus (Venice: Gardane, 1545).
3) Orlando di Lasso. 6 voices. Modulorum secundum volumen (Paris: Le Roy & Ballard, 1565).
4) Orlando di Lasso. 4 voices. Patrocinium musices, prima pars (Munich: Adam Berg, 1573).
5) Orlando di Lasso. 6 voices. Cantica sacra sex et octo vocibus (Munich: Adam Berg, 1585).
6) G. P. da Palestrina. 5 voices. Mottetorum liber tertius (Venice: Gardane, 1575).
7) G. P. da Palestrina. 8 voices. MS from the archives of the Capella Guilia in the Vatican. Date unknown.
Figure 13. Selected "Pater noster" settings: composers, number of voices, first publications, and editions used.
3.3 Editorial issues. The analyses presented in this chapter were performed with computer encodings of the motets (see "Apparatus" below), based on the editions listed in Table 2. A possible confound to these analyses that must be addressed relates to source and transmission issues in general and to the issue of editorially-supplied text underlay in particular. For various reasons, including the print technology of the time, the notated sources of this repertoire do not always display the perfect note-syllable alignment taken for granted in modern notational practice. The more syllabic style of the younger generation (mid- to late-sixteenth century) creates less potential ambiguity in this regard than does the more melismatic style of older generations, but still an editor's judgment must come into play when setting the underlay in stone for the edition, as it were.
While the practical realities of the encoding task led me to rely on editions, it was important to assess the reliability of those editions. An example of the types of issues that arise is provided by the Willaert (1542) print. Probably as a practical expedient, the compositor rarely divided words into syllables, opting instead to keep entire words together without regard for accuracy of note-syllable alignment. The first syllables of words are in their proper positions, but subsequent syllables can become misaligned, especially with longer words. This presents no real problems for words having a one to-one ratio of syllables to notes, i.e., words set syllabically, since only one text underlay solution is possible, as Figure 14 a) and b) demonstrate.
a) syllabically-set word (sanctificetur): appearance in the print (cantus part, mm. 26-29
b) syllabically-set word (sanctificetur): editor's solution
c) melismatically-set word (tua): appearance in the print (cantus
part, mm. 46-49)
d) melismatically-set word (tua): editor's solution
Figure 14. Willaert, "Pater noster," 1542. Examples of editorial issues regarding text underlay.
For words having a melisma set to one or more of its syllables, however, the potential for ambiguity arises. Figure 14 c) and d) show one such case and the editorial solution. If the appearance in the print of the word tua were to be taken literally, it might be set under the semiminim B, but the text-setting rules examined in the previous chapter forbid that (specifically, Older Rule #2). In fact the only legal solution in this case is the one that the editor has chosen. This is a simple but excellent demonstration of text-setting rules in action; the early print alone is ambiguous, but a knowledge of the rules, apparently taken for granted by the compositor, renders it semantically sufficient. Although the Stoquerus treatise was discovered and studied after the preparation of the Willaert edition, certainly the terse but substantive rule system of Zarlino was known at that time.
The Willaert (1542) print brings another issue to the fore, namely that it contains many brief, untexted segments. As the theorists tell us, these signalled an opportunity for the singer to repeat immediately the previous phrase, coordinating notes and syllables to the best of his ability, based on absorbed or learned knowledge of text setting principles. In prints, such phrase repeats are often indicated with an "ij" symbol centered under a group of untexted notes, i.e., an indication to "sing the preceding text phrase a second time to these new notes." In these cases, the modern editor is put into the position of the historical singer by being required to supply text underlay, although not "on the fly." In these cases of editorially-supplied underlay (as opposed to source-supplied underlay as discussed in the previous paragraph), it must be understood that the modern editor has expanded the notational shorthand for phrase repeats found in the early prints. These expansions are indicated with italics or angle brackets or some other indicator. While the potential for error here seems greater, the situation is not in fact much different from source-supplied underlay of the type describe above. If the number of untexted notes matches the number of syllables in the previous phrase, there is only one solution. If there is a surplus of notes, rules of text setting come into play.
On the basis of these observations we can assume that the Willaert edition is adequate for present purposes. The Lasso prints and editions bring up a related but distinct set of issues. Whereas the compositor for Willaert (1542) rarely divided words into syllables, the compositors for the Lasso motets did it as a matter of course, allowing a much better alignment of notes and syllables. This alleviates most of the potential ambiguity for source supplied text underlay revealed in Willaert (1542). The situation with editorially-supplied underlay remains the same.
Without delving into the historiographical concerns surrounding "authorial intention," it is assumed that a close study of style and technique such as the present one should seek to be grounded in works that resemble as closely as possible the original intentions of the composer. As noted above, the computer encodings for the Lasso motets were based on the Haberl edition. As his primary source, Haberl used the Magnum opus musicum, a large, posthumous volume of motets collected and edited by Lasso's sons, Ferdinand and Rudolphe, in 1604. One may rightly question the relationship of this publication to the original motet publications. Aside from the fact that the Magnum opus musicum completely reorders the motets, which obscures a sense of Lasso's historical development as a composer but which is of only minor importance here, "[t]hey include arbitrary changes or omissions in the musical texts, incorrect placement of the words under the music, and in extreme cases replacement of the original words altogether (contrafacta)." Clearly this state of affairs poses a problem. After the encodings based on the Haberl edition were complete, newly-edited versions of the motets became available to me (see Figure 13 above). The new motet edition does in fact use the original publications as its primary sources rather than the Magnum opus musicum. This facilitated a comparison between the motets as they appear in the original publications and as they appear in the 1604 publication, in order to assess the degree to which the types of alterations quoted above affect the three motets of interest here. Fortunately, none of the three "Pater noster" motets in the 1604 volume is a contrafactum. Without performing a note-by-note collation, I did not detect any substantial changes to the "musical texts" (i.e., the notes). There are scattered cases of altered underlay. Rarely these take the form of a syllable shifted to a different note; more often they concern phrase repeats. For whatever reason, the 1604 print sometimes leaves different segments untexted (with "ij" beneath) than the original prints. This may result in a different phrase segment (usually about two or three words long) being laid under a given segment of notes. However, these text settings still "work," that is, they do not seem to represent stylistic violations. Presumably the alterations were performed by or allowed by the Lasso sons, competent musicians in their own right, whose stylistic judgments, to the degree that the sons were attempting a positive representation of the father's work, can perhaps be taken on par with those of Orlando. In other words, it could be argued that for the purpose of text-setting analysis, the judgment of the Lasso sons as represented in the 1604 alterations need not be immediately dismissed.
In a certain limited circumstance, the discrepancies are instructive in a roundabout way. Sometimes an expanded (i.e., editorially-supplied) underlay in the old edition (based on the 1604 print) shows the same phrase segment as the explicit (i.e., source-supplied) underlay in the new edition (based on the original print). In the large majority of these cases the expanded underlay (old edition) presents an identical reading to the original underlay (new edition), providing independent confirmation of the accuracy of the editorial expansion process in general.
Regardless of the stylistic status of the alterations in the 1604 print, they are not sufficiently numerous to cast into doubt the broad findings presented later in this chapter.
Original sources for the Palestrina motets were not accessible. In this absence, we might be content to assume that the comments offered for the Willaert (1542) print, published by Gardane, are applicable to the Palestrina (1575) print published by the same firm. With regard to the manuscript of uncertain date (the source for the Palestrina eight-voice motet), nothing can be said, except to suggest that the work's predominantly syllabic style considerably diminishes the potential for text underlay ambiguity.
On the basis of these considerations of editorial issues, we can conclude that the editions used are sufficient for the purposes of this study.
3.4 Mensural placement. A discussion of what is meant by "mensural placement" was already offered in the introduction. We have only to say a few things about the mensuration of the selected motets. While a variety of mensurations developed over the course of the late Middle Ages and Renaissance, the most commonly used mensuration during the sixteenth century was tempus imperfectum diminutum, also known as tempus imperfectum alla breve. The term "alla breve" and its sign (¢) survive to the present day. All seven of the sample motets are in this mensuration. A short, six-measure segment of one of the Lasso motets (1585) switches to a triple mensuration, for which reason that segment has been left out of the analysis. In ¢ , each note value stands in duple proportion to the next larger note value. It is not possible to precisely map these durations onto modern note shapes, because modern editions from the late 19th and early 20th centuries often preserve the original durations undiminished, whereas more recent modern editions usually diminish the note values by a factor of two or four to improve readability for modern musicians. Figure 15 should clarify the rhythmic relationships of the various note values.
Figure 15. Values and proportions of mensural notes in tempus imperfectum alla breve (¢), and corresponding modern equivalents.
3.5 Apparatus. The sample was analyzed with the aid of the Humdrum Toolkit running on a Unix platform. The seven motets were manually encoded in Humdrum format, working from the editions cited in Figure 13. The texts were proofread visually, paying particular attention to accent placement. (Misspellings, although corrected, would not affect the analyses). The voice parts (notes only) were exported to notation software so they could be both visually and aurally proofread. In addition, various syntactic Humdrum tools proved particularly helpful in ferreting out mis entered notes and syllables. Using a double-entry method of re-encoding a randomly selected passage, the error rate for both the text and music is estimated at below 1%. With corrected encodings in hand, the Humdrum software was used to analyze the motets for trends relating to textual accent and mensural placement.
3.6 Frequency of note onsets. One of the methods employed by Boone to demonstrate the existence of hierarchical organization in mensural music is a tally of note onsets (called "attacks" in his study) across the various mensural positions. As an expedient way to suggest the applicability of Boone's conclusions to the present music sample, a similar tally was performed on it. Figure 16 presents the results of this tally.
Figure 16. Frequency of note onsets across mensural positions.
At least four different frequency strata become immediately apparent: the breve-semibreve stratum (positions 1 and 5), the minim stratum (3 and 7), the semiminim stratum (2, 4, 6, and 8), and the fusa stratum (not labelled). The differences between strata (e.g., minim to semiminim) are clearly significant, but the question arises as to whether the differences within strata (i.e., between breve and semibreve positions, and between the two minim positions, four semiminim positions, and eight fusa positions, respectively) are significant. A chi-squared test on the breve to semibreve (1 to 5) difference results in a p value of 0.175. In other words, there is a 17.5% probability that the difference between the observed breve-semibreve ratio and the "expected" ratio is a result of chance and not of some significant musical feature. From a statistical point of view, this relatively high p value does not pass muster as an acceptable confidence level. In order to establish that the observed difference is significant, a larger sample would be required. Interestingly, the p value for the difference between the first and second minim positions (3 and 7) is 0.026--a 2.6% probability that the observed difference is due to chance, which does fall within the 0.05 confidence level. The p values for differences within semiminim and fusa positions are relatively high (perhaps due to the comparatively small number of note onsets in those positions) and therefore cannot be judged to be significant from a statistical standpoint.
Notwithstanding these results of the chi-squared test, a repeating pattern within each level (i.e., b-sb, m, sm, and f) can be observed, namely an alternation between slightly depressed and slightly elevated frequencies. (This pattern is observed on the b-sb level when one considers that the breve position also follows the semibreve position, i.e., sb-b.) This pattern is a result of the fact that the figure is more prevalent than , the figure is more prevalent than , and so on down through the shorter durations. This phenomenon is a symptom of the positive correlation between mensural position and agogic (durational) accent, a relationship that shall be further explained below.
The most significant result to emerge from the tally of note onsets across mensural positions is that the highest significant articulative level (with regard to note onsets) is the semibreve level or tactus minor.
3.7 Cadences. Boone also examines the mensural placement of cadences to demonstrate the existence of mensural hierarchy. Without attempting to deal with the subtleties of relative cadential strength or of thwarted cadence-like motion, "cadence" for present purposes can be defined strictly as closest-approach movement to an octave or unison between any pair of voices (i.e., M6 expanding stepwise to P8, or m3 contracting stepwise to P1). The arrival on the octave or unison is taken to be the salient moment. Under this definition, 75 cadences (54% of the total) occur on breve (1) positions in the present sample, 53 (38%) on semibreve (5) positions, and 11 (8%) on minim (3, 7) positions. A chi-squared test on the breve-semibreve difference gives a p value of 0.05 (i.e., a 1 in 20 or 5% probability that the difference is due to chance), suggesting that, from the point of view of cadences, the breve level or tactus maior is a significant articulative level.
3.8 Frequency of syllable onsets. A similar measurement on syllable onsets can be performed as on note onsets. Figure 17 represents the frequency of syllable onsets in the various mensural positions.
Figure 17. Frequency of syllable onsets across mensural positions.
A comparison of syllable onsets with the foregoing note onset results are instructive. No syllables whatsoever begin in fusa positions, which should not surprise us, since for that to occur either a syllable would have to be completed within the duration of a fusa (too fast, according to Stoquerus), or syllable syncopation on the fusa level would have to occur. This leaves at least three strata of syllable onset frequencies: the breve-semibreve (1, 5), minim (3, 7), and semiminim (2, 4, 6, 8) strata. Can the breve and semibreve positions be separated into two strata, i.e., is the difference between them significant? A chi-squared test on this difference results in a p value of 0.001, indicating that it is a significant difference. So the breve-semibreve position difference is more significant for syllables than for notes; we can link this finding to Stoquerus' Necessary Rule #1 which enjoins musicians to put the first syllable under the first note of a phrase and the last syllable under the last note. An informal visual survey of the scores indicates a greater number of the first and last notes of phrases beginning in breve (1) positions than in other positions.
Another instructive difference between the note-onset and syllable onset results is that the minim positions (1, 7) have been levelled; the minute difference between them is not at all significant. As for the semiminim positions, we can attribute their relative paucity to the restrictions placed upon them by the rule system discussed in Chapter 2: only a note coterminous syllable can occur in a semiminim position, and the only situation in which that happens is in this type of setting:
As with note onsets, we continue to see a slight elevation-depression alternation of syllable-onset frequencies on the semiminim level (positions 2, 4, 6, and 8).
3.9 Distribution of accented and unaccented syllables. Given the hierarchical stratification of syllable onsets just observed, we shall propose to test that idea that accented syllables are rendered more salient by being placed in stronger mensural positions (e.g., breve vs. semibreve (position 1 vs. 5), semibreve vs. minim (position 5 vs. 3 and 7), and so on). To that end, the occurrences of each syllable class (first, second, third, fourth, and fifth, highlighting the accented syllables where appropriate) in each word class where applicable (monosyllables, disyllables, trisyllables, tetrasyllables, and pentasyllables, both of antepenultimate and penultimate accent for words of three syllables or more) will be tallied and compared across mensural positions. Since so few syllables occur in semiminim positions (relatively speaking), minim and semiminim positions will be conflated in order to streamline the presentation but at the same time to avoid ignoring semiminim positions altogether. To avoid cumbersome labelling, it will be understood from now on that the minim 3 position will incorporate semiminim positions 2 and 4 (i.e., the positions immediately surrounding it) and that the minim 7 position will incorporate semiminim positions 6 and 8. This procedure will slightly elevate the status of semiminim positions in the mensural hierarchy, yet they will remain low enough for the comparative purposes at hand.
Figure 18 presents the mensural position tally for monosyllables, expressed as percents rounded to the nearest integer. Monosyllables display a moderate but statistically significant (p <0.01) tendency to avoid the stronger mensural positions and to gravitate toward the weaker mensural positions.
Figure 18. Frequency of monosyllables (N=1070) in mensural positions. Monosyllables display a moderate tendency to avoid stronger mensural positions (i.e., breve and semibreve positions) and to gravitate toward weaker mensural positions (i.e., minim positions).
Figure 19 presents the results for all disyllables, which always receive the accent on the first syllable. One might expect a greater tendency for first syllables to occur in stronger mensural positions and a lesser tendency to occur in weaker mensural positions. Indeed the results bear out this expectation, but notice too that second, unaccented syllables display the same, even more marked tendencies. This is the first glimpse of an issue regarding final syllables that will be addressed again later. Partly for visual clarity, and partly so that final syllables can be addressed as a whole, final syllables for three- to five-syllable words will not be considered until later.
Figure 19. Disyllables (N=1165): frequency of syllables in mensural positions. Accented first syllables display a tendency to occur in stronger mensural positions. The unaccented second syllables display the same tendency, however.
Proceeding with trisyllables, which can have an accent on either the antepenultimate or penultimate syllable, some interesting trends begin to emerge. Figures 20 and 21 present the results for the antepenultimate and penultimate (i.e., first and second) syllables of trisyllables.
Figure 20. Antepenult-accented trisyllables (N=200). The accented antepenults tend to occur in stronger mensural positions, whereas the unaccented penults tend to fall in weaker mensural positions.
Figure 21. Penult-accented trisyllables (N=172). The unaccented antepenults tend to fall in weaker positions; the accented penults tend to occur in stronger positions.
In contrast to Figure 6 (disyllables) in which the two lines follow a similar contour, the lines in these figures pursue opposing contours. Notice also that the behavior of each syllable type (i.e., antepenult and penult) inverts as the accent-type changes (i.e., moving from Figure 20 to 21). Trisyllables, then, seem to follow the expected tendency that accented syllables fall in stronger mensural positions and unaccented syllables fall in weaker mensural positions.
Since the "Pater noster" text contains no penult-accented tetrasyllables, only results for antepenult-accented tetrasyllables can be presented, which Figure 22 does.
Figure 22. Antepenult-accented tetrasyllables (N=114). Accented antepenults tend to occur in stronger mensural positions; unaccented penults tend to occur in weaker mensural positions. The first-syllable contour is similar to the penult contour, though shallower.
The final syllables have again been left out, but now a first syllable line can be included as well. The accented antepenults reveal a contour consistent with the expected tendency, as do the unaccented penults. The first-syllable line (unaccented) follows a contour similar to that of the penultimate (third) syllable, though it is somewhat shallower.
Figures 23 and 24 present the results for pentasyllables.
Figure 23. Antepenult-accented pentasyllables (N=34). Accented antepenults behave contrarily to the pattern observed in shorter words; accented penults continue trends found in shorter words. First and second syllables behave somewhat equivocally.
Figure 24. Penult-accented pentasyllables (N=189). Both antepenults and penults continue patterns found in shorter words. First and second syllables present similar but shallower contours compared to the antepenults and penults, respectively.
In Figure 23, the (accented) antepenults behave contrary to the expected manner, while the (accented) penults do behave in the expected manner. Figure 23 also reveals that the behavior of first and second syllables is somewhat equivocal. No explanation for these apparent idiosyncracies can be offered at this point, except to note that the population of antepenult-accented pentasyllables in this sample is small compared to other word-types and therefore may not be representative of their treatment in the repertoire as a whole. When rolled into summarial tally of all three- to five-syllable words (see Figure 25), these antepenult-accented pentasyllables do not negate the overall trends observed.
Figure 24 presents a clearer picture. Here the (unaccented) antepenults and (accented) penults stand in an unequivocally inverted relationship. First and second syllables present similar (albeit shallower) contours in comparison to antepenults and penults respectively, which may suggest the existence of a secondary accent on the second syllable, or the effect of purely musical exigencies, or both.
As a consolidation of these various results, Figures 25 and 26 track the mensural positions of the antepenultimate and penultimate syllables of all three- to five-syllable words. The contours of the graphs clearly indicate that accented syllables tend to occur in stronger positions while unaccented syllables tend to occur in weaker positions, an observation that confirms the idea put forth for testing at the head of this section.
Figure 25. All three- to five-syllable antepenult-accented words (N=348). Accented antepenults tend to occur in stronger mensural positions, whereas unaccented antepenults tend to occur in weaker positions.
Figure 26. All three- to five-syllable penult-accented words (N=361). Unaccented antepenults tend to occur in weaker mensural positions, whereas accented penults tend to occur in stronger positions.
Figure 27. All three- to five-syllable words, final syllables only (N=709). Although final syllables are unaccented according to the rules of Latin accentuation, they show contours similar to those of accented syllables.
There remains the task of considering final syllables. According to the rules of Latin accentuation, final syllables are unaccented. But as Figures 19 and 27 reveal, final syllables display a mensural-position contour similar to those of accented syllables. An explanation for this trend might be found in Necessary Rule #5: "The first syllable of a phrase must be assigned to the first note of a phrase, the last syllable to the last note." An informal visual survey of the scores seems to confirm that more phrase-final notes or notes groups occur in breve and semibreve positions, possibly causing the tallies for final syllables to reverse the expectations for unaccented syllables.
Such an hypothesis could be tested by subtracting all phrase-final syllables from the tallies. When this is done, however, the final-syllable contours change only minimally, let alone reverse. It would seem that final syllables do indeed present an exception to the trends observed for other types of syllables. It seems that a musical context engenders a treatment of final syllables that is different from the treatment they receive in speech.
3.10 Correlations among mensural position and textual, agogic, and melodic accents. Up to this point we have been exploring textual accent in relation to mensural position. The question now arises concerning the possible interaction of textual accent and mensural position with other forms of musical accent. There seems to be no reliable way to assess dynamic accent in this style, if any, for the simple reasons that dynamic accent is not encoded in the notation and that, barring time travel, no sound trace from sixteenth century performance is available. Boone raises the possibility that our perception of hierarchy need have nothing to do with dynamic accent:
The perceptual trap involved for us, as late- or post-common-practice listeners judging of a distant musical tradition, might seem to be well illustrated by computer performance. Despite the rigorously unvarying dynamic and durational parameters of simple computer programs for rendering music, and despite an acute awareness of the silence of early theory on the subject of punctual hierarchy, I (and other students of early music) still hear regular strong and weak functions in such performances of mensural music, suggestive in certain ways of what is commonly described, in other music, as "metrical" organization. What stimulates this kind of perception, however, may not be simply our biased ears, if it can be shown that the mensural notes transmit a consistent hierarchy of musical events.
Earlier, hierarchies of three types of musical events were shown to exist in the sample: note onsets, cadences, and syllable onsets. In addition to these, agogic (durational) and melodic accent might also contribute to a perception of hierarchy, and these accent types are encoded in the notation and thus can be subjected to analysis.
Agogic accent is predicated on the notion that a longer note stands out or is easier to perceive. Melodic accent is much more difficult to define. Huron and Royal tackled this problem by investigating the various models of melodic accent that have been put forth by theorists. One of the models, proposed by Joseph Thomassen, was derived experimentally and was shown by Huron and Royal to be the model that is best supported by musical practice. "Thomassen's algorithm uses a moving window containing three pitches. The accent value for any given note is determined by the interaction of three overlapping three-note contours associated with that note."
Taking this as our model of melodic accent, we can ask what correlations there may be among mensural position and the various types of accent in the sample. Deriving a correlation coefficient for each possible pairing will help to answer that question. This method assesses the similarity of contour of a set of matched data pairs. No attempt is made to deal with magnitude of change, only direction of change (i.e., positive change or negative change). Each event (i.e., note or syllable) can be assigned a trajectory in terms of mensural hierarchy and the various accents. If a given note occurs on a stronger mensural position than the previous note, it has a positive trajectory, and vice versa; if a given syllable is accented whereas the preceding one is unaccented, it has a positive trajectory, and vice versa; if a given note is longer than the previous note, it has a positive trajectory vis-à vis agogic accent, and vice versa; if it has a greater melodic accent than the previous note, it has a positive trajectory, and vice versa.
The possible range of a correlation coefficient is between -1 (completely negative correlation) and +1 (completely positive correlation). A coefficient of 0 would mean that no correlation whatsoever exists between the featured pair. Figure 28 presents the correlations that exist in the musical sample among mensural position and the various types of accent.
Figure 28. Correlation table for mensural position (mp) and textual, agogic, and melodic accent.
The positive correlations suggest a significant degree of coordination among the various pairs in this style, which may contribute to the perception of hierarchy in the absence of dynamic accents as discussed above by Boone. One could go further and say that metric hierarchy, and by extension mensural hierarchy, is a mental construction--a thing that does not exist in the physical sense that sounds exist--that is abstracted from the physical parameters of sound that are organized hierarchically.
While the correlations are all positive, two in particular invite further comment. First, the mensural position / agogic accent correlation is the highest of all. A positive correlation between this pair was foreshadowed by the subtle, recurrent pattern found in the note onset profile, as discussed above. Second, the mensural position / textual accent correlation is the lowest of all. This might seem surprising given the distribution patterns of accented and unaccented syllables across mensural positions discussed above. However, recalling that final syllables display a countertrend in this regard, the correlation jumps to +0.328 when final syllables are left out of the calculation.
These correlations present a broad view of the relationships among mensural position and the accent types. A more detailed view has already been given for mensural position and textual accent. It will be informative to pursue a similarly detailed view of the relationship between textual and agogic accent and between textual and melodic accent.
3.11 Textual accent and agogic accent. In order to provide a detailed view of the relationship between this pair, a mean duration, measured in minims, was calculated for each syllable class (first, second, and so on) within each word class (monosyllables through pentasyllables, both penult- and antepenult-accented where applicable). These calculations, arranged in Figure 29, incorporate both note-coterminous and melisma-coterminous syllables.
Figure 29. Mean duration in minims for all syllables within each word class (1 through 5 indicates number of syllables, a = antepenultimate accent, p = penultimate accent).
The mean duration for all syllables lumped together is 1.86 minims, which provides a baseline duration against which to measure other syllables. Monosyllables are slightly below average. The first, accented syllables of disyllables are (on average) somewhat longer than the following unaccented syllables. The first, accented syllables of antepenult-accented trisyllables (3a) are significantly longer than the second, unaccented syllable, and the reverse is true for penult-accented trisyllables (3p). Similar trends can be observed for the penultimate and antepenultimate syllables in four- and five-syllable words (4a, 5a, 5p). Given the overall mean duration of 1.86 minims, it seems that in some cases (e.g., 3p's), the accented syllable stands out as much or more due to the shortness of the preceding or succeeding syllable as due to extra length conferred upon the accented syllable itself. The final syllables of certain word classes tend, on average, to be slightly longer than the overall mean syllable duration, which seems to resonate with the unusual status of final syllables witnessed earlier. These results provide a more precise understanding of the relationship between textual accent and agogic accent. They also seem to confirm an interpretation offered above concerning Newer Rule #5, that the "long" and "short" syllables mentioned in that rule refer not literally to syllable quantity but metaphorically to word accent.
3.12 Textual accent melodic accent. To complete this program of analysis, the relationship between textual accent and melodic accent is considered. In a manner similar to the mean duration method used above, a mean melodic accent for the syllables of each word class was calculated (using Thomassen's model; a score of 0 is minimum, 1 is maximum). The overall mean melodic accent for the sample is 0.31. Monosyllables got a mean score of 0.29. The first and second syllables of disyllables got 0.35 and 0.36, respectively; this result does not seem to reflect the disyllable accent profile (i.e., accented first syllable). The results for the remaining word classes will be more easily presented in graph form (see Figures 30 - 32). The contours that arise might be taken as something like "archetypal melodic accent contours" for the various word classes. (It is worth emphasizing that the contour heights are not analogous to pitch heights.)
Considering trisyllables (Figure 30), the antepenult-accented ones exhibit a contour that seems to be consistent with their pattern of textual accents, with final syllables forming a possible exception (which one may have come to expect by now). Penult-accented trisyllables show a flat line moving from first the second syllables, with third (final) syllables dropping off somewhat. It is interesting to note that this rather vague contour forms a crossing pattern with the contour of its opposing word class.
Figure 30. Mean melodic accents for trisyllables.
Antepenult-accented tetrasyllables (Figure 31) conform to the same general contour as do antepenult-accented trisyllables. Regrettably, the lack of penult-accented tetrasyllables deprives us of the opportunity to see if another crossing pattern emerges. Pentasyllables (Figure 32) reinstate this opportunity, and confirm to a large degree the general trends witnessed with shorter words. The low value of first syllables in antepenult-accented words, creating an upward ramp rather than a zig-zag when moving from first to third syllables, is the only deviation. Note again the relatively high final syllable values for both classes of pentasyllable, as well as the crossing pattern that emerges even given the deviation just mentioned.
Figure 31. Mean melodic accents for tetrasyllables.
Figure 32. Mean melodic accents for pentasyllables.