The Evolution of the 6/3 and its Relationship to Other Dissonance Formations in the English Conductus

 

 

 

Olga E. Malyshko

 

In an unfinished article of 1958, entitled "The Changing Aspects of Medieval and Renaissance Music", Manfred F. Bukofzer expressed the view that source study, or what he referred to as the first phase of philological investigation, had laid the foundation for the second phase "a stage of stylistic study which concentrates on the music itself and relies on the analysis of the music as its primary method and evidence". He added that "unfortunately we still have a long way to go to make stylistic evidence the basic method it ought to be".^[1] Contemporary medieval research has concentrated largely on source study, almost to the exclusion of musical considerations in terms of the style of the music, and, more specifically, with respect to compositional processes and procedures. In fact, in the last forty years only a handful of such stylistic studies of Continental medieval music has appeared,^[2] and even fewer in the area of medieval English musical developments,^[3] initiated mainly through the pioneering efforts of Ernest H. Sanders,^[4] whose remarkable musical insights have brought us to a closer understanding of the rhythmic aspects of the repertory.

 

The current study came about as a result of a long-standing interest in compositional processes and procedures in early music, and the realization that if indeed medieval music was ever to be regarded as more than just an abstract phenomenon, reinforced by its historical distance from the present, an interpretive study of its style would be critical in raising it to the level of a living art form. The point of departure for this study is the music itself. Thus, it is often the music itself that comes to our aid in interpreting the somewhat ambiguous remarks of medieval theorists, dependence on which has always been necessary for a basic understanding of stylistic developments. The treatises serve as essential guidelines for establishing a relative chronology for these developments. They consider earlier and closely contemporary tastes, or may discuss long-standing traditions; in some cases, they indirectly provide insights into the influences under which certain repertories have evolved. If pedagogical tracts by nature, they tend to discuss the conventions rather than the exceptions of the time.  By extension, even certain conventions may not be discussed at length. In view of such limitations, much of what occurs in the repertory as seemingly unconventional is either briefly discussed or not discussed at all.

 

One of the thorniest problems arising in an effort to reconcile theory with practice is the relation of dissonance to consonance. What is the nature of the medieval theorists' discussions concerning the phenomena of consonance and dissonance? What are their explicits and implicits? What insights can be gained from these theoretical writings with regard to compositional process? The value of medieval theoretical accounts in this capacity is particularly critical, and can only be fully appreciated if understood from the perspective that the medieval period was an era during which scholars were attempting to develop a theory of sound and acoustic phenomena as well as a foundation for polyphonic theory. It was an era that strove to expand and elaborate upon the empirical concepts of Aristotelian and Pythagorean philosophies concerning sound and intervallic formations - the Aristotelian premise that an imperfect sonority has the potential for becoming perfect, and the Pythagorean, that all imperfection strives for perfection, or the simpler a sonority, the more perfect it is. Medieval musicians attempted to develop a theory of intervallic relationships, based on the differing intensities of intervals, and, in turn, construct a hierarchy of sonorities, in the order of descending degrees of relationship, beginning with the most perfect of the consonances and proceeding to the most perfect of the dissonances.

 

By the mid-thirteenth century, the impression given by the treatises is that the use of consonance was well established and substantiated with numerous examples and precise procedures as to its musical placement, while the application of dissonance was limited to only a handful of specific situations, discussed in any detail. Despite the theorists' meagre accounts on the subject of dissonance, and given the experimental stage in the evolution of sonorities and progressions, the discords seem to have served a structural function in these repertories. Within this context, the 6/3 emerges as a fascinating harmonic phenomenon, assuming the quality and function of both a dissonance and a consonance.

 

The 6/3 sonority has long been recognized as the hallmark of English conductus^[5] style. Generally, its tension-generating quality has been associated with that of thirds and sixths in two-voice settings. This tension-generating quality may also be attributed to other intervals and intervallic formations, variously classified by theorists as perfect, intermediate and imperfect discords. I have demonstrated elsewhere^[6] that these discords figure prominently in the English conductus repertory of the thirteenth and fourteenth centuries in both strong and weak positions, and are systematically used to counteract static entities, to introduce contextual variety, to heighten the syllables of regular and irregular poetic texts through occurrence in identical positions in consecutive strophes and on the rhyming elements of strophes, and as part of a series of specific tonal progressions featuring consecutive discord occurrences. In short, their importance cannot be limited to their "coloristic" or ornamental effect at cadences, but extends to large-dimensional structural function. My findings have also indicated that discords in general, and 7/3 and 7/5 sonorities, in particular, are rarely followed by a 6/3 on consecutive strong parts of the perfection.

 

Spanning a period from circa 1250 to circa 1380, and interpreting the theoretical and practical evidence, the present article^[7] develops and proposes a functional theory of systematic dissonance treatment by discussing the manner in which the 6/3 developed, and the reasons underlying this development, with regard to the functional and theoretical relationship of the 6/3 to other dissonant formations, specifically the 7/3. This development is centred largely on the use of strong-beat dissonance,^[8] which is a thirteenth-century phenomenon, evident in the English conductus from circa 1250 to circa 1280, and superseded by the 6/3 - 8/5 construct, featured in settings after circa 1280.^[9]

A handful of selective theoretical statements constitute our points of departure. The earliest of the thirteenth-century treatises to discuss dissonance is the Discantus positio vulgaris (circa 1225), preserved in the compendium of musical knowledge drawn up by Jerome of Moravia (after circa 1272). Its author points out that:

 

Among the concords, however, there are three that are better than the others,namely, the unison, fifth and octave. Indeed, others are more dissonant than consonant, though in greater or lesser degree.Inasmuch as the second seems to be more dissonant than any other interval.^[10]

 

After discussing the mensurability of discant in terms of longs and breves, the author points out:

 

            It should be known that all of the odd-numbered notes, when consonant, are more consonant
than the even-numbered notes; when dissonant, less dissonant than the even-numbered
ones.^[11]

 

Although this passage is not without its ambiguities in some respects, the gist of the first part surely is that perfect concords alternate with "lesser" concords on the strong and weak parts of the perfection respectively. In view of the general rule applied to the rhythmic alternation of consonance and dissonance, the passage concerning dissonance is perhaps more ambiguous if taken literally, since two consecutive discords would then appear. In this case, the author provides no example to illustrate his point. The intention here may be to express the idea that all intervals falling on strong parts of the perfection must be relatively "better" harmonically, whether they be consonantias or discordantias meliores (lesser discords), than those falling on the weak parts. Therefore, a literal interpretation of the passage would suggest two consecutive discords, whose placement would depend on the varying degrees of their "dissonant" quality.

  

Garlandia in his De mensurabili musica from circa 1250, draws up the categories for consonance and dissonance^[12] outlined in Figure 1:^[13]
 

       

 

 

                        Figure 1:Categories of Consonance and DIssonance after Garlandia

 

 

It should be noted that at the turn of the fourteenth century, by which time the 6/3 sonority was fully developed in the English repertory, the designation "imperfect consonances" came to refer not only to the major and minor thirds in Garlandia's intervallic schematization, but also to the major sixth. Additional information regarding the Discantus positio's two consecutive discords may be gleaned from Garlandia's treatise, in which the author elaborates the notion of lesser or greater degrees of consonance and dissonance, outlining several instances of the use of discords; he states:

 

It should be noted that every discord before a perfect or intermediate concord is equal to an intermediate concord, and this is properly observed before the unison  or octave: A tone before a unison. A tone before the octave and so on for the others. And this is improperly observed before middle concords. But this is found in many places in organum . . . as in this example: Semitone before a fifth. Tone before a fifth. Tone before a fourth. And it must be noted that a discord is never placed before an imperfect concord except for the sake of color or beauty of music.^[14]

 

The examples promised in the discussion are omitted, but would probably have taken the form in Figure 2:

 

 

Figure 2: Probable forms derived from Garlandia’s discussion

 

 

According to his instructions, the major sixth, although not directly mentioned would have been incorporated as in Figure 3:

 

 

Figure 3: Incorporation of M 6

 

 

The notion in the Discantus positio of intervals being dissonant or consonant to a greater or lesser degree is suggested in Garlandia's instructions, when he states that discords may harmonically achieve the status of intermediate concords, if they are properly used, as in Figure 2. In addition, he points out that a discord may precede an imperfect concord for the sake of musical color. Color may imply local effect or structural result. Although he regards the major sixth as an imperfect discord, its acceptance as an imperfect concord by later thirteenth-century theorists extends the applicability of his rule to the progression 7-6. Therefore, a discord followed by an imperfect concord might suggest the progressions in Figure 4,

 

 

                                                              

Figure 4:  Progressions implied by and derived from Garlandia's discussion.

 

 

which may also relate to the rule of the Discantus positio vulgaris involving two consecutive discords. On the whole, Garlandia advocates concords on strong parts of the perfection and discords on the weak parts, generally allowing discords to occur on strong parts, and on both strong and weak parts for the sake of musical color, but only if they are properly resolved. He illustrates this with several examples in his treatise, but none provides cases of dissonances occurring on consecutive longs; in all of his examples, the strong-beat discords are resolved on the weak parts of the perfection.

 

Anonymous IV (circa 1275) distinguishes himself from the other thirteenth-century theorists by alluding to English practice in his appraisal of major and minor thirds.^[15] He still views the major sixth as a discord, but discusses it as the best penultimate before the octave.

 

Thus, we have shown that worthless and disgusting discord, which is the sixth, and which is, for the most part, avoided. If it is the penultimate note before a perfect consonance, which is the octave, it is the best consonance in such an arrangement of notes or sounds.^[16]

 

In a subsequent passage on the use of discords, he describes a progression largely outlining sixths:

 

There are those who increase discords manifold before a perfect concord such as the octave, and for that reason are both excessively praised and ridiculed, and the fact that this can be done accordingly d f c d c b c  in the upper voice and D D E F E D C in the lower, it is viewed by them to be of extraordinary greatness.^[17]

      

Anonymous IV, whose treatise is largely based on the doctrines of Garlandia's De mensurabili musica, provides additional information on dissonance in his brief discussion of the use of the second:

     

There are certain good composers and creators of polyphonic song who sometimes  use discords instead of concords even in view of what has been said, and to achieve subtlety of phrase we can use notes or sounds, such as a whole tone before a perfect concord. This [the whole tone] will also form a consonance, whether this is the penultimate note, or is found elsewhere, since this is a proper rule. Every penultimate note before the rest, which is the end of a section, is a long. If the penultimate note is a whole tone above the tenor, as in organum purum, it will form a good consonance, although a p\whole tone is not a consonance.^[18]

In a further section dealing with the irregular modes, he goes on to say that:    

 

Some end [the composition] with a single note on the octave, unison or fifth . . .There are those who use either a consonance or a dissonance on the penultimate before the . . . octave, however, as long as it will sound well. Others place one, two, three or more [dissonances] before the penultimate, provided that the sound is balanced in one or several ways, and that this does not extend excessively, without reaching the end.^[19]

 

Anonymous IV's application of the second is as a penultimate dissonance within organum purum.^[20]  Regardless of the notation, he says that penultimates should be long and may be dissonant. However, he also points out that certain composers use discords in place of concords, not only in penultimate positions, i.e., the perfection before the cadence, but also "elsewhere," possibly implying on the strong parts. The reference here is probably to the use of dissonance for musical color, as discussed by Johannes de Garlandia. Anonymous IV's commentary in the section on the irregular modes offers one case of the occurrence of discords "elsewhere," that is, in positions before the penultimate, and draws limits for their use, with conditions based generally on considerations of harmonic balance. Since the discussion deals with a strong-beat discord as a penultimate, discords preceding the penultimate are contextually likely to involve those appearing on strong parts of the perfection.

     

Jerome of Moravia's compendium of musical knowledge also includes a discussion of the discord as one of four means of achieving musical color:^[21]

 

Dissonance, so that it becomes a concord, is a single or double dissonance between

twice the octave and the octave and fifth which concords well, as in the following:^[22]

 

 

 

Example 1:Jerome of Moravia's example of dissonance.

 

 

The example he provides does not directly correspond to what he has just said; rather, the text would seem to indicate the following progressions:

                       

 

Example 2a - d: Progressions derived from Jerome of Moravia's discussion

 

The two progressions 5-2-1 and 5-6-8 are clearly related in that both the second and the sixth have already been recognized as effective penultimate intervals before a perfect final. Therefore, the author is saying that the case he has just described in his text corresponds exactly to the situation illustrated in his example, thereby commenting on the identical nature and function of the two discords. In this position the discords achieve the status of "concords," as discussed by Garlandia and Anonymous IV.

 

Odington, writing circa 1300, makes reference to the progression "per concordias et concordes discordias",^[23] which in his listing include major and minor thirds, sixths, tenths and the eleventh. His notion of concordant discords relates to the discussions in the Discantus positio vulgaris and in Garlandia's De mensurabili musica, concerning the degrees of consonance achieved by discords in proper positions.

 

In conclusion, the general idea transmitted in the passages cited is that consonance and dissonance were integrated into a system, the rules of which could be suspended for reasons of melodic and structural color. More specifically, the treatises discuss or imply the tension-generating quality of imperfect consonances as well as that of imperfect, intermediate and perfect dissonances. Anonymous IV alludes to local practice in his appraisal of thirds, regarding the sixth as an ideal penultimate before the final, and comments on the use by some composers of consecutive discords. Garlandia not only argues against the conventional use of discords preceding imperfect concords except for the sake of color, but also gives a lengthy commentary on the changing status of consonance and dissonance in terms of their placement, providing examples which illustrate the use of discords on strong parts of the perfection, but not, it seems, on consecutive strong beats.

 

What insights can be gained from the above treatises with regard to the relationship of the 6/3 to the 7/3, bearing in mind that the theorists' points are illustrated with two-voice examples? My stylistic observations of thirteenth-century compositional processes and procedures lead to the deduction that two-voice progressions yield the three-voice formations outlined in Figure 5a - f:

 

  

 Figure 5a - f : Three-voice sonorities derived from two-voice patterns

 

 

Novel three-voice sonorities emerge as derivatives of two-voice patterns, retaining the latter's positions and functions within their respective contexts. As advocated in the treatises until and throughout the thirteenth century, the third voice follows the same rules as the lower two, whether in the context of octave doubling "in infinitum" as in the Musica Enchiriadis, or in the context of reducing all three voices so that they operate within the octave range. Jerome of Moravia's gloss of Garlandia refers to the triplum thus:

 

Triplum is a proportioned melody which fits and harmonizes with the discant . . . Triplum in its
            stricter sense must be consonant, though at a greater distance, with the first and second voice,

if one does not represent the intervals reduced by one octave which means the same.^[24]

 

As Jerome's gloss points out, the triplum must be consonant with the other two voices, whether it occurs within or beyond the octave. The addition of a third voice does not bring an increase in the number of voices, but rather increases the textural effect and the possibilities for more varied intervallic combinations. The triplum is not regarded as being an expansion of the vertical sonority. By means of voice-crossing the interval of a fifth in a two-voice framework, for example, sounds the same fifth in a three-voice framework through a doubled unison or fifth. As a result, progressions such as 5/1 - 5/3 - 5/1 - 7/5 - 5/1, the equivalent of 5 - 5/3 - 5 - 7/5 - 5, theoretically represent an increase in the variety of progressions, basically from doubling of the lower voices at the fifth. The same principle applies to octave doubling, where the same progression might read 8/5 (or 12/1) -12/3 - 8/5.

 

As demonstrated in Figure 5, the progression 3-1 becomes assimilated into 5/3 - 5/1 through doubling at the fifth, a common progression at cadences. The interval of the second with its resolution to the fourth in contrary motion becomes the seventh through octave transposition with a consistent resolution to the fifth in contrary motion. The resolution of the second to the unison, or the seventh to the octave, is virtually abandoned, and appears only once in the repertory dating from circa 1250 to circa 1280 in octave transposition as a ninth resolving in oblique motion to the octave. The reluctance to use 9-8 probably has to do with the restriction of writing within the octave range, and the preoccupation with penultimate 5/3 sonorities, and their later 6/3 extensions before a final 8/5.^[25] The resolution of the second to the third in oblique motion, through octave transposition, would necessarily involve sevenths resolving to sixth chords in the same manner, and then 6/3 formations resolving to 8/5, a progression which becomes common in the later conductus with expanded range.

 

In the majority of three-voice pieces dating from circa 1250 - circa 1280 where the progressions 7-5 or 7-6 are outlined, the lower two voices outline a third. In two-voice settings, the progression of a tension-generating third resolving to a unison is a strong cadence. This quality becomes emphasized in a three-voice texture, through the introduction of dissonance: 7/3 - 5/3 - 5/1 or 7-6/3  - 6/3 - 6/1 as in Figure 6:

 

 

 

Figure 6: Assimilation of the 3rd into three-voice patterns

 

 

The practice of using the progression 2-3-1, for example, continues to be functionally represented in the thirteenth-century three-voice conductus, where the third is assimilated into the 5/3 sonority, and the second, through octave transposition, becomes part of 7/3 and 7/5 formations, yielding additional variants, such as 7- 6- 5/3 - 5/1 cadentially and 7/5 - 5/3 - 5/1 or 7/5 - 7/5 - 5/3 - 5/1 in mid-phrase as illustrated by the progressions in Examples 3a 3b and 3c:

 

  

Example 3a - c: Assimilation of the 2nd and 3rd into three-voice progressions

 

 

The interval of the seventh assumes the position of a tension-generating penultimate before the fifth. Thirds and seconds filtered into the texture in two-voice repertories, and continue to do so in transformations in the thirteenth-century three-voice settings.

 

The progression 7-6 outlined by the outer voices occurs more frequently in a situation where the sixth appears on the weak part of the perfection in a rhythmic configuration before the resolution to a 5/3 or 5/1 sonority, as in Examples 4a, 4b and 4c:

 

  

Example 4a - c: 7-6 progressions resolving to 5/3 or 5/1 sonorities with 6^th on weak part of perfection

 

 

In only two cases the 7-6 progression is found in a motive where 6/3s occur, as illustrated in the conductus Transit nature semitas^[26] (see transcription of this entire piece in Appendix 11^[27]) in Examples 5a and 5b:

 

 

                    Example 5a: Transit nature semitas, m. 45            Example 5b: Transit nature semitas, m.49

                            (Ob 497^[28])                                                                     (Ob 497)

 

 

This example brings to mind Garlandia's rule involving the use of a discord before an imperfect concord for the sake of color. Unfortunately, he does not provide an example in his treatise, so it is impossible to say whether both intervals would have occurred on strong parts of the perfection. However, in the absence of practical evidence from Garlandia to support the latter, it is possible that if we extend his rule, it would refer to situations similar to those in Examples 5a and 5b. However, in view of the scarcity of progressions such as those in Examples 5a and 5b, more likely, his rule applies to the situation on the first perfection, as in Example 4a, where a 7/3 is followed by a 6/3 on a weak beat. In fact, in the conductus of this period, discords in general (4/2, 6/5, 5/2, 4/3, 5/4 etc.) will rarely, if ever, be followed or preceded by a 6/3 or a 6/1 sonority on consecutive strong beats.

 

Why should this have been the practice? In the case of the seventh in either a 7/5 or 7/3 formation, the reason may lie in the latter's theoretical connection to the resolution interval and sonorities of the fifth and 5/3 or 5/1 respectively, a phenomenon repeatedly borne out in practice. The rationalization for this lies in the evolution of the third as a tension-generating interval before the final, interchangeable with and often preceded by the second, also recognized for its tension-generating quality. A further explanation may be given for the absence of the sixth or the 6/3 on a strong beat, if we consider the scheme of intervallic derivation in Figure 5. It is noteworthy that the only interval subjected to "finite" inversion is the dissonance of the second. I present the term "finite" as that which cannot be doubled "in infinitum". The consonances of the third and fifth, on the other hand, belong to a category which I have labeled as "doubling" intervals. In his study of English discant, Georgiades explains the evolution of the 6/3 through the linear integration of the sixth occurring in the triplum between a 5/3 and 8/5, that in itself being an obvious step in that the interval of the sixth was viewed as an ideal sonority before the octave final.^[29] I take this notion further. That the sixth, as a dissonance, is not included in the category of what I label or to which I refer as "inverted" intervals reinforces its linear development as discussed by Georgiades, since theoretically the consonant third, capable of being doubled at the fifth, is therefore incapable of being inverted as a sixth in a three-voice context; thus, the 6/3 eventually became an independent vertical entity, drawing on such parallels as those in Examples 6a and 6b:

 

 

  

            Example 6a: Salve virgo virginum, m. 7                 Example 6b: Virgo valde virtuosa, m. 9

(Lbm 248)                                                                       \(Cgc 334)

 

 

 

The reference of Anonymous IV to English partiality to thirds no doubt extends theoretically to their 5/3 counterparts. The 6/3s on the first perfection in Examples 5a and 5b are therefore theoretically unrelated to the 6/3 that later emerges as a penultimate before 8/5. Because the seventh's resolution to the fifth on a strong beat seems natural in either 7/3 - 5/1 or 7/5 - 5/3, and since the forerunner of the 6/3 is the 5/3, the 6/3 will rarely, if ever, occur on a strong beat, preceded by a 7/3 or 7/5, also on a strong beat. Furthermore, the position of a 6/3 on a strong beat, preceded by a 7/3 on a strong beat would cause ambiguity as to whether the former should resolve to an 8/5, or whether the latter to a 5/1. Once the 5/3 develops linearly into 6/3, the seventh and its counterparts (7/3, 7/5) become obsolete, because of the tension-generating quality of the 6/3 sonority, which permeates the texture of English conductus after circa 1280, appearing on strong and weak beats in tempus perfectum. Consider the hypothetical situation in Examples 7a and 7b:

 

 

  

Example 7a, b: Resolution of the 7/3 and 6/3

 

 

It is because of this situation that the 7/3 and the 6/3 could never occur on consecutive strong beats, as implied by Garlandia's instruction concerning cases where dissonances were allowed to precede imperfect concords for the sake of "color". Their correct resolutions in mutually exclusive 0contexts comply with Garlandia's "properly and improperly observed usage," raising them to the status of concords.

 

From circa 1250 to circa 1280, the 7/3 and 7/5 permeate the texture and take on the nature of vertical structures with consistent resolutions to the fifth and its counterparts. These sonorities also appear on consecutive strong beats with prolonged resolutions, in the manner of later consecutive 6/3s resolving to 8/5 as in Example 8, thereby illustrating and amplifying the points of the Discantus and Anonymous IV, concerning consecutive dissonance occurrences:

 

  

Example 8: Transit nature semitas, mm. 24-26 (Ob 497)

 

 

Ninety-one percent of thirteenth-century conductus within octave range use discords on strong parts of the perfection. These dissonances can be grouped into two basic categories, depending on their levels of intensity: the 7/3 and 7/5 formations with proper resolutions to the fifth or its three-voice counterparts, function as vertical structures, occurring singly or on consecutive strong beats. As stabilized entities, their harmonic capacity allows them to function unchangeably in larger dimensions. What I term linear discords, which are illustrated in Example 9a, 9b, 9c, 9d, and 9e, belong to a different category of dissonance, and are found in two types of situations: as a single polydissonance appearing on the strong part of the perfection with a resolution to a strong or a weak beat; or as one or more polydissonances occurring on consecutive strong beats or on subdivisions of the perfect long with a resolution either to a strong or weak beat:

 

 

.

                        

  

Example 9a - e: Linear discords

 

 

Significantly, in the English conductus settings after circa 1280, where the range is expanded beyond the octave, resulting in an increased number of new sonorities, with series of parallel 6/3 formations introduced as tension-generating intervals, virtually all strong-beat dissonance disappears. The treatment of discords after circa 1280 differs considerably from that in the settings prior to this date. The introduction of individual note symbols in the Franconian, Petronian, English long-breve, the early fourteenth-century French notations, and the fully-developed mensural system with prolatio minor does not affect the pattern of pulsation, which remains proportionally identical to that of the modal principle. The comments of Jacques de Liège,^[30] writing in the early fourteenth century, on how the semibreve has now the same speed as the breve had previously (and, by implication, the breve, the same speed as once the long) suggests that although symbols have changed, the stress patterns have remained the same. As in the earlier settings with perfection and tempus declamation, the "metric" movement is still from long to long, or later, from breve to breve (see Figure 7). Even with the continued effort of adding symbols to the notational spectrum (minim, semiminim, etc.), musical space was still controlled by major anchors, outlining movement from one point of stability to the next. However, in some cases, the inevitable creation of superstructural pulsations, not reconciled with in theory, as opposed to regular pulsations, nevertheless had a definite, inescapable impact in practice. Given the derivations in Figure 7, theoretically the "metric" pulsation for settings in prolatio major would be felt as movement from breve to breve.

 

 

Figure 7:  Long and breve metric pulsations (L = long; B = breve; S = semibreve; > = accent)

 

 

In view of the rhythmic complexity often associated with the elaborate conductus of the fourteenth century, as well as with some pieces in Petronian notation, it sometimes becomes difficult in practice to maintain the stress patterns over long durations, particularly in tempus perfectum. A considerable increase in rhythmic activity, particularly if extensive modular structures emerge, will ultimately cause a decrease in tempo, however slight, and inadvertently create a within-the-beat pulsation, as in the following examples:

 

 

  

Example 10a^[31]: Generosa iesse plantula, mm. 90-92 (US-NYpm)

 

 

   

  

Example 10b: Virgo salavit hominem, mm. 4-8 (Lbm 1210)

 

 

On the other hand, numerous fourteenth-century text settings tend to confirm a breve-to-breve pulsation by predominantly presenting one syllable on each breve or occasionally on every two or three-breve units:

 

                                     

Example 11: Singularis laudis digna, mm. 43-48 (US-NYpm; Occ 144)

 

 

Example 12: Regem regum collaudemus, mm. 56-63 (US-NYpm)

 

 

Movement by three-breve units is suggested in the Pierpont Morgan setting of Salamonis inclita mater in tempus perfectum prolatio major, on the basis of its concordance in Cgc 512, where it is preserved in Petronian notation. Whether we take this to be a case of representing the same rhythms in different notations, or one of producing a modernized version of the piece, the "metric" stresses will remain constant. The     stress pattern in Cgc 512 is clearly reflected in   in the US-NYpm source. However, if the earlier concordance had not been available, it would be difficult to conclude that the strong  beats occur on the first breve of every three-breve unit. The pulsation pattern could just as easily be viewed as movement from breve to breve.

 

In the absence of concordances to prove otherwise, several aspects tend to indicate long-to-long pulsation in pieces written in Franconian, Petronian and English long-breve notations, and breve-to-breve pulsation in those written in prolatio minor and major. The tendency to place single syllables on breve units has already been mentioned (see Examples 10a and 10b).

 

The use of structural dissonance provides additional insight into the location of the strong beat. In the earlier mensural systems, as well as in tempus perfectum prolatio minor, a dissonance often results from a plicated note, suggesting the non-structural nature of that discord. Consequently, any discords not caused by plicated notes, but occurring on the same subdivision of the beat will also be non-structural as in Examples 13a, 13b, 13c and 13d:

 

 

 

Example 13 a - d: Includimur nube caliginosa (Cgc 334; Lbm 62132A)

 

 

Dissonance in the later repertory also appears on secondary rather than on initial notes of cum littera ligatures as in Examples 14a, 14b, 14c, 14d and 14e.

 

                                                       

 

 

The applicability of Garlandia's rule of a discord never preceding an imperfect consonance, except for the sake of musical color, and, as we have seen, never on consecutive strong beats, is evident in Examples 15a, 15b, 15c, 15d and 15e.

 

                   

 

 

In view of what has been said about the relationship between the 7/3, 7/5 formations and the 6/3 sonority, it would be logical to assume that theoretically the same ambiguity would exist in their resolutions, if the 6/3 preceded a discord on two consecutive strong beats. Such a situation would be avoided. 6/3s precede discords, but suggest movement from strong to weak as in Example 15b.

 

In the light of these features in the late thirteenth and fourteenth-century repertories, the level of strong-beat dissonance is considerably diminished. As stated previously, the introduction of a new tension-generating element, that is, the 6/3, both in strong and weak positions, separately and in a series of sometimes up to thirteen, as well as the expanded sonorities, caused strong-beat discords to become virtually obsolete. Indeed, in the new harmonic context, there were more possibilities of generating tension, and the use of strong-beat dissonance was unnecessary. Out of a total of forty-six complete and fragmentary conductus settings, dating from the late thirteenth and fourteenth centuries, only twelve pieces use strong-beat discords in theoretically prescribed long-to-long and breve-to-breve pulsations. If we consider within-the-beat pulsations for rhythmically complex settings, then our total is increased by only two, giving, at maximum, a thirty percent as opposed to the earlier ninety-one percent usage of strong-beat discords. An expansion of the fundamental sonorities through octave transposition results in the following basic equivalents:

 

 

Figure 8: Equivalents derived from expansion of fundamental sonorities via octave transposition

 

The earlier thirteenth-century progressions are retained, therefore increasing the capacity for harmonic vocabulary by half. In addition, the dissonant formations are also subjected to expansion. Virtually all belong to the "linear" variety, thereby avoiding any ambiguity regarding proper resolution, as in the case of 7/3, 7/5 versus 6/3. Occasionally, a linear 6/5 will replace a 6/3 in a resolution to 8/5. The occurrences of 7/3, 7/5 and their expanded counterparts, 10/7, 12/7, respectively total 15 for the entire, provisional conductus repertories between circa 1280 and circa 1380. Of these ten appear on weak beats with only four instances of proper resolution (see Examples 16a, 16b, 16c and 16d):

 

 

 

 

 

and five appear on strong beats with only two cases of proper resolution:

                     

 

 In the remaining nine cases, they resolve linearly.

 

With the complete assimilation of the 6/3, the harmonic language is enriched to its fullest capacity, supporting the capabilities of innovative rhythmic techniques. There is a gradual shift from harmonic control in the thirteenth century to rhythmic control in the fourteenth century. In view of the developing notational systems, and their effort to accommodate increasingly complex texts, combined with the newly-discovered harmonic fluidity, experimentation in the area of rhythm was inevitable. In the elaborate conductus settings from the mid- to the late fourteenth century, rhythmic considerations often prevail over harmonic details and expectations, with the result that, in general, dissonances sometimes emerge incidentally. More importantly, the rare occurrences of strong-beat discords in the fourteenth century are reduced to local embellishments, in contrast to their use as continuing vertical structures of 7/3 and 7/5, or as integral parts of basic progressions in the thirteenth century.

 

 

 

 

 

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Appendix I: Manuscripts and Source Abbreviations

 

B-Br 266	Brussels, Bibliothèque Royale, MS II, 266
Cgc 334	Cambridge, Gonville and Caius College, MS 334/727
Cgc 512	Cambridge, Gonville and Caius, MS 512/543
Cjc 84	Cambridge, St. John's College, MS 84 (D. 9)
Cpc 228	Cambridge, Pembroke College, MS 228
Lbm 248	London, British Library, MS Arundel 248
Lbm 1210	London, British Library, MS Sloane 1210
Lbm 38651	London, British Library, MS Add. 38651F
Lbm 62132A	London, British Library, MS 62132A (olim Leeds, Central Library, Archives Department, MS VR 6120 [LEc6120]
Occ 144	Oxford, Bodleian Library, MS Corpus Christi College 144
Ob 497	Oxford, Bodleian Library, MS Corpus Christi College 497
Ob D. 6	Oxford, Bodleian Library, MS Dep. Deeds Christ Church C. 34/D. 6
US-NYpm	New York, Pierpont Morgan Library, MS M. 978
WO	Worcester, Cathedral Library, MS Add. 68

 

 

 

Click to view Appendix II: Transcription of Transit nature semitas (Ob 497)

 

 

 

 

  
 

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