Polyrhythm, Figural Construction and Formal Ambiguity in Fon and Yoruba Repertoires

While collecting in a book essential parts of studies on Yoruba and Fon music from Benin, I had the opportunity to pull back from the close focus that was needed when analyzing repertoires separately.¹ That became a need to overcome the limitations of interpreting the styles individually, and I tried to find common elements in the behavior of musicians regardless of stylistic resources that may set them apart. Most of both repertoires can be segmented in structures that indicate a level of completeness within themselves. There are remarkable phrases formed by hierarchically organized and stable constituents placed in well-defined musical contexts, indicating a reasonable independence of the musical structure from other events that constitute the whole performances. Nevertheless, I do not feel this music as a flow of clearly marked sound events: the effect of any non-redundant fixed parts in the rhythmic texture, the alternation of phrases with particular constructions, and the sequence of varied rhythmic structures within formal units created by the master drummer provoke different perceptions of these structures. Approaching these issues as a group highlights conceptual aspects that have not been satisfactorily solved within the considerable amount of information produced in those studies—-aspects still worthy of attention in the specific literature on African repertoires.

Therefore, the aim of this essay is to examine some aspects of Fon and Yoruba percussive music in Benin and how they relate to specific topics of African music theory, as well as to draw these styles nearer to some general concepts that govern the formal construction of a musical performance. I would like to draw specific attention to the performance of the master drummer within the global context of this music: namely, the use of resources that transform certain rules of rhythm and figure performance and add other types of processes. These resources impact the extension of segments of equivalent form and rhythm, the choice of differentiated timbers and intensities, and produce remarkable metric displacements.

The specificities of this music definitely place it in a singular, unique style category in the scope of general music theory. Nevertheless, there are concepts behind the phenomena within these styles that intersect with some aspects of musical styles from other cultures. That is why, at the end of this article, I search for insight from contemporary theoretical works on recent Western music. They may help us understand phenomena from a more abstract level of the musical discourse, purposefully based on general matters of musical theory and perception. Recent Western music is also the ground for discussions on polyrhythm, wherefore it may be useful to study the performance of African musicians in this context.

1. Metric displacement and addition

It is the understanding of African music researchers that there are stable and permanent metric values in several hierarchical levels during a particular musical performance². In an abstract or concretely performed sequence of beats, a certain point coming at regular time intervals becomes a reference for inserting fixed configurations or configurations created by the solo drummer. Nketia (1974)—-and then Anku (2000)—-called this point the regulative beat. This may seem to be a simplistic statement if one is describing pieces where the regulative beat occurs at up to 4-beat intervals, as in 4/4 or 12/8 time. However, in pieces with 8-beat intervals (i.e. in 24/8 or 8/4), the concept of a regulative beat becomes crucial. That is because in these pieces the intermediate interval of 12/8, for instance, will be important for creating the solo-drum configurations, but always in association with a double articulation of this time interval. In other words, whenever a certain configuration is present, it will take place at the precise middle of the 24/8 interval. This establishes longer time cycles, objectively defined in the relationship between the various instrumental parts. (This also holds true in 12/8 pieces, where the two halves are important for the creation of figure structures.³)

Example 1 shows the instrumental texture from Solejebe, a piece from the Fon repertoire. The alekle 1 support drum and the assan rattle produce 3-pulse-long rhythmic articulations, defining the beat (tactus, tempo or metronome value) that regulates the dance movements. The gan plays the standard pattern, establishing a hierarchically superior metric level. Together, these two rhythmic strata give us the regulative beat, which coincides with the first articulation of the gan pattern. These tiers also define the 4-beat module as the metric determining value. The second support drum, alekle 2, accents the first pulse after the tactus, adding a delayed reference to the texture, which will enable displacements in the hunda ho (solo drum) part. I call this additional reference the first offbeat position (offbeat A), It is also metrically dependent on the presence of the same regulative beat, since the master drummer will follow the offbeat position following the regulative beat, including the use of anacruses. The example contains one such configuration in the solo drum part, which we will look at later in this article. I will also comment on the complementing effect of the support drums’ parts.

The hunda ho solo drum will create another textural contrasting tier, since several of its configurations in Solejebe have two-pulse values and always come in groups of three (not two) units. Cross rhythm is the name given by African music theory to the relationship between these configurations and the sequence of beats.

In example 2, we see the gan’s part and a complete solo drum phrase from Wede, another Fon piece. The support drums and the assan perform the same patterns as in Solejebe. The example contains a remarkable case of cross rhythm: the gan executes a pattern suggesting a binary organization of the tactus and establishes the cross-rhythm relationship in 8:3 ratio, with values set by the alekle 1 and assan articulations. The gan pattern is repeated three times to create a full cycle of the meter used in the piece—-a sequence of 8 beats (dotted quarter note). Cross-rhythm is therefore the resource of superposing or juxtaposing segments based on different values within the same time interval to create a ratio between the segments: 3:2, 4:3, 6:4, 8:3 etc. If stable intervals of 2, 4 or 8 beats are kept in ternary pieces, we see that this group’s master drummer is able to freely alternate between these values.

The analysis of this resource has been recently reviewed in terms of the complementarity between parts. But that happens only when patterns are formed by articulations from instruments with the same timber, because their relationship creates composite configurations. In Wede, the bell pattern offers an independent configuration that does not merge with the other parts’ articulations. On the other hand, one can observe the complementary effect in the relationship between the support drums alekle 1 and 2. In that case, the accent on the first articulation of each alekle 2 group works as the down beat, and the parts become one single offbeat pattern.⁴ The example also contains a full phrase, typical of this piece, consisting of a dislocated introductory structure followed by a figural-periodic structure (starting at cycle 108a), which follows the binary rhythm suggested by the gan. The structure is finished on the regulative beat by using a closing figure found in several contexts in Wede.

In both pieces, the master drummer also uses another offbeat position as a base for specific configurations. That is the second offbeat position (offbeat B), coinciding with the second articulation in both timelines. Example 3 shows one of these occurrences. This is a recurrent configuration in both Solejebe (12/8) and Wede (24/8). The player uses the second offbeat position (always starting at the regulative beat) as a reference and then inserts a figure that encompasses three pulses. The structure can be segmented in two parts: a figural-periodic structure and a closing structure. The first one can be split into two equal parts, consisting of a slightly varied repetition of the same figure. I named these configurations, formed by contiguous repetitions of the same figure, periodic models.

Examples 2 and 3 offer good basis for comparing the use of rhythmic addition. Each of these configurations is usually associated to a certain metric position. Or, inversely, each metric position that deviates from the regular metric structure is assigned a restricted set of predefined figures. In example 2 all of segment A is built on the underlying three-pulse value, on offbeat A, parallel to the alekle 2. This segment will always be in this position. In this same example, the underlying 4-pulse value suggested by the gan pattern determines the figure-period structure (from 108a onwards). Between these two phrase members (in 107b), the player adds a segment with irregular underlying values (/3+3+4/) so that the insertion of the figural-periodic segment occurs in 108a, starting from the regulative beat.

The segment in example 3 also results in a case of addition. The player always tries to close on the regulative beat. To achieve that, he uses a closing figure (/x+y/) that works cross-rhythmically, unlike the offbeat B base used for the periodic structure. Similarly to segment A from the previous example, these example’s configurations always take place on the same rhythmic positions.

The closing structure in example 3 (as well as the closing figure in example 2) is typical in Wede. Considering the way it is used and the various contexts it appears in, it may be segmented in two parts. The rhythm of these parts can be analyzed through the 4-pulse underlying values. As seen in the figure-period structure in example 2 (starting at 108a), this piece admits the basic value of 4 pulses (a half note) for the building of figures and motives, with a high degree of stability. The segment in example 3 is also typical of Wede, mainly for its closing structure. What we see here is that the construction of stable constituents naturally depends on the primary metric structure of the piece. However, the coinciding tempos and the constant presence of a three-pulse texture may create objectively equivalent moments in the performance of both pieces. Solejebe is the piece with the greatest variety of structures in this repertoire. It is more of an assimilator of structures regularly found in other pieces than a supplier of structures to others.⁵ It is certainly more “practical” to occasionally double the 12/8 meter to accommodate figure structures from 24/8 pieces.⁶

That said, example 4 shows a structure that is placed strategically in the performance of Solejebe and is entirely derived from segment A, which is typical of Wede, as seen in example 2. It creates a periodic model on the first offbeat position: after figure A and its complement are presented, the player builds a sequence based on the repetition of /a’/, a derivation of /a/. The sequence is interrupted by adding the interpolating figure just as in example 3, but without the complete closing structure. Instead, by using the /x/ articulation, the player accents and reassumes the offbeat A position, reintroducing figure /a/ and proceeding with the /a”/ variation. This figure is a sequence of two-pulse values, also starting on offbeat A. The player creates an actual cross-rhythm relationship here from the offbeat position. After the third articulation of /a”/, some articulations are inserted that dissolve the previous figure relationships and the phrase is closed with the regular closing motif, also presented in example 3. The performer actually fragments the closing structure (in cycle 358) onbeat, to recover the offbeat A position and continue the periodic model with variations, following the same rhythmic orientation. This means the performer changes rhythmic orientation twice, resulting in additive structures.

In examples 2 and 4, the same segment A is present in the same offbeat position. The element created here, though rhythmically and metrically stable, clashes with the basic meter assumed for the respective pieces where the segments appear. David Locke (1982) called this expedient consistent offbeat timing. He interprets it when discussing polyrhythmic processes in Ewe drum music, opposing it to the concept of cross-rhythm. Per this definition, the complete configuration from example 4 contains both resources; the first configuration on offbeat A implies underlying three-pulse values, while the second configuration has two-pulse values, even though it is not oriented by the cross-rhythm beat chain that presupposes the regulative beat. Because it is a clear process of derivation from the same figure, this example reveals the proficiency of African musicians in shifting from one surface value to the next. That is, if a certain time interval is respected, the player may freely alternate between three and two-pulse values. So I consider offbeat timing to be the technique that juxtaposes concurrent rhythmic layers not only to beat-defined values, but also temporarily neutralizing the regulative beat action. For which reason it seems more relevant to highlight the effect of this resource on the metric level of regulative beat-regulated time intervals, than on beat-sequence level.

Example 4 also contains a significant case of additive segments. In this segment, after creating an offbeat configuration, the player returns to the regulative beat twice, for the partial and final closure of the phrase. Note that examples 3 and 4 use the same closing segments. These perfectly stable and recurring configurations are used in several performance contexts and directly presuppose the presence of the regulative beat. They work together here with structures with different rhythm bases, which calls for some adjustment intervals at both points. Most of the time, additions result from the process of returning to the regulative beat, which is departed from according to a series well defined rules.

Polyrhythm and Polymeter

The objection to the notion of polyrhythm as a resource applied by African musicians such as the ones from this Fon group seems foreign to me.⁷ I understand polyrhythm as an overarching concept embodying the simple notion of distinct rhythm planes being juxtaposed or layered. However, that happens discriminately. The rhythm level concurring with the one established by the regulative beat depends on the latter. Furthermore, the application of these shifts tends to imply a reduction in figurative potential for each of the segments. Thus, segment A on offbeat A, from examples 2 and 4, is complemented by a configuration of simple articulation groups of one pulse length. The derivate version in example 4 (cycle 360) consists of repeated two-pulse articulations. Similarly, the predominant figure in example 3 consists of repeated values that split the three-pulse tempo in two halves (a dotted quarter note). The following can be drawn from these examples: when shifting rhythmic processes do not coincide with the basic rhythm structure, the figure structure tends to be simpler.

Polymetry, specifically, may entail varied metric formulations during a musical performance, through the application of several possible types of operations. But in this music, we witness a restrictive strategy for generating metrically concurrent structures. Take constituent /A/, from example 3, consisting of two occurrences of /a/. The performer inserts the first figure, which consists of three articulations, to mark the start of each segment; he limits the time interval at which the occurrences succeed each other. In examples 2 and 4, Segment A is constructed in a like manner. Figure A starts in anacrusis, leading to an accentuated articulation on the first offbeat position. The following term leads to closure of the whole structure, in the same relative position. Both structures describe 4-beat time intervals with extensions that meet the basic metric structure. The poly- prefix here refers therefore to a multiplicity related to the metric structure insertion point, resulting in well-defined figure elements. There is no extraordinary variation of time intervals, i.e. none of the indistinct sequencing of metric units that can be found in other repertoires. The formal elements represented herein presuppose metric regularity, returning to a central point, and are used discriminately. As mentioned before, addition in these cases results from leaving that center and then returning to it.⁸ Adding displaced bars in relation to other patterns in the texture would eliminate the notational representation of this center, expressed by the regulative beat.

The performance of additive segments varies according to context, breaking the regularity implied by the above comments. For instance, example 2 represents a productive phrase pattern in the structure of Wede. The player may prepare for it by using some sparse articulations in the metric cycles preceding the introduction of segment A. After those segments, one will nearly always see a motivic or figural-periodic structure that is similar to the example. Thus, the additive segment connecting segment A to the periodic structure will be identical or similar to the one in the example. In example 4, the player applies a variational procedure: a new figure is derived from figure A and articulated in a sequence (periodic model). In this case, the addition created by returning to the regulative beat will also be different. Note that the 4-beat regularity of the complement is sustained in both phases. The articulation designed by /y/ is displaced by one pulse from the first offbeat A position. This shift is an “expressive” resource, also used in other contexts, to mark the end of an important event. If we consider the offbeat flow as a primary flow, the closing structure in the last segment (cycle 363) would be functionally unnecessary. But, as previously mentioned, it results from the need of reestablishing the direction implied by the regulative beat’s presence.

The type of offbeat construction in examples 2, 3 and 4 could be described by a chain of generative rules. A figural formation is established in the regular 4-beat metric framework, considering some simplification or redundancy rule; a rule is then established to displace figures to the first or second pulse after the regulative beat; and, finally another rule creates an additive, metric compensation pattern to re-establish the regulative beat.

2. Motivic Structures

Fon Repertoire

As mentioned above, Solejebe is the piece with the greatest rhythmic and figural diversity. It is remarkable for creating configurations based on motifs, that is, figures that can be isolated in different contexts, not necessarily contiguously, and can be submitted to variations or just repeated within the same phrase.

Examples 5a, 5b and 5c show some of the recurrent phrases in Solejebe containing even more remarkable rhythmic processes, as well as the combinatory structure that builds this music. In 5a, after a preparatory structure (not shown), the performer inserts motif /a/, followed by a short interpolation element and a longer repetition of motif /a’/. A ternary structure is used to create the main motif and its repetition in turns, and cross-rhythm is also used to insert the intermediate figure and one extension element to /a’/. This constituent is followed by a closing structure and the phrase runs totally onbeat. In 5b, the phrase has the same motivic structure, but the closing structure that follows is different. This closing figure occupies offbeat B: it is ternary in organization, extending for 4 beats with a final articulation on the second pulse. A connective segment precedes it, creating an additive relationship between the phrase constituents. The closing segment contains 4 regular beats and the regulative beat is temporarily suspended here. The same closing structure is used in 5c, but the performer builds another motivic structure, based on the first offbeat position. The main motif here is not simply repeated, but submitted to variations, as we will see later.

So there are three phrases with distinct rhythmic structure. The phrase in 5a runs onbeat (with the added internal switching between ternary and cross-rhythm); in 5b, the phrase has the same motivic structure, but shifting from onbeat to the second offbeat position, while phrase 5c shifts from the first to the second offbeat position. All of these phrases are “prepared” by the same segment, which consists of rhythmically distant and relatively neutral articulations.

If we consider each of these phrases as autonomous moments in the performance of Solejebe, only the phrase in example 5a would match the previous examples in terms of closing on the regulative beat. However, these phrases form a block and are repeated and associated to phrases that indicate a related motivic structure.

Example 6 presents the motivic constituents of these phrases. Each of them ends in the closing structure on offbeat B from examples 5b and 5c. An exception to that is the phrase containing the motivic structure from example 6a, which, as in example 5, may also end onbeat with the closing structure from example 5a. In the most stable presentation of this sequence of phrases, the onbeat closing structure is introduced right at the end, closing the sequence. Furthermore, the player always presents the phrase from example 6d—-which is predominantly cross-rhythmic (see below)—-before reintroducing the phrase from 6a to close the block. So if this phrase is seen as an organism whose parts act interdependently, the importance of the regulative beat position is again confirmed.

Let us consider motivic organization. One notices that the configuration of example 6a, opening and closing the sequence, reproduces the most common pattern of phrase building in this piece—-namely, the presentation and repetition of the same motif in the exemplified metric position. In example 6b, the performer creates a new constituent, with the same formal characteristics and metric positioning, but changes the motivic configuration itself. (This configuration may be slightly varied.) Example 6c shows a segment very similar to this last configuration, starting on the first offbeat position. (We can imagine it is a variated transposition of the 6b motif onto offbeat A, which is extended to compensate for the new metric position.) Finally, on 6d, the player starts the same configuration from 6c on the first offbeat position. This time, he adds a group of articulations that entails shifting the accent of the articulations in motif 6c, as seen in example 7. What is seen in 6c as /x+y/ becomes /x’+yz’/ in 6d. That creates a new cross rhythm configuration, repeated after the pause. On the final presentation of this configuration, the player inserts three articulations into the preceding figure (half note) time. Thus, besides the linear rhythmic configurations represented by the alterations between the motivic and the closing constituents (as seen in example 5), we can see a vertical motivic transformation in this phrase sequence. We will study this example in more detail below.

Bàtá (Yoruba) repertoire

This article intends to offer a joint appreciation of elements from two repertoires where common characteristics may be noticed, however in a more abstract level of musical practice. We have concentrated on the Fon repertoire to this point because of the rhythmic and figural variety of this music, and corresponding theoretical implications. These factors invite broader discussions on rhythmic organization principles noted in correlated works. But traditional Yoruba music is far from being less important for understanding the African music thinking. The repertoire being examined here—-music for Bàtá drums—-lacks the technical uniqueness brought about by the frequent use of offbeat in the Fon repertoire. However, Yoruba music is remarkable for its motivic proliferation, with important implications for the formal outline of musical performance.

Example 8a shows the support drum parts of the Ako piece, from the Bàtá repertoire. I chose this moment for the amount of textural redundancy. The music allows for exuberant variability in support parts without presenting structural rhythmic changes: there is a sequence of pulses from the omele ako, while the omele abo and the eki play two-pulse values in parallel. The ako does not have to play this timeline continuously: in this piece, it is played only during pauses of the iya ilu (mother drum) part. Examples 8b and 8c show two consecutive phrases created by the soloist.⁹ As in all other phrases from Ako, these can be clearly segmented into /a-a-b-a/: a motif is presented and repeated in the same metric position; an improvisational and denser segment is then inserted in a less redundant position, before the regulative beat; and finally, the same motif from the introduction closes the phrase, giving way to a pause that encompasses one or more complete four-beat metric cycles. In these phrases, the ako does not play the four-beat metric pattern, which is then maintained by the regularly alternating iya ilu motifs.

In example 9a, there is a phrase from the same piece that follows the exact formal plan as phrases 8b and 8c. Phrase 9b is a variated repetition of phrase 9a. In the beginning, it maintains the regular formal categories, but adds new configurations at the point dedicated to motifs. The player fragments the motif and the segment from part /b/ of 9a to extract segments /x/ and /y/, then used to compose phrase 9b. The second metric cycle configuration in 9b consists of /z/ and the fragment /y/. All fragments are joined to build the densest part of the phrase. At this point, fragment /x/ from the initial 9a motif reappears, together with three variations of /y/: an augmentation, a timber variation and an extended inversion (/y’/, /y”/, and /y”’/, respectively). Upon closer inspection, one notices that all fragments of this figural proliferation are versions of the same rhythmic figure, with different timber dispositions. According to the basic phrase model, 9b would be missing a final reintroduction of the motif, as well as a rhythmic anticipation of part /b/. Instead of a final motif insertion, the performer inserts fragment /y”’/ several times. One may see the densest area of phrase 9b as a succession of segments derived from the initial 9a motif, since these segments start with fragment /x/. The phrase in 9b represents therefore a figural and formal dissolution of components from a well-established phrase structure.

These examples are from the mother drum part in Ako, consisting mostly of structures equivalent to the ones above. The structures, either repeated or modified, are scattered through all of the repertoire, even in pieces based on ternary rhythms. The other pieces are also marked by varied figural structures.¹⁰

3. Mutant Structures

Fon Repertoire

The Solejebe segments shown in examples 3-6 have a common formal structure, consisting of a figural-periodic or motivic structure followed by a closing structure. The phrases in examples 5 and 6 are presented twice as a group, occupying a strategic position in the performance. The periodic models from examples 3 and 4 are placed mainly as a type of preparation for these groups. The player may adopt certain structures more frequently at different points during the performance. They can be either sparse or more concentrated. The presentation of these structures is similar to the model used for Segment A in examples 2 and 4: there is an introductory figure followed by a segment I will simply call a complement, and a specific closing figure I will call segment Z for now. A sample of a structure of this kind can be seen in example 10. This example also contains a second motif /b/, which may either be freely permuted with /a/ or used as an introduction to the segment.

I have called the introductory figure a motif considering its recurrence in the performance. Note that this motif is presented only once and does not follow the same repetition and derivation-based structure from previous examples. The motif leads to the second offbeat position, whence the player starts the complement. The complement is formed by a periodic pattern based on figure /x/, encompassing three two-pulse beats (secondary beat). So with this figure /x/ the player creates a segment that manifests cross-rhythm and offbeat timing relationships simultaneously. The result, in this case, is a weakening of the regulative beat. The phrase is usually closed by segment Z—-a virtual displacement of the standard pattern—-with a final articulation on the first offbeat position.

There is some idealization in the form from example 10. This is possible, but not mandatory. After presenting the introductory figure, the segment becomes unpredictable: the complement may be sustained for several cycles, adding accents to the first articulation of the triplet fragment, the introductory figure may be reintroduced by itself or followed by the complement, before the closing figure. Furthermore, the closing figure can also be split in two figures, played in succession before the closing figure itself. The segments in example 11 offer a glimpse of the range of variational procedures resulting from these elements.

In example 11a, about halfway into the performance, the drummer plays an introductory figure followed by one of the possible complements, twice. This introductory figure is an alternative to the one in example 10. Interestingly, the player uses the final articulations from segment Z to wrap up both the figure (in 290 and 292) and the ensuing complement (in 291 and 293). Next (in 293), he uses the final articulations from example 10’s introductory motif to create a periodic model, which will not be extinguished until the full structure is inserted, starting at cycle 294. At that point, there is a very long version of the complement. Note that in the cycle following the introduction of this complement, the regulative beat is not marked by a precisely-timbred articulation (in 296), which contrasts with the expressive marking of this position in the two following cycles. Considering the complement starts at the offbeat B position, this results in the creation of additive segments. On top of that, the player retrieves the introductory figure from 289 before presenting the closing figure, shown here in its expanded form (Z+Zexp.)

Both examples below were extracted from parts of Solejebe well into the performance. They remind us of the figure used to construct the complement in examples 11 and 11a. This figure is, however, transposed here to the first offbeat position. Both bypass any introductory figures. Nevertheless, the player builds segments marking the triplet fragment that closes the introductory figure in example 10. This fragment is also present in the complement figure and in the second part of segment 11b, starting at cycle 506, together with a polarization of the offbeat A position started at 503. At the opening segment, the sequence of bass articulations define a dotted rhythm (dotted eighth plus dotted sixteenth notes) starting at the offbeat A position. Note that the player executes a ternary division in the following segment (eighth + quarter notes). The complete segment is usually closed by segment Z. Finally, the player rescues the regulative beat position in example 11c, inserting a cross-rhythm configuration that is typical of Wede (in 570 and 574), creating another segment based on the concluding fragment from the figure in example 10. He then replaces segment Z with a variation of the closing figure used in the phrase from 5a.

Yoruba repertoire

Finally, let us consider some excerpts from the solo Bàtá drummer in Ogogo, as seen in example 12. It may be clearer to define these examples through those things they lack, especially when compared to examples 8 and 9. There is no clear motivic form in this case, whether in clearly grouped articulations or in regular placements within the metric structure. Irregularities are also unsystematic. Most often, the groupings define varied metric relations by themselves. The notes below the transcripts are just a summarized and approximate description of the musical structures. Thus, in example 12a, segment /a/, the player strikes a configuration offbeat and repeats it only once; in /b/, a longer group of repeated articulations creates relative unity in a segment (sometimes resulting in a motivic figure); in /c/, after the treble articulation, the drummer plays two similar syncopated groups; and, in /c/, he choses varied timbre combinations with no specific rhythmic regularity. In example 12b, there are alternated longer segments, better described as cross-rhythm and offbeat timing resources. Both segments are closed by the short /alpha/ segment, which consists of three syncopated articulations. In both examples we can also hear the muffled hand strike, not accented in this case, and a partial neutralization of timbre differences by using two membranes at once. Both segments include rapid alternation between configurations with different timbres and rhythms. The player creates moments in a fragmented discourse, which can hardly be accurately perceived.

4. Dichotomies

This article selectively resumes some basic rhythm concepts developed in African music theory. In short, the presence of a pulse value can be verified by the presence of groups of three or four units that create ternary or binary time units. These, in turn, create a concrete or abstract sequence of performed beats. For subsequent modeling in the metric level, one must admit this music contains not an abstract sequence of rhythmic values, but a materialization through individually identifiable patterns or figures in the instrumental parts. Solejebe has a specific timeline—-the standard pattern—-maintained by the bell, creating a 12-pulse time interval. A hierarchy within this time interval is offered by the articulations of the rattle and the alekle 1, corresponding to the beat; on the other hand, the bell part extension in Wede is not metrically relevant until it is subordinated to the actual beat of the rattle and the alekle 1.¹¹ In the case of Ako Bàtá piece we see here, the timeline is not necessarily sustained during the whole performance. Thus the 4-beat time interval can only be inferred together with the articulation of well-marked figures (motifs) produced in the solo drum part.¹²

The concept of offbeat timing has proven useful from both the rhythmic and formal standpoints. If in relatively less intricate situations—-Bàtá music, for instance—-the presence of a hierarchically superior 4-beat time interval proves essential, it is all the more relevant when offbeat timing is used. One can see the dynamic application of offbeat timing by the Fon group’s master drummer, who drives the execution toward a strategic point. But the movement of distancing and coming back to a predefined center is where polymetry arises, however restricted to the relationships determined by the referent beat. It is the presence of this dynamics that produces additive segments, or an additive relationship between specific configurations.

But abstract rhythmic relationships are established by actual configurations. Both repertoires present a considerable collection of figures distinguishable by function or meaning. In sections 2 and 3 of this article, there are two groups of examples from structures created in the solo part. On one hand, we have configurations articulated with the utmost sharpness (examples 5, 6, 8 and 9.) The configurations in examples 2, 3 and 4 also belong to that group. On the other hand, there are less marked structures (examples 10, 11 and 12), with what we will risk calling a secondary formal role—-if we consider the structure of an execution to be based on well-defined configurations.

When there are well-marked segments, we notice motif constituents formed by varied or just repeated configurations, clearly presented and indicating a precise choice of timbers. Likewise, the closing constituent is chosen from a restricted set of configurations and is therefore perfectly predictable; it is clearly articulated as well as particularly noticeable for the long pauses that often follow it. That is not entirely clear from the transcript, but in both cases what we have are predominantly strong and quite loud hand and beater articulations. In the structures from examples 5 and 6, the change in the rhythmic base does not disturb the clarity of articulation, but rather display the skillful ability for metric transposition and fluctuation developed by these African musicians. In examples 8 and 9, the regular 4-beat metric structure is clear from the articulation of the motifs, which also indicate the function of establishing the valid meter for all other parts.

The structure in examples 10, 11 and 12 are different: they do not constitute clearly stable patterns in the musical discourse. For the Bàtá structures in example 12, it is clearly irrelevant to establish shifting bases for the rhythmic orientation. In the Fon style examples (10 and 11), these configurations tend not to confirm the pieces’ established metric relations during the flow of events. They are not either evident cases of offbeat timing, as seen in other Fon music events. Of course these are not detached articulations, but that does not mean unequivocal figure groupings can be inferred for them. These random groups cannot be submitted to specific segment categories. And finally, in these and other examples, articulations often use unaccented hand strikes, or frequently neutralize the difference in timbers by striking at both membranes at once.

In example 10, events in the configuration succeed each other more strictly. Nevertheless, we can affirm that its initial segment /a/ is just the presentation of a figure; it is supposed to introduce the next segment and by itself it does not produce a rhythmic constant that can be perceived as a definitive metric discourse. There is an ambiguity in the fact that it marks both the referent beat and the second offbeat position. It is even elided from the structure in some contexts, as seen in examples 11b-c. The next configuration is the complement, formed by a continuous figure based on a treble sound, which can be considered secondary. As demonstrated by examples 11a-c that follow, this figure is variable in extension, cut by occasional accents, and may be fragmented or exceptionally transposed into other metric positions. And the closing figure, however constant, does not establish a two- or three-pulse orientation by itself. It does not mark a relevant metric position in the metric cycle that follows it. An articulation in the first offbeat position finishes it off, but the previous segment does not mark this offbeat position as a guiding rhythmic foundation.

These formal dichotomies are also demonstrations of the master drummer structures’ function along the performance. Several of those structures are aligned to the (spoken or sung) language and, on the other hand, to the (individual or collective) dance. But as demonstrated by these examples, the theoretical field of instrumental music is also the place to look for properties inherent to the events of which this music is part.¹³

Smooth and striated

I presume the observations up to this point have already reminded the reader of Pierre Boulez’ contribution to musical technique with his considerations on what he called smooth and striated space and time in music. I will not dwell on the definition of these terms except for the following note: a smooth surface is abstractly defined as a continuum, in which musical events may be inserted at any point. Striated surfaces are those where the location of events is pre-established according to regular or irregular underlying patterns. Events gathered in a smooth surface would behave statistically, while a striated surface combines them systematically. So there is an opposition between predictability and unpredictability. Musical structures defined by one trend or the other can be combined by juxtaposing or superposition.¹⁴ In layering, events defining a smooth surface may take place at the same time as a tempo containing fixed reference values.

A regular pulse in striated time carries the same significance as the semitone cut does for the creation of a tempered striated space. The music we are dealing with here is much more about the time parameter than about diversity of pitch. Hence, we would have to imagine a parameter for durations analogous to the octave and its division in semitones, for instance. African music usually establishes two stable metric measurements that serve as a perfect analogy: the pulse and the grouping of pulses in 12 and 16 (or 8) units.

So, if instead of comparing modules and minimum subdivision values (such as pulses and intervals between beat referents) we consider an intermediate metric value, we could maintain the opposition between elements aggregated for non-systematic reasons—-which create smooth surfaces—-, and systematically applied values—-which create striated surfaces. That is, this music admits the creation of a rhythmic tier that complements the tactus. The resources used in this tier may add considerable unpredictability to the discourse. It seems thus valid and functional to oppose elements from the Bàtá texture and the unstable and unsystematic solo part from example 12 by superposing them. Likewise, the striated and smooth time moments in the solo part from examples 8 and 9 on one hand, and in example 12 on the other, are associated by juxtaposition. The same can be said of the Fon structures in examples 10 and 11, as examples of smooth surfaces. Considering the complete configurations instead of the individual groups that form them, we can see the effect of an unsystematic performance, engendering groupings that are perceived only more generically or as statistically relevant. They alternate with the type of striated structures seem in examples 1 through 5, which are regularly and predictably presented in these formats.

A relevant differentiation between trends in smooth and striated times is that smooth time is occupied without being counted; striated time, on the other hand, is counted so it can be occupied.¹⁵ As seen above in the Bàtá music examples, the longest rhythmic pattern (timeline) may be omitted, giving way to a performance that is parallel to the solo part. That is: inversely, the support drum player necessarily plays the fixed pattern when the solo part is tending to smooth time; in these cases, counting time through the support drum is a necessity, once the solo part excuses itself from this function. In the Fon style, however invariable the texture elements may be throughout the execution of one piece, the structures in examples 10 and 11 become most acoustically pregnant at the moment they are presented. That is, only in “substantial” parts of the execution does the master drummer set perceptually relevant time and meter.

Evidently, the textural structure of African repertoires described here points towards styles marked mainly by elements that define striated time. This structure consists of fixed or restrictedly variable elements. Fixed tempo is crucial for regulating dance, for instance. However, in these musical groups, the presence of the solo drum is remarkable from the very acoustic standpoint. The various timbre and intensity modulations, performed according to its multiple solo functions, exuberantly compose the general sound structure of the music.¹⁶

Motivic work: from figure to gesture

A foreign researcher needs a pragmatic attitude when trying to uncover musical structures in a repertoire based on oral transmission, and the nomenclature used should be as objective and neutral as possible. But an analytical corpus, i.e. a sufficient body of reasonably perceived musical events, cannot be established until the descriptive activity is quite advanced and some concepts are already widely used.¹⁷ Through analysis of the Fon repertoire mainly, I adopted the word figure to designate any segment that might be isolated from the context by following the procedures of structural linguistics,¹⁸ which are also used in traditional music analysis, albeit not always systematically and sometimes almost anarchically. I also qualified figures according to their recurrence during one performance, and proceeded to call motifs those figures with relative power and pregnancy, whether in circumscribed and compact contexts or scattered throughout the performance. (Motifs usually define striated surfaces.) I chose to keep the term figure for repeated segments with a certain formal and distributive stability, but in which I could not see the accented pregnancy of other segments. These issues also pertain to musical significance, an even more pressing matter when we do not interact intensively with the musical practice. The terms are not used homogeneously in analysis works. Constituent is another term that has become common to designate prominent configurations in a complex body of sound events, regardless of potential recurrence, contextual differences and potential normative syntax.

Similar issues are relevant in works on contemporary musical culture, which put the word gesture in the order of the day. Brian Ferneyhough used figure to express this dichotomous value. The composer uses a metaphor that says both the apparent staticity of waves in the sea and the dynamic elements revealed by the same waves when hitting the rocks are equal. They are, therefore, a single set of formative factors exposed to different contexts. These two states of the same thing are what he calls, respectively, figure and gesture. The gesture assumes and indicates the presence of its constitutional elements, but does not contain them integrally. It acts as an effect of the power lines at its source. These power lines materialize in the processes of creating parameters for the figure. What the author seems to be trying is to reestablish the constructive value of figure instances while also expanding them towards dissolution by altering their constitutional elements. That is to say, he critically reaffirms the importance of the figure as a structuring element in a musical composition.

Ferneyhough’s study offers a brief musical example. It presents a varied sequence of discrete rhythmic events, unified by the presence of a long note, followed by a short one. Changes are added to these events so as to distance them further and further away from the initial figures: by maintaining the duration of the sequence as well as some sort of relationship between internal configurations, conditions are set for the surfacing of concrete elements that pace towards gesture. What fuels that is the accumulation and ensuing dissolution of the energy set forth by successive parametric modification of the figures. Motivic work is no news in music theory. What draws our attention here is the concept of gesture as a result of destructive transformation in the relationship between the figure and its constitutional forces.

Let us consider the motivic structures in example 6 again. There are two ways through which the motivic constituent in example 6c alters the generally accepted model of figure constitution in Solejebe: by transposing the preferential metric insertion point and by reaching for temporal compensation. Instead of driving motivic repetition, the result is an unexpected figural variation based on fragmentation and permutation. Example 6d, in turn, brings an even more unexpected change. The performer shifts from the first offbeat position to cross-rhythm without intermediation, that is, within the same phrase constituent! The cross-rhythm relation is sustained, based on a two-pulse value. When the performer finishes the constituent by inserting triplet quarter notes expressively (gesturally) articulated, the half note temporarily becomes the base value. But the half note—-i.e., the basic 4-pulse value—-entails a parametric dissolution here, since it is not regularly adopted for creating figure structure in Solejebe (in 12/8) and is restricted to pieces in 24/8. In spite of the borrowings between pieces, figural configurations such as the one in example 2 (starting at 108) are excluded from Solejebe. During the same time interval, the Fon player performs operations that imply changes in basic duration values, entering the realm of expression suggested by the concept of gesture.

The Bàtá master drummer works in similar fashion in the segment from example 9b. Note that, at first, he keeps space for presenting a motive twice, replacing it afterwards with different configurations of the same length. The original motif comes back in the form of fragment /x/, introducing the densest and most contrasting part of the phrase structure. The whole phrase structure is finally diluted both by the extended length of this part and by the fact that the closing motif is replaced by a figure derived by parametric changes.

Solejebe ends with what can be considered a result of the expressive and diluting action of the master drummer. It is at the end that we find the modified structures in examples 11b and 11c. It is also at the end of Solejebe that the introductory figure from example 10 is exceptionally placed on the second beat of the metric cycle and used simultaneously with new and known segments, causing the references that had been used throughout the piece to be lost.

5. Conclusive note

The music presented here is transmitted orally. It is used in various types of social events and its elements are created by combination of song and dance elements. These factors limit our freedom in aestheticizing African music. Considering the context of these musical performances, the liberty given to the master drummer to interfere in general aspects of the execution with formally defined elements is remarkable. Furthermore, I believe that the variational process activated in the sequence of phrases in Solejebe (example 5) and in Ako (the Pobè Bàtá piece in example 8) corresponds to the type of musical signification expressed by the idea of gesture as an amplification of figural development. Considering the regular metric and figure relationships in these Western African styles, what we have here is a development of constitutional elements subordinated to processes that dissolve metric parameters in precise contexts of musical execution.

To sum it up, the following conclusions can be drawn from these observations:

• Polyrhythm is systematically used by Fon musicians both in the rhythmic texture and in the solo drummer part. It takes place in ternary rhythms and consists of a one- or two-pulse displacement (offbeat timing) within a timeframe defined by a sequence of 4 or 8 beats, and by the presence of a regulative beat.

• Polymetry is preferably defined by pre-established segments that maintain a 4-beat metric dimension.

• The use of metrically displaced configurations creates the need to readjust to the basic module. This mechanism results in additional segments, or additive relationships between well-defined segments.

• Configurations used in displacement processes tend to use simpler figure forms.

• Metric predictability and figure pregnancy (striated time and smooth time) vary in the performance of Bàtá and Fon repertoires.

• Both repertoires define figures of greater acoustic pregnancy and may submit them to parameter variations that neutralize regular construction aspects and lead to expressive moments (gesture).

Bibliography

Agawu, Kofi. Representing African Music. New York: Routledge, 2003.

_____ “The rhythmic structure of West African Music.” JoM, 5 (3), 1987.

Anku, Willie. “Circles and Time. A Theory of Structural Organization of Rhythm in African Music.” Music Theory Online 6, 2000.

Branda-Lacerda, Marcos. Música instrumental no Benim: Repertório fon e música bàtá. São Paulo: Edusp, 2014.

____ “Música de ritual africana e alguns conceitos contemporâneos de organização musical.” Anais do IV Seminário Música, Ciência, Tecnologia: Fronteira e rupturas. USP, 2012, pp. 49-58.

____ “Instrumental Texture and Heterophony in a Fon Repertoire for Drums.” TRANS, 2007a.

____ Estruturas ritmicas da música instrumental fon do Benim - as peças Solejebe, Wede e Gobahun. Tenure Thesis, 2 vols., Escola de Comunicações e Artes, Universidade de São Paulo, 2007b.

____ “Yoruba Sacred Music and the Barform.” In Sonus 22 (2), p. 32-55, Cambridge-Mass., 2002.

____ Kultische Trommelmusik der Yoruba in der Volksrepublik Benin. Bata-Sango und Bata-Egungun in den Staedten Pobè und Sakété. 2 Vols. Hamburg: Wagner, 1988.

Boulez, P. Penser la musique aujourd'hui. Éditions Gonthier/Schott, 1963.

Ferneyhough, B. "Il tempo della figura." PNM, 31 (1), 1993.

Lerdahl, Fred & Ray Jackendoff. A Generative Theory of Tonal Music. Cambridge, Mass.: MIT Press, 1983.

Locke, David. "Principles of offbeat timing and cross-rhythm in southern Eve dance drumming." EM 26 (2): 217-246, 1982.

____”The Metric Matrix: Simultaneous Multidimensionality in African Music.” AAWM 1(1), 2012.

Nketia, Kwabena H.K. The music of Africa. New York, 1974.

Nattiez, Jean-Jacques. Fondements d’une sémiologie de la musique. Paris, 1975.

Waterman, Richard Alan. “African influence on the music of the Americas.” Sol Tax, ed., Acculturation in the Americas, Chicago University Press, pp. 207-18.

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