The Proximate Three in Practice: Mandeng Jembe Repertoire, Part 1
Excerpt from, “The Harmonic Perspective of Rhythm”
For a bit of evidence from traditional music in practice, I’ll turn to the African genre most familiar to me and perhaps most well documented in terms of numbers of pieces, that of the Mandeng Jembe[1] and the accompanying Dunun bass drums with bells. I’ve chosen pieces randomly from the Billmeier and Keïta book, A Life for the Djembe (Billmeier and Keïta 2004), dismissing those in a ternary metre until I reached five[2].
Djagbe
The first piece, Djagbe[3], known as Madan in Mali, is quite familiar to me as it was highly favoured among the friends who hosted and taught me in a stay near the town of Siguiri in upper Guinea in mid-2000. There are regional and personal variations with all of this music, but Keïta’s version is quite similar to what I played in Guinea.
Here are the accompaniment patterns he shows for the Jembe and Dunun with bells:
Figure 1. Djagbe.
Audio Example 1. Djagbe (CD Track 21). Not meant as a ‘performance’, the parts enter sequentially then fade into
The first two characteristics that stand out clearly with regard to the tresillo rhythm are the first Jembe part and the bells for the second two Dunun parts. The Jembe part, with or without the bass hit in the middle of beat three is ubiquitous in this repertoire; it is usually the second accompaniment given in binary pieces, with the first being often, but not always, something more unique to the piece in question. It is clear that it outlines the tresillo rhythm with the first two slaps and the first open tone, in each pair of beats (it repeats within the cycle, as does the tresillo), as well as the contrasting four beat (two for each half /each tresillo). This alone presents a clear reference to the hypothesized dichotomy of metres, and as I mentioned, this part is common in most of the binary pieces.
Tresillo as Three: From Two Possibilities to Eight
To follow Toro’s point of view further, however, the concept gets a bit more complex. According to him, the three pulse has only two options, the on-beats of three and the offbeats. With the correlate that I am referring to as tresillo, however, there are not three, but eight possibilities, one for each of the subdivisions used. According to Toro, the pool of these eight possibilities is the source of all rhythms in this African, binary feel. He goes so far as to say that it is the source of anything you or I or anyone else will ever play. I choose not to speculate with the same degree of confidence, but it does point to the idea that any phrase, within a given matrix of minimum pulsation (here referred to as subdivision), will be made up of those pulsations in groups of twos and threes. With twos and threes, any other combination can be derived.[4] (Toro 2012b, 2014a) With this point noted, let us still consider how these West African examples compare to the eight possibilities.
Figure 2. Eight Tresillo Permutations.
Audio Example 2. Tresillo Permutations with and without Original Downbeat Reference (CD Track 22).
I have used an ‘x’ here to indicate the downbeat/’one’ of the original pattern, and derived the others by shifting the whole sequence one subdivision to the right, through the first two beats, the length of the pattern[5]. We can now examine some of the other accompaniment parts to Djagbe against these archetypes.
Quintillo
Along with the first Jembe accompaniment part, I mentioned that the bells for the second two Dunun parts clearly state the tresillo rhythm.
Figure 3 Bells for Djagbe Kenkeni and Dununba.
This pattern is also ubiquitous in the Mandeng repertoire represented here as well as in much of the wider African Diaspora; it even has its own name, in Spanish, in colloquial Caribbean music discussions: quintillo. This means, ‘quintuplet,’ but, as with the tresillo designation, refers not to an actual, evenly spaced quintuplet. It refers in this case to the rhythm repeated in the first line above, and in the first half of the second line[6]. (Mauleón 2011, 1999; “Merengue Music” 2014; Acquista 2009)
Toro suggests that it does indeed have a relationship to a literal quintuplet, but we will come to that in another discussion. For now, note that besides stating and therefore implying the tresillo, this pattern is also comprised of the normal tresillo and the permutation numbered ‘3’ above. We will see in this short examination of binary Mandeng Dunun repertoire, as I have gathered over many years playing the style, that this bell pattern is a foundational pattern; not only is it played in some guise in most of the pieces, it also seems to generate the various dunun patterns with which it is paired. That is, it is commonly played with different drum patterns that articulate different combinations of the basic quintillo strokes. Two of these can be seen in the Djagbe kenkeni and dununba parts which underlie the bell patterns above (Figure 3). The quintillo seems to be the backbone or the foundation from which many different dunun rhythms are built. This lends partial evidence to Toro’s idea that these tresillo permutations (of which two are represented in quintillo) generate ‘all’ the repertoire.
Cascara/Pallitos
And what of the first dunun part? This is the sangban, considered by Keïta to be the heartbeat of a rhythm composed in this style. (Billmeier and Keïta 2004, 32) Here are the bell and drum parts again:
Figure 4. Djagbe Sangban with Cascara-like Bell.
Interestingly—and uncharacteristic in this repertoire—the bell part is the same pattern known as ‘pallitos‘ in Afro-Cuban rumba (played by two sticks) and as ‘cascara‘ as played by the timbale player in a salsa band. (Malabe and Weiner 1990; Mauleón 2011; Spiro and Ryan 2006; Hernandez 2000; Peñalosa and Greenwood 2009; Goines and Ameen 1993) When I played the Djagbe rhythm in rural upper Guinea, we did not normally use a bell with this drum part, so I cannot say for certain if this is an old, traditional part or if perhaps it has been adapted after Caribbean music made its way ‘back’ to Africa through recordings from the middle of the 20th century on. Keïta is usually sincere in his attempt to preserve his culture’s rhythms as they were taught to him during his youth spent in upper Guinea. Fara Tolno, in his recorded collection of Mandeng Jembe and Dunun accompaniments gives a slightly different interpretation for the drum rhythm but with the normal quintillo bell pattern[7]. (Tolno 2009)
Binary Clave: Contrary Terminologies
But what of its relationship to the tresillo permutations? Trying to make the cascara pattern out of two interlocked tresillo patterns is not possible because it is not the same on each half. The possibilities inherent in mixing and matching more than two permutations seem, to me at least, to scale to such number that any meaningful relationship would be difficult to prove[8]. So, I decided to look at the drum part first. Unlike its fellow accompaniment parts, this pattern needs the entire cycle to be completed. It is not made of half a cycle that is repeated. This fact, along with the use of the cascara-like bell pattern, makes one think of clave. As we saw above, clave, in its ternary form consists of roughly half the cycle articulating the on-beat three metre (or three pulse cycle or three cross-rhythm) and the other half articulating the offbeat three metre. In common use among musicians trying to make sense of clave based music in binary styles such as salsa,[9] however, the thinking is a bit different. When trying to decide which way a particular melody or percussion part fits with clave, for example, people often speak of the three side, which is the tresillo rhythm[10] as being the offbeat side of clave, and the two side as being the on-beat side. That is, an accompanying rhythm such as this common piano montuno (a montuno is simply a repeated pattern, here in d minor),
Figure 5. 2/3 Son Clave with Piano Montuno Written as One Bar.
is unequivocally heard in ‘2/3’ clave, as shown on top, even though there is only one rhythmic coincidence per half (or ‘side,’ as in, ‘the 2 side,’ and, ‘the 3 side’). Anyone familiar with Latin music in written form has probably seen it like this:
Figure 6. 2/3 Son Clave with Piano Montuno, Half Time/Two Bars.
In this case, the ‘on-beat/offbeat’ designation is clearer: on the ‘2 side’, the montuno plays on beats one and two and everything else, including all the notes on the ‘3 side’ are in between the main beats, i.e., the ones you would count with the numbers, ‘1, 2, 3, 4,’ in one bar. This type of notation seems to be easier to read for some players, and keeps the two sides of clave clearly in two bars—clave and clave music is often thought of as being in two bar phrases. However, the ‘beats’ that are actually danced to and otherwise felt as the primary grouping, are those indicated by the one bar clave phrase, with sixteenth note subdivisions of those beats, as used elsewhere in this discussion. This is consistent with the idea of tresillo being a three correlate against two main beats. There are four main binary beats (not eight) and six ternary or tresillo beats, to a measure, or time cycle unit. It is also the preferred convention for the notation of this music in Cuba[11]. (Cruz et al. 2004)
All this seems to work well enough in practice. However, there is an inconsistency in our line of thinking: In a ternary feel, the first (in common practice) or ‘3’ side of clave is on the three pulse metre and the following or ‘2’ side is off of the three metre. In binary interpretation, these designations are reversed, or rather, they are called, ‘on’ and ‘off’ in relation to the predominant metre, which is binary, and the result is this reversal of designations between the binary and ternary interpretations. In other words, in common Latin (Caribbean, USA) music parlance, the ‘3’ side of the clave emphasizes the offbeats and the ‘2’ side emphasizes the on-beats. (Mauleón 1999) Two new points of view present themselves which will hopefully make for a more consistent picture.
Tresillo Permutations and Polarity
In the tresillo and permutations view, the two halves of clave would correspond with two permutations of tresillo. Looking at the Djagbe sangban pattern, and even at its cascara-like bell pattern, this explanation seems to fit:
Figure 7. Djagbe Sangban.
The first half of the drum pattern (bottom line) corresponds to permutation 6 from figure 2 above and the second half to permutation 3. I wondered if the eight permutations could each have a primary relationship to either the on-beat or offbeat ternary form? On its own, this potential relationship is only mildly interesting. What is important is whether it will help to establish the basis of the polarity—what is usually referred to as clave—which seems to exist in African Diaspora music, and tie that concept to the poly-metric foundation under discussion. In order to compare the tresillo permutations to their correlates in three, and in two, they are shown below in graphic and box form.
Figure 8: Each Tresillo
Permutation with Three and Two, On Beat and Off Beat.
Figure 9. As Above, in Box Notation.
So far, what seems clear is that anything representing the ‘3 side,’ or on-beat three, has an articulation that falls just after the second articulation of the pure three (the ‘a’, or last sixteenth of one); this spot is important enough to also have its own name in Spanish: Bombo. Furthermore, the patterns that represent the ‘2 side,’ and possibly the offbeat three metre, land squarely on two sequential instances of the two metre, within the same cycle; that is, not on the end of one cycle and the beginning of the next, as we see with the basic tresillo. It also seems clear, however, that more empirical evidence is in order, especially if it will clarify the polarity of the remaining four tresillo permutations.
Kuku
The next binary Jembe rhythm on my randomized list is Kuku. This form of Kuku is an adaptation from the original as played by the Manian people of Guinea and Côte d’Ivoire; the original was played on three Jembe drums only, as it is on Keïta’s recording Wasolon. (Billmeier and Keïta 2004, 150; Mamady Keïta & Sewa Kan 1989) I played this rhythm many times in Odienne, western Côte d’Ivoire, near to where it originates, and in Korhogo, in north central Côte d’Ivoire. In both those settings it was played with dunun, close to the form notated below, as it appears in Keïta and Billmeier. It is possible I played it in Mali or Guinea as well, as it is a very popular rhythm.
Figure 10. Kuku.
Audio Example 3. Kuku (CD Track 23).
The first Jembe part in Kuku is also a fairly common accompaniment and gives a strong feeling of the offbeat; this is articulated alternately with doubled tones and single slaps, thus adding a bit of question and answer dimensionality, rather than one simple offbeat note. Bass drum hits on beats one and three ground the part and articulate the other side, the downbeat, with another sound. The second Jembe accompaniment is characteristic to Kuku, but also played with two drums in Calypso music. I was also taught the same rhythm many years ago by Congolese traditional musicians as part of their music, probably of the Kikongo people. Here again, I do not know if this was somehow ‘borrowed’ in antiquity across the relatively large swath of mostly dense forest that separates the Manian of present day Eastern Guinea with the Kikongo of the central Africa, or if the exchange came about much later, through recordings or personal observation. It seems remotely feasible it was co-created, as the underlying components are very common across Africa. I will not speculate any further than that. The part itself, along with the Kenkeni in this orchestration, grounds the whole rhythm very strongly by playing and doubling every on-beat. Around those tones, however, we find the tresillo rhythm (minus the first note) articulated with slaps. This suggests a very strong on-beat two and tresillo/three in one part. This is perhaps due to its original use without Dunun (bass drum) accompaniment. The Sangban plays quintillo and tresillo on bell and drum, with the bombo spot differentiated by muffled strikes (still highly audible but with a higher pitch).
The lowest drum, the Dununba, uses a combination of quintillo and straight eighth notes on the bell. The drum rhythm likewise articulates the every other bombo and the two beats in between play straight eighths or nothing at all. This seems to be the key part in this discussion as it is only here that the rhythmic polarity is clear. The other parts are, to use Mauleón’s term, ‘clave neutral.’ (Mauleón 1999, 10; Peñalosa and Greenwood 2009, 172) Here, however, rather than supporting our nascent thesis that each half of the polarity must relate to alternate permutations of the tresillo rhythm, we see tresillo and non-tresillo, or consecutive on and offbeats in two. This seems to disagree slightly with Penalosa’s ‘displaced tresillo‘ model as well (Peñalosa and Greenwood 2009), but agrees with the aforementioned observation that the 2 side of clave polarity matches with two successive articulations of the two metre, i.e., ‘1 and,’ ‘and 2,’ or ‘2 and,’ in the same cycle of two beats; that is, not, ‘and 1,’ as in the normal tresillo rhythm.
Kassa
Next on the list is Kassa. Kassa is farming rhythm of the Malinke people, played to encourage group cultivation or harvesting work. I participated many times in these work parties as both a worker and musician when I lived in a small village in northwest Côte d’Ivoire. The feeling of group synchronization and the energizing effect of a strong groove was remarkable. I daresay it was more powerful for the multi-dimensional nature of the music, but that is opinion. Keïta and Billmeier’s basic version is shown below.
Figure 7.27. Kassa.
Audio Example 4. Kassa (CD Track 24).
This rhythm is less obvious in its clave polarity, but it led me to search for other clues. Rhythmically, the sangban is essentially the same as that seen in Keïta’s version of Kuku, but with the open and muffled tones reversed. It is of course the tresillo in pure form, with the cinquillo on bell. Note that each of these sangban patterns singles out the bombo note, though with opposite sounds; this note by itself seems key to suggesting the tresillo/three metric correlate. The kenkeni bell presents a modified cinquillo, not uncommon in this repertoire. It can also be seen as a displaced cinquillo, with the single strike that is normally on the downbeat now on the bombo. It still contains the tresillo figure, but the added notes in this permutation of the cinquillo allow for a different drum melody, emphasizing the downbeat of each half of the pattern with two strokes. These interlock with the other drum parts to make a composite melody which emphasizes simultaneously on-beats, offbeats (of two) and tresillo (three). This is typical in African and Diaspora percussion ensemble music: multiple parts that interlock and overlap. Either quality on its own is linear and one-dimensional.
Still, these patterns, though interesting, repeat in the second half of the bar and therefore present as ‘clave-neutral.’ What about the hypothetically necessary polarity, or clave? The dununba part does not repeat exactly in the second half but is not clear cut either. The cinquillo pattern does repeat on the bell, with the drum playing in unison to different parts of that cinquillo bell. Now we see that the cinquillo, though clearly suggesting tresillo, might also contain the capacity to suggest either side of the polarity. Without reference to other subdivisions than those of the cinquillo, the drum articulates the downbeat and bombo, as the tresillo/on-beat three correlate is likely to do, in the first half, and in the second half, it leaves off the ‘downbeat’ (secondary downbeat; the reference is to beat three in the notation) and articulates the same two following notes as the first half, including the bombo. In this instance, without the downbeat, the ‘and’ of beat three suggests the two feeling, though there are not two articulations (on beat, offbeat or ‘and’ in two) in succession as noted with the previous two rhythms. I noticed that it seemed easier to play this rhythm together with a three-two clave pattern than the other way around, though three of the five clave strokes match in either orientation:
Figure 11. Kassa Dununba with 3/2 and 2/3 Clave.
Audio Example 5. Kassa Dununba with Claves (CD Track 25).
Still, this doesn’t prove each side exhibits its polarity in a clear and unique fashion. It is playable with two-three clave and doesn’t sound bad to my ears, just less ‘together.’ As the third note of the tresillo figure is on-beat in an ‘and’ position it seems to suggest ‘two-ness‘ as well as to simply complete the ‘three-ness‘ in tresillo fashion. It is interesting to note that this position (the third note of tresillo, which falls on the ‘and’ of beats two and four above, or on beat four in the two-bar rendition counted in eighth notes) as demonstrated in figure 9 above (and figure 12, just below), is not the closest note in the binary quantization of the three metre. This note also has a Spanish name,
Figure 12. Timing Focus, Tresillos 1 and 6.
Here is another mini-hypothesis to consider: Emphasis on ponche, especially on one side of the rhythm, can suggest two even from the hypothetical three-like tresillo in its original position. From another point of view, the clave two-side/offbeat three side of Djagbe, or tresillo permutation 3, added to the normal tresillo, gives us cinquillo! Thus the cinquillo itself can refer to either dimension.
Figure 13. Tresillo and Its Permutation Gives Cinquillo.
Audio Example 6. Two Tresillos Make Cinquillo (CD Track 26).
Tresillo and its Permutations Together
Though it was not clear to me at the time, Toro pointed this out in one of our early lessons, without reference to Djagbe, but rather talking in a general way about West African rhythms (or, as noted above, ‘all’ rhythms). He demonstrated the two permutations above to make quintillo with his two hands and then played tresillo with his bass drum foot while adding, in succession, several other tresillo permutations with his hands, showing in a sense his original point and the one that we are examining here: that tresillo and its permutations stand for on-beat and offbeat three in a binary feel. (Toro 2012b) Being uneven, however, there are points of overlap instead of the steady alternation when playing the actual on-beat and offbeat three together. This complicates the matter and produces many interesting possibilities as well. Here are all those possibilities:
Figure 14. Basic Tresillo with its Permutations.
Audio Example 7. Basic Tresillo withPermutations, with and without Original Downbeat Reference (CD Track 27).
Of course, one could also combine them using each in turn as the static base, rendering 64 possibilities, assuming separate sound sources. The point here, however, is to show how some nearly align with the normal tresillo—our hypothetical three correlate—and some others mostly fall in the spaces that tresillo leaves open.
The Jembe Break and Other Observations
Though I have given this rhythm more attention than the others, there are still a few other observations brought out by its difficult nature regarding clave orientation, or polarity. The first is the break used to call the rhythm, end a dancer’s solo, end a percussion solo, call a unison pre-composed group section, to end the rhythm, etc. This figure is also ubiquitous in the repertoire.
Figure 15. Binary Jembe Break.
Audio Example 8. Jembe Break (CD Track 28).
This figure is clearly in the three-two clave position; though the downbeat and bombo show up in both halves, the second half merely plays through the bombo with a strong and final slap phrase from the ‘and’ of beat three to beat four. The first half, interestingly, seems to use the same permutation six to demonstrate its ‘three-ness’, as does the identical first half of three-two cascara, as well as Fara Tolno’s version of the dununba accompaniment to the rhythm Aconcon:
Figure 16. Dununba for Aconcon.
Since most of these binary jembe rhythms use this break or a facsimile such as,
Figure 17. Binary Jembe Break 2.
I remembered a point made by Peñalosa that all folkloric rhythms begin on the three side of clave. Actually, he says that the three-two/two-three clave concept is not a factor, citing examples in his notes of various Cubans and Africans saying that clave is a concept employed by westerners or outsiders to understand the music. But, he says that in folkloric music, the one/beginning/primary downbeat is always on the three side of the clave polarity. If the vocal part lines up with the two side, then the direct, insider interpretation is that the vocal just enters on the other side of the rhythmic structure. (Peñalosa and Greenwood 2009, 158) This agrees with the discussion of the Jembe break above. However, this, ‘folklore always begins on the three side,’ idea, assuming it is true and reliable, is merely a helpful pointer in this discussion, which has been about how this three-ness is manifested.
Finally on this rhythm, Kassa, it is interesting to note how the polarity is subtly indicated in the jembe parts themselves. Both accompaniments appear to be clave neutral, except for a lone bass note on beat four in the first accompaniment and on the ‘and’ of beat three in the second. I have heard, played and been taught both these parts in other rhythms; the second, as noted previously, is very common, and I’ve seen it with and without the bass note, never giving much thought to the strategic placement. The first part, I’ve seen also in the rhythm Lamban; it might be used in other rhythms as well. Both these bass note positions, as we have seen, are solid indicators of two-ness, and, taken together, articulate the two side of son or rumba clave.
Djole
The next rhythm in my random selection is Djole, or Jole. Jole was originally a festive mask dance of the Temine people, now popular around West Africa. It has been adapted for dunun and jembe from the square siko drums. (Billmeier and Keïta 2004, 138–39)
Figure 18. Djole.
Audio Example 9. Djole (CD Track 29).
Pedagogically, this is a very simple rhythm and I have used it to good effect with a beginners’ class. Given its two bar (or two clave) phrase length, it can be difficult for jembe 2 to remember where his or her variation belongs, especially as it falls in the middle of the cycle, not at the end as may seem natural. Indeed, this is the only accompaniment I will mention in this discussion as it is the only one that seems to indicate the hypothesized ever-present polarity. It is clear once again that the three-two orientation is indicated by the bombo note in the first half of each measure only. The second halves are marked only by on-beat articulations plus the on-beat to on-beat ‘roll’ at the end of the first bar. In his recording, Keïta on solo jembe refers repeatedly to a break figure to mark the end of his improvised ideas:
Figure 19. Djole Break.
In similar fashion, this phrase marks the three-side of the polarity, and is always placed so that it is answered by the ‘roll’ phrase of jembe 2 on the two-side; together they state in question and answer form the intended polarity. This is rendered more potent as it always follows one of Keïta’s solo improvisations which, in typical fashion, accent different parts of the beat structure. Often, this is achieved by linear figures that cross the normal beat and sub-divisional hierarchy, accenting different spots in turn. Or, as Penalosa puts it: “Over the rhythmic foundation…the lead articulates varied phrases, carrying on contrapuntal “conversations” with the repetitive parts.” (Peñalosa and Greenwood 2009, 179) After presenting his personal, dynamic rhythmic-melodic vision thus, the soloist returns to clearly state the normal polarity being kept by the ensemble, thereby strengthening the impression that he or she was not lost, but merely on a journey of perspective. We will touch on this subject several more times in this narrative.
Yankadi/Makru
The fifth and final rhythm in the selection is a two-part piece called Yankadi/Makru. Yankadi and Makru are courtship dances of the Susu people, played in succession. The first is a slow line dance, and the second, Makru, is fast, danced by couples that had paired up during the slower Yankadi section.
Figure 20. Yankadi.
Audio Example 10. Yankadi (CD Track 30).
By now, the analysis procedure is quick and clear. The first jembe part, along with bass strokes on each beat, plays the quintillo rhythm in its first half, which includes the bombo and ponche notes; the second half clearly outlines two, ending in beat four with the same notes played in beat two. This structural repetition emphasizes the difference between beats one and three. Furthermore, as we have seen previously, it illustrates how ponche can function as three or two. Jembe 2 uses the same rhythmic figure, with contrasting sounds, in beat one to articulate bombo, then clear, powerful flam and slap sounds on the two in its second half.
The sangban is outlined by quintillo on bell. Here again, the exact repetition in the two halves provides a shorter backdrop groove against which the other, polarized parts standout. It also shows again that ponche (emphasized as the second in a two-note motif) can stand in the three side or two side. The kenkeni is very clearly stating the three-two polarity with the same elements discussed all along—bombo then (including the last stroke on bell) all four two articulations. The dununba, though it plays bombo, uses that same subdivision before every beat, emphasizing the beats and the sixteenth note sub-structure, which in the recording swings considerably; this grounds the ensemble in another manifestation of multidimensionality vis-a-vis two and three—feel—to which we will turn shortly. Here another juxtaposition is offered from the slow, swinging Yankadi to the fast, much straighter Makru.
Figure 21. Makru.
Audio Example 11. Makru (CD Track 31).
Here, the first Jembe part is almost the same as that for Yankadi, with a few strokes removed: the bass notes on beats two and four and the slap before bombo, or the ‘and’ of beat one. The analysis is the same as for Yankadi Jembe 1. The strokes are most likely left out to help the player execute the part at high speed, about double that of Yankadi. Jembe 2 of Makru articulates rumba clave, with an added ‘secondary downbeat’ (written in two bars, as discussed previously) on beat three, and another as a pick-up to beat one. As discussed above, this static figure before and on beats one and three anchors the groove and creates a dialogue with the other elements, which are not static but rather polarized into their three and two functions. The first half of the third jembe part shows another way to articulate the three dimension; if taken without the bass notes on the beat, it uses tresillo permutation 4. Different from the normal tresillo by only one note, this pattern seems another candidate for a clear articulation of the on-beat three in binary time. The second half of jembe 3 is clearly articulating the two.
The sangban bell plays clearly in two as well, with the drum on the downbeats and ponche notes of each half. I hear this as exploiting the same ambiguity of the ponche note; it is with the two but suggests the three as well. This is one of the most commonly articulated rhythmic ‘spots’ in music from all over the African Diaspora, usually played with the ‘tone’ sound on a drum. This tends to stand out against (or within) the background. We’ve seen this in all the jembe rhythms presented thus far; it is standard in Cuban Rumba, Salsa, Merengue, much Brazilian music, Rhythm and Blues from the US, and so on. If there is a ‘go-to’ rhythmic position for African based folkloric music or for a percussion pattern in popular music (usually played around the basic time articulated by the drum kit), ponche is at the top of the list. The preceding discussion suggests that metric ambiguity, being an essential aesthetic locus of the aforementioned music, is perhaps the reason for the popularity of the ponche rhythmic placement.
The kenkeni plays the bombo and ponche, but repetition on the last two subdivisions of every beat suggests its function is rather to articulate the upbeats, as a static anchor contrasting with the downbeats and the three-two polarization. This is also a very common pattern in African Diaspora music. The dununba in clever fashion plays all the on beats, but also states the three two polarity quite clearly; from beat one to two the movement is via the bombo, giving us three. From beat three to four, it is via the ‘and,’ giving a clear two.
Polarity, Contrasting Metres and Dimensionality in the West African Sample
This detailed discussion of five primarily binary pieces from the Mandeng repertoire does not constitute a large sample size, nor does it attempt to represent a large cross section of West African music, much less African Diaspora music. To present a statistically significant analysis of the clave/polarity concept is beyond the scope of this study. What was accomplished by this line of inquiry, however, was the development of a germinal methodology for analysis of this type. Moreover, small though it was, the pool of rhythms so far examined has garnered a 100% pass rate. If the null hypothesis was to show a counter example, that is, one that does not demonstrate a clear polarity between the proximate three and contrasting two metres, then, so far, it would be rejected.
However, as this investigation began, I suggested that the polarity in the ternary modality is not between three and two—though that is one ever present point of multi-dimensionality—but rather between on-beat three and off-beat three. In a sense, these two contrasts equate to harmonic and linear ways of increasing dimensionality, although those terms will take on other significance in later discussions; the three and two that we have examined as this:
and this:
Figures 22 and 23. Three and Two, Ternary and Binary Forms.
present a harmonic dimensionality, whereas the on-beat/offbeat three, which has in binary clave terms mostly been referred to this in discussion as three-side and two-side, increase dimensionality, or complexity, if you will, in a linear way; they are are sequential…cyclical yes, but sequential nevertheless.
A Polymetric Perspective Clarifies Terminology
But why the confusion in terminology? Why do we go from talking about on-beat three and offbeat three with two in ternary mode and then switch to (proximate) three with two and then just two with two in binary mode? The answer seems to lie in the observation made somewhat earlier and mentioned as a cornerstone of Toro’s perspective that the primary offbeats of odd metric cycles—the ones in the middle—will land together. This means that the primary offbeat of three (or five, seven, etc.,) coincides with the offbeat of one, which is, of course, the second note of two. This coincidence of metric cycles lends a point of resolution between the two making the offbeats of the odd cycle (three) agree with the latter half of the even cycle (two). This idea is also noted by Peñalosa when he states: “Rhythmic tension is generated on the first half of clave and resolved in the second half. Tension is initiated on primary bombo and resolves where the main beats and clave coincide.” (Peñalosa and Greenwood 2009, 104) The tension in this case is from the meeting of the ‘primary’ and ‘secondary’ beat cycles, to use his terms, that is, two (primary) and three (secondary). Though I debate the use of these terms and perspective elsewhere in this study they are meaningful given the perspective from which Peñalosa works. He goes on to say, “The two cells of clave cycle in a call-and-response or antecedent-and-consequent sequence. The three side of clave is commonly referred to as ‘strong,’ (‘fuerte’), ‘positive,’ and ’round,’ while the two-side is called ‘weak’ (‘débil’), ‘negative’ and ‘square.’” (Peñalosa and Greenwood 2009, 104) These perceptions of weak and strong, round and square, and so forth speak to the type of interaction that takes place between the two and three in each half of the patterns. The strong side characteristically shows unison rhythmic agreement on the downbeat, the ‘one,’[13] followed by a rapid divergence to tension of the bombo against beat two (of two); the bombo placement makes us feel as if we are potentially in three, and this causes tension against the ‘primary’ (or, just ‘other’) beat cycle, two. The second half brings a resolution on beat four which can be felt as a singularity of metre, a lack of metric confrontation, or a point of less dimensionality, but in the view espoused here, it is rather the meeting of primary offbeats. The first half shows agreement on beat one then divergence, the second half divergence on beat three (downbeat of the second half) then agreement on beat four, the primary offbeat of the second half. The middle of the rhythm floats in tension, the beginning and the end are points of resolution but between different aspects of the three and two poly-metric phenomenon. This applies in ternary or binary interpretations without a change in terminology. Of course, most players of this music have historically been more interested in expressing themselves with the music than with the conceptual terminology, but this discussion lends necessary support to the proposed change from a ‘primary’ and ‘secondary’ point of view to a harmonic grid, where the juxtaposition of metres and metric perspectives is ever present, and the feeling always multi-dimensional. This is the hypothesized backdrop which lends AT/Musics of the world their rhythmic potency.
Continued in Part 2.
[1] Note the usual spelling for this very popular, mortar or goblet shaped hand drum is Djembe. This spelling, however, is leftover as an attempt to use French sounds for our common Latin Alphabet characters to represent this African word. Having spent several years learning the Jula language (also spelled ‘Dioula‘, a dialect similar to Malinke and Bambara) with more consistent, less colonial, phonetic spellings, (outside of Ethiopia there are no traditional alphabets) I prefer to write the word as Jembe which sounds something like ‘gem’ and ‘bay’. There are regional pronunciation variants as well, e.g., Polak, in his early writing, used Jenbe. (Polak 1998)
[2] I numbered the pieces from the index and used http://www.random.org/sequences/ to generate my random sequence.
[3] I’ll retain Keïta and Billmeier’s ‘Dj’ spelling as this is a less common word than jembe/djembe, and a proper noun used by a cultural insider thus.
[4] My initial reaction was, “What about one?” But two articulations, or ‘ones’, in a row is really two. In any case, the point seems too pedantic even for this rather detailed discussion. Toro’s reaction to my question seemed to indicate a similar point of view.
[5] For the sound file, I recorded the permutations both with and without the original reference downbeat distinguished by a different tone. With it, it is interesting to try to hear/imagine the original motif, even as it shifts its position within the rhythmic cycle. Without it, we hear the various permutations without bias from the original.
[6] The second line is also known as baqueteo. (Mauleón 1999, 2011)
[7] Keïta on the
[8] But it can be made from two quintillos:
Cascara from Two Quintillos.
[9] ‘Salsa’ is not one style but a generic term representing many popular dance music styles of mostly Caribbean origin. It was originally coined for marketing purposes. (Gast 1972)
[10] In son clave, that is. In rumba clave, as we have seen, the third note is displaced by one subdivision.
[11] Another option is to write in 2/2 or ‘cut’ time, indicating that there are two beats per bar, with subdivisions of four written as eighth notes. This makes sense, as the note values are consistent with common usage, but with two beats to a bar, or four to a two-bar, clave-length phrase; this is Toro’s usual method, but he ends up referring to those same four subdivisional units (written in eighths) as ‘sixteenths,’ and other such mixed terminology. In the end, I compromised between ‘sense’ and common usage.
[12] It is also commonly but less correctly referred to as Tumbao, probably because it is arguably the most notable sound from the common Tumbao, or repeated pattern played by the conga player in many Latin arrangements. I learned to refer to the, ‘bombo-tumbao‘ figure of the conga, bass drum or bass player, but as Peñalosa shows this is more accurately known as ‘bombo-ponche.’ (Peñalosa and Greenwood 2009; Peñalosa and Greenwood 2010)
[13] Although the ‘one’ isn’t necessarily articulated, it is understood as the primary reference point in the cycle by all those who understand the style.
Bibliography
As you’ve seen in the text, I have included links to most of these works. If you are interested in purchasing any of them, please consider clicking through and helping to support this labor of love. Thank you! YIR (Yours In Rhythm), John
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