From Mali to Ghana:

Pulsation Non-Isochrony in West African Percussion Music Genres

Rainer Polak

Abstract

Most theories of African music emphasize the diversity of musical styles in Africa. Still, many also hold on to the notion of Africa being a uniform area with a high degree of stylistic coherence. This paper questions that latter notion by comparing different genres of West African percussion ensemble music from Mali and Ghana concerning the temporal structure of the fast pulse (metric beat division). On this basis, the paper asks whether it is empirically plausible to represent African music by identifying a singular ideal type of African rhythm. The main result is that uneven beat subdivision timing patterns (pulsation non-isochrony) and the superimposition (nesting) of binary and ternary subdivision layers play a substantial role in genres from Mali (Mande) and northern Ghana (Dagbamba) but not in southern and central Ghana (Ewe, Asante). This finding contradicts the widespread assumption that, in African rhythmic systems, the fast pulse in general is structurally isochronous and either binary or ternary. The paper concludes that African rhythmic systems exhibit a greater diversity than theories of African rhythm have indicated and that Africanist music research should emphasize this diversity more consistently than it has done so far.

Keywords 

African rhythm; rhythm and meter; beat subdivision; Mali; Ghana

Introduction

[1] “It is actually quite risky to use the term ‘African music’ for there is no such thing as African music, only many types of African music,” wrote Gerhard Kubik nearly forty years ago (1983, 27); nevertheless, Kubik would go on to use the term in the title of his influential two-volume Theory of African Music (Kubik 1994, 2010). When Simha Arom’s magnumopus, Polyphonies et Polyrythmies Instrumentales dʼAfrique Centrale (1985) appeared in English translation as African Polyphony and Polyrhythm (1991), the geographical specificity of “Central Africa” was simply elided in favor of the generality “Africa.” Kofi Agawu has done more than anyone to deconstruct essentialist concepts of African music and African rhythm in particular (Agawu 1995b, 2003). However, in his recent book, The African Imagination in Music, he considers it possible to determine an essence of African musicality, suggesting that groove is that essence (Agawu 2016).These examples indicate a tension between two contradictory tendencies in the field of Africanist music research: on the one hand, an emphasis on the diversity of music in Africa and, on the other hand, an adherence to the notion of Africa being a uniform area with a high degree of stylistic coherence. 

[2] This latter trend, to generalize from single case studies to “African music,” has been called into question on political and ethical grounds by Chris Waterman (1991) and Thomas Pooley (2018). In this paper, I ask whether determining an ideal type or essence of African music is even empirically plausible. My focus is on music-analytical theories that show a clear trend towards constructing “African rhythm” as an ideal type. Arthur Jones’s influential postulation that the core idea of African rhythm is polyrhythm—the sophisticated coordination of inherently simple patterns in cross-rhythmic and contrametric multipart ensemble constellations—was informed by detailed analyses of Ewe drum ensemble music from Ghana (Jones 1934, 1937, 1959, 1954). But these analyses were highly speculative in their claims to Africa-wide validity. However, many key works in the study of rhythm in music from Africa have taken up Jonesʼs idea or have come independently to similar conceptualizations, those revolving around the assumption that polyrhythm is a core component of African music in general (e.g., Waterman 1948, 1952; Chernoff 1979, 1991; Kaufmann 1980; Locke 1982, 2009, 2010, 2011; Arom 1984, 1991; Kubik 1994, 2010; Anku 1997, 2000, 2007; Friedson 1996, 2009; Burns 2010; Agawu 2016). These works are far from forming a monolithic block; for example, there is a sharp contrast between theories that propose metric ambiguity to be a key musical intention of African polyrhythm (e.g., Chernoff 1979, 1991; Locke 2009, 2010, 2011; Friedson 1996, 2009) and others that claim that, on the contrary, it is underpinned by an unambiguous metric beat (e.g., Anku 2000, 2007; Burns 2010; Agawu 2016). Thus, there is no single coherent theory of African rhythm. However, many of these works have in common the trend to generalize from case studies to “African” rhythm without revealing in detail how they arrive at this generalization. The selection of musics they study shows biases, such as the underrepresentation of North African material and the overrepresentation of that from southern Ghana, tendencies that Pooley (2018) and Julian Gerstin (2017), respectively, have highlighted. The potential consequences of such biases are as yet unclear.

[3] In order to shed light on this latent problem, this paper weighs up the significance of such biases empirically. By comparing different genres of percussion ensemble music from Mali and Ghana, I will examine whether the metrical systems in these musics are indeed similar to a degree justifying the notion that there is a coherent ideal type. To add sharpness to this comparison, I will focus narrowly on a single aspect, the temporal structure of the fast pulse.

The fast pulse in theories of African rhythm

[4] Until recently, research has been largely unanimous in assuming that the performance and perception of polyrhythm in African musics relies on a fast pulse establishing a temporal grid and a reference point for metric density. This fast pulse has been addressed under various terminologies, including “fastest pulse” (Koetting 1970), “density referent” (Nketia 1974; Anku 1997), “time-point set” (Anku 2000, 2007), “pulse” (Locke 1982, 2009, 2010, 2010), “Nennwert” (nominal value, Dauer 1983), “valeurs minimales opérationelles” (minimal metric units, Arom 1984), and “Elementarpulsation” (elementary pulse, Kubik 1988; 1994). According to some of these conceptualizations, the fast pulse represents a subdivision of a regulative beat that provides the main metric reference layer (e.g., Locke 1982; Arom 1984; Agawu 2006; Anku 1997, 2000, 2007; Burns 2010). Other authors question the regulative metric function of a main beat (e.g., Koetting 1970; Merriam 1982; Chernoff 1991; Locke 2009, 2010, 2011).¹ These conflicting views have partly emerged in the study of musical forms, such as the music of the Ewe people of Ghana, that are of common interest to different authors mentioned, suggesting that interpretive inconsistencies play an essential role. More basic research thus is required to shed light on the beat question. The approach of this paper is to address the issue of similarity and difference in the metric systems of African musics by shifting focus from the beat to the subdivision level. I will start with a statement of an assumed similarity and then question this assumption. 

[5] Most theories of rhythm in African musics agree either explicitly or implicitly that the individual pulse units forming the fast pulsation are categorically equivalent and follow each other at approximately even intervals. This structural property is variously referred to as equidistance (e.g., Kubik 1988, 1994; Anku 1997, 2000), isoperiodicity (e.g., Arom 1984), or isochrony (e.g., Locke 2010). According to Gerhard Kubik (1972, 33), minor deviations from such temporal evenness are unconsciously bent into a regular series and thus “corrected” in the process of perception. Kubik here anticipates the concept of categorical rhythm perception, which was later developed in music psychology by Eric Clarke (1987, 1999). For a pulsation to be experienced as isochronous, performing with quasi-metronomic accuracy is unnecessary; instead, the timing of pulses only needs to be close enough to evenness to be perceived as an isochronous pulse train. In what follows, I will use the term isochrony in this sense and accordingly write of “pulsation non-isochrony” (Morford 2023) when the timing of a fast pulse at the beat subdivision level is strongly and consistently different from isochrony.²

Recent research on musics from Mali

[6] Based on my ethnographic research and personal experience as an apprentice professional djembe player in Bamako in the 1990s, I first proposed more than two decades ago that pulsation non-isochrony is widespread in the djembe music of the Maninka (also: Malinké) and other Mande-speaking groups from Mali (Polak 1998). Later, I empirically tested this assumption in a study combining music analysis with computer-assisted timing measurements in multitrack recordings of djembe drum ensembles (Polak 2010). The latter study revealed a clear picture: various patterns of non-isochronous beat subdivision occur in traditional djembe music from Mali and, while pieces based on pulse isochrony exist, the majority of pieces are characterized by some pattern of non-isochronous subdivision that is part of the composition and only minimally varied from performance to performance.³ These pulse timing patterns consist of at least two pulse classes, a long one and a short one. For example, some of the ostinatos most widely used for accompaniment in djembe ensemble music are based on a binary beat subdivision that is consistently timed according to the pattern long–short. In most of these cases, the durations of the long and short elements relate in ratios that range from about 1.3:1 to 1.6:1. This is markedly different from the 1:1 ratio that nominally underlies an isochronous beat subdivision but also from the 2:1 ratio that can be mapped to an isochronous ternary subdivision (see Figure 1).

Figure 1. Schematics of non-isochrony at the beat subdivision level in the example of two-note rhythms. Top row: Range of ratios between 1:1 and 2:1, giving only the first value for the sake of readability (1:1=1, 1.1:1=1.1, etc.). Second row: Approximation of the subdivision ratios in percentages (100%=beat span). Third row: Degree of non-isochrony defined by the distance from isochronous subdivision options (isochronous binary subdivision=1:1 and isochronous ternary subdivision underlying 2:1). Fourth and fifths (bottom) rows: Possible time values for two-element rhythms exemplifying the 1:1 and 2:1 ratios in staff notation. I abstain from suggesting staff notation for ratios such as 1.4 (58:42), because the necessary time values (e.g., 64^th notes) would hardly make sense, especially considering the rapid pace with which fast pulses at the subdivision level are usually realized. 

[7] The same study (Polak 2010) found that in some pieces, two subdivision levels with different tempos and cardinalities occur simultaneously, one binary and one ternary, or one ternary and one quaternary. In these cases, the binary, ternary, and quaternary subdivision layers all are non-isochronous and merge seamlessly; they nest smoothly into each other due to their asymmetric timing patterns (see Figures 2 and 3). Thus, the co-occurrence of binary and ternary or ternary and quaternary subdivision layers does not entail metric ambiguity or polymeter at the subdivision level, but is coordinated in a coherent hierarchy of metric pulse layers (see Figures 4 and 5).⁴ In what follows, I address this type of coordinating metric pulse layers as “asymmetric nesting” and thus differentiate it from the symmetric nesting that occurs when binary and quaternary pulsations or ternary and sextolic pulse layers are coordinated, e.g., the levels of eighth and sixteenth notes in the context of a meter characterized by a quarter-note beat. 

Figure 2. Schematics of hierarchic nesting of non-isochronous binary (short­–long) and ternary (short–medium–long) subdivisions. The smoothness of this nesting results from the second binary and third ternary subdivision units in each beat occurring very close to each other and potentially being perceived as simultaneous.    

Figure 3. Schematics of hierarchic nesting of non-isochronous ternary (long–medium–short) and quaternary (short–medium–long–medium) subdivisions. The smoothness of this nesting results from the second and third ternary subdivisions occurring close enough to their third and fourth counterparts in the quaternary layer to be perceived as simultaneous.  

Figure 4. Schematic hierarchic tree illustration of metric 4-beat cycle with two non-isochronous subdivision levels: binary (long–short) and ternary (short–medium–long). Color-coded tiers from top to bottom: yellow=cycle level, blue=beat level, green=first subdivision level, orange=second subdivision level. Modified from Polak 2022, Figure 14.4).

Figure 5. Schematic hierarchic tree illustration of metric 4-beat cycle with two non-isochronous subdivision levels: ternary (long–short–short) and quaternary (short–medium–long–medium). Color-coded tiers from top to bottom: yellow=cycle level, blue=beat level, green=first subdivision level, orange=second subdivision level. Modified from Polak 2022, Figure 14.4).

[8] A follow-up study showed that both pulsation non-isochrony and asymmetric nesting also apply to other, non-djembe-based percussion music traditions of other Mande-speaking groups in the region, specifically the dundunba-centered drum ensemble of the Khasonka (Xasonka) from western Mali and the bònkolo-based ensemble of the Bamana (Bambara) from central Mali (Polak and London 2014). Two further studies, one examining the precision of ensemble synchronization (Polak et al. 2016) and one psychological experiment testing the perception of complex ratios such as 58:42≈1.4 (Polak et al. 2018), found that non-isochronous beat subdivisions represent an aspect of metric structure for Malian musicians, i.e., not a deviation from isochronous meter.⁵ In summary, research on musics from Mali contradicts the earlier assumption that African rhythm is generally based on pulsation isochrony.

[9] In addition, there is indication of an even wider distribution of pulsation non-isochrony in Africa. Specifically, Gerhard Kubik (2010, 48–50) has asserted the presence of the so-called swing feeling in the Sahel and Sudanian savanna zones to the south of the Sahara desert. Kubik borrowed the swing concept from jazz research, where it refers to a complex phenomenon with both experiential components, particularly a sense of rhythmic drive, and musical patterns used to create such a sense of propulsion, including uneven (long–short) spacing of the eighth notes that constitute the beat subdivision in swing jazz (Butterfield 2011). While this so-called swing timing has often been theorized as based on underlying triplets (ternary beat subdivision), empirical timing analyses of large sets of recorded performances reveal that the duration of the two uneven (long–short) eighth notes per beat is rarely in a ratio of about 2:1. Instead, ratios vary widely over a vast range depending on various factors, including player, tempo and substyle; however, the range of 1.25 (≈56:44) to 1.6 (≈61:39) predominates (Benadon 2006; Dittmar et al. 2017; Corcoran and Frieler 2021), and this overlaps with the range of non-isochronous subdivision ratios used in Mali (see above, Figure 1). Therefore, Kubik’s assertion that swing occurs in the Sahel and Sudanian savanna zones of sub-Saharan Africa points to a hypothesis that pulsation non-isochrony is a widespread phenomenon in this vast region. In what follows, I present some comparative evidence that sheds light—focuses some spotlights, at least—on how widespread non-isochronous beat subdivision actually may be in Africa.

From Mali to Ghana: A comparative perspective

[10] This section contains the main empirical contribution of the present paper. It investigates whether or not the phenomena of pulsation non-isochrony and asymmetric nesting as found in Malian drumming genres also occur in forms of percussion ensemble music from Ghana. The latter have attracted considerable research interest. Arthur Jonesʼs works were followed by those of Joseph Nketia (1963), James Koetting (1970), David Locke (1982, 1990, 1992, 1998, 2009, 2010, 2011), John Chernoff (1979, 1991), Willie Anku (1997, 2000, 2007), Kofi Agawu (1995a), Andreas Meyer (2005), and James Burns (2009), among others. My own perspective on percussion music from Ghana is based on reading this scholarship and analyzing corresponding field recordings, first by ear and then by means of computer-aided timing measurements.

Dagbamba

[11] Dagbon, the land of the Dagbamba (also known as Dagomba) people, is located in northern Ghana and thus shares with Mali belonging to the “swing belt” hypothesized by Kubik (2010). The traditional drum music of the Dagbamba has been studied by Chernoff (1979) and Locke (1990, 2009), among others, and extensively documented by these authors on respective websites (Chernoff n.d.; Locke n.d.).⁶ Some of Locke’s analyses indeed provide evidence for the occurrence of non-isochronous subdivisions in Dagbamba music. For example, in reference to a piece called Damba, he notes that the lead drum part frequently operates in the intermediate range between binary and ternary subdivision (Locke 1990, 51). I scanned the pieces presented by Chernoff and Locke on their websites by ear, found several pieces with perceptually salient pulsation non-isochrony, and selected two of them for analysis: Nun Da Nyuli and Tora. 

[12] I follow Locke’s (n.d.) analyses in describing three ensemble parts that are particularly characteristic of Dagbamba drumming. These parts are played by two hourglass-shaped drums called lunga, whose pitch can be controlled by manipulating the cords that connect the membranes on both sides of the shell, and one drum called gungon, which produces two basic timbres, one resonant and clean bass sound and one softer and higher-pitched buzzing sound. The first lunga plays a highly variable lead drum part, the second lunga a short and minimally variable ostinato for accompaniment, and the gungon provides groove and orientation while its patterns offer different degrees of variability, depending on repertoire and context; the gungon sometimes supports the second lunga’s accompaniment role by playing ostinatos and at other times takes on lead drum functions in tandem with the lead lunga (Locke n.d.).  

Nun Da Nyuli

[13] The piece Nun Da Nyuli is based on an eight-beat metric cycle with ternary beat subdivision, which Locke transcribes in four two-beat measures (Locke n.d.; see Figure 6). Among the three instruments that constitute the ensemble polyrhythm, the dense and repetitive second lunga’s time-keeping ostinato lends itself particularly well to the quantitative study of the subdivision timing. In the following analysis, I will thus first focus on a recording of the second lunga in isolation and then zoom out to a field recording of an ensemble performance.

Figure 6. Simplified transcription of the ensemble thematic cycle for Nun Da Nyuli (after Locke n.d.). Upper tier: measures 1 and 2 (beats 1–4 of the eight-beat cycle); bottom tier: measures 3 and 4 (beats 5–8). The vertical black lines represent Locke’s bar lines. The notation does not transcribe pitch contrasts but differentiates basic stroke types; specifically, round noteheads mark open, fully resonant strokes, whereas x-shaped noteheads mark edge strokes (gungon) or muted strokes (lunga).

[14] The second lunga’s rhythmic cell for Nun Da Nyuli consists of a pair of one eighth and one quarter note (see Figure 6), which nominally would relate in a 1:2 durational ratio. Measurement of a studio recording of this rhythm from Locke’s website (listen to Audio Example 1) shows a perfectly even beat span, suggesting isochrony at the tactus level. This beat span is consistently divided by the two notes according to a duration ratio averaging 41:59 (in percent of the beat span). The standard deviation from this average is very small (<1% of the beat span), indicating that the performing musician controlled the timing with great accuracy and consistency. The duration ratio of 41:59 entails that the second stroke in each beat (marked with red arrows in Figure 7) is delayed relative to the expectation inherent in the isochronous ternary pattern (33:67), which the notation nominally suggests. The stroke indeed falls approximately midway between the isochronous ternary and isochronous binary expectations (see Figure 7). Accordingly, the two strokes in each cell are relatively far apart and the rhythmic contrast between short and long durations is flattened. This 41:59 note pair thus sounds markedly more “rounded” than a 33:67 note pair would. In summary, the performance of the second lunga’s ostinato for Nun Da Nyuli is based on a clearly non-isochronous subdivision of the beat.

Figure 7. Waveform of a 2-beat excerpt containing two 2-stroke cells of the analyzed sound recording of the second lunga in Nun Da Nyuli. The top row gives the note values according to Locke (n.d.) and Figure 6. Numbers and green triangles mark the hypothetical isochronous ternary (upper row) and isochronous binary (lower row) subdivision grids.

 

[15] As expected, the more variable patterns of the other ensemble parts, i.e., the first lunga’s lead part and the bass-drum gungon, also show more variability in timing than the ostinato of the second lunga’s accompaniment part. However, a recurrent feature is that the duration of the first of the three pulses per beat often stands at 35–40% of the beat span and thus is audibly longer than the other pulses. 

[16] Listening to stereo field recordings (e.g., Chernoff 1992, track 20; Rakhra 2003, track 2; Audio Example 2), I hear a consistently non-isochronous beat subdivision timing pattern with a long onbeat pulse (long–short–short). Sometimes the long first pulse seems so long that it can suggest the interpolation of a fourth, silent pulse (cf. Figure 3). Frequently, pairs of strokes beginning on the beat sound very rounded, as in the ostinato analyzed above. I tried to verify this auditory experience by timing measurements of the stereo field recordings. Defining event onsets in stereo recordings of multi-part ensemble performances is difficult because the waveforms of the different ensemble parts are aggregated and thus partially mask each other; the results should therefore be interpreted with some caution. However, what I did find is a long–short–short timing pattern of the beat subdivision, often with values of about 40% for the long onbeat element. These values appear plausible as they are consistent with both my subjective listening experience and the quantitative finding that the second lunga’s ostinato on average grants 41% of the beat span to the long onbeat subdivision. 

[17] Taken together, the analyses above show that the piece Nun Da Nyuli is based on pulsation non-isochrony in a ternary beat subdivision that is structured according to the pattern long–short–short.

Tora

[18] The piece Tora, like Nun Da Nyuli, is based on an eight-beat metric cycle which Locke (n.d.) renders in four two-beat bars. While the two lunga parts are both based on ternary subdivision, Locke suggests that there is no clear fast pulse serving as a density referent for the gungon part, which oscillates between binary and ternary subdivision timings yet mostly leans towards the binary side. Two different pulsations—one ternary and one binary subdivision—thus may be used by different ensemble parts in Tora. Accordingly, Locke notates the ensemble rhythm partly in triplets and partly in duplets (especially the gungon) and postulates a kind of metric ambiguity or polymeter at the subdivision level (see Figure 8). 

Figure 8. Simplified transcription of the ensemble thematic cycle for Tora (after Locke n.d.). 

[19] In the ostinato of the accompanying second lunga part, a ratio of 2:1 (67:33) might be expected for the two strokes in the first half of the two-beat motif (beats 1, 3, 5, and 7). By contrast, timing measurements of recordings give an average duration ratio of about 1.3:1 (57:43; listen to Audio Sample 3). This timing is non-isochronous to a drastic degree (see Figure 9); it is even further removed from the isochronous ternary expectation than the timing in Nun Da Nyuli is. 

Figure 9. Waveform of a 3-stroke motif (spanning two beats) of the analyzed sound recording of the second lunga ostinato for Tora. The onset of the second stroke (marked with red arrows) is so highly anticipated relative to the isochronous ternary expectation (1.67) that it is even closer to the isochronous binary (1.5) grid.

[20] My own listening experience with ethnographic field recordings of Tora (Chernoff 1992, track 9; Rakhra, track 4; Audio Example 4) is that of an integrated ensemble groove where the gungon’s timing is still conceivable within a coherent ternary framework based on a non-isochronous short–medium–long ternary subdivision (see Figure 10). From this perspective, the gungon and the two lunga parts are not based on rival subdivisions (binary vs. ternary) but use different degrees and layers of the same non-isochronous metric hierarchy (cf. Figures 2 and 4). Indeed, my measurements of the ethnographic recordings yield a mean duration ratio of 25:32:43 for the ternary subdivision, which appears consistent with this listening. 

Figure 10. Revision of Figure 8 based on a non-isochronous ternary subdivision as suggested by timing measurements and subjective listening. 

[21] Locke’s interpretation (metric ambiguity) and my own listening (metric integration based on asymmetric nesting) represent two different ways of theorizing the superposition of binary and ternary beat subdivisions in Tora. In the context of the subject matter of this article, however, what is most relevant is that neither mode of listening can be reconciled with the assumption of a categorically isochronous metric beat subdivision. 

[22] To summarize, there are at least two prominent pieces in the repertoire of traditional Dagbamba percussion music that consistently use non-isochronous beat subdivisions. In one of these, Tora, non-isochronous binary and ternary subdivision layers are asymmetrically nested into each other. Structural similarities with drum ensemble rhythms from Mali are evident. For instance, the 57:43 timing ratio of the basic ostinato and its embracing of a short–medium–long ternary subdivision in Tora is similarly characteristic of the Mande drumming pieces Wolosodòn (see Polak 2010) and Bire (see Polak and London 2014). 

Ewe

[23] Ewe percussion ensemble music is one of the most well-researched musical styles in Africa, e.g., in monographs by Jones (1959), Chernoff (1979), Locke (1992, 1998), Agawu 1995a), and Burns (2009), and it is arguably the most important reference point for theories of African rhythm. Eweland lies in southeastern Ghana and neighboring Togo, and thus outside the area where Kubik assumes swing feel plays a role. To the best of my knowledge, the relevant literature indeed does not provide indications of swing feel or non-isochronous beat subdivision in particular—with one exception, Locke’s (1992) analysis of the genre Kpegisu, to which I will come below. Ewe drumming is documented on a number of published CDs and DVDs, as well as in archives.⁷ I have analyzed the timing of five pieces found in these materials: Gahu, Kinka, Slow Atsia/Agbeko, Fast Atsia/Agbeko, and Kpegisu. In four out of these five pieces, I found no evidence of pulsation non-isochrony; the exception is Kpegisu, to which I will come back below.

Gahu

[24] One well-documented genre of Ewe drumming is Gahu, which Locke (1998) detailed in a monograph. A chapter entitled “The Time” describes three instrumental parts whose common function is to jointly establish the fundamental rhythmic structure of the piece (Locke 1998, 16-36). These are the bell gankogui, which provides a timeline, the calabash rattle axatse, which embellishes that timeline, and the accompanying drum kagan providing an offbeat ostinato for acccompaniment (Figure 11). I have analyzed various recordings of the bell and the kagan patterns which Locke (1998) provides on an accompanying CD. The percentage of the beat span which the notes of the bell pattern take are always close to 75:75:100:100:50; e.g., the mean timing ratio in one recording is 75:76:100:98:51. This nearly perfectly matches the nominal expectation inherent in a sequence of two dotted eighth notes, two quarter notes, and one eighth note (see Figure 11). Similarly, the timing of the kagan pattern always grants about 25% of the beat span to the interval between the first and the second stroke in each beat. When performed in conjunction with the beat, the kagan’s timings are close to 50:25:25 (e.g., 48:26:26), which meets the nominal expectation for an eighth and two sixteenth notes. While not all timings in Gahu, especially not the complex lead-drumming can be mapped to an isochronous pulse with this degree of precision, the timings of the “Time” instruments I have analyzed are all consistent with the assumption that there is an isochronous quaternary pulse. To put it differently, I found no indication of pulsation non-isochrony in Gahu. 

Figure 11. Simplified transcription of the “Time” section’s thematic cycle for Gahu (after Locke 1998). 

Kpegisu

[25] Kpegisu is the only piece in the Ewe repertoire in which I found evidence of non-isochronous subdivision timings. To start with, Locke’s (1992) analysis of the piece indeed contains clear references to this effect. For instance, the kagan accompaniment drum motif, which consists of a pair of strokes on the second and third ternary subdivisions in each beat (see Figure 12), is played with “the first tone in each [motivic cell] just a bit early. In other words, [the player] evens out the kaganʼs short–long triplet quality” (Locke 1992, 111). In this regard, Ewe master drummer Godwin Agbeli explains: “The swing style feels faster and more lively, [giving the part] more push or kick without rushing the tempo or becoming unsteady” (Locke 1992, 111–112). My listening impression and timing analysis of studio recordings included with Locke’s book (1992) confirm the author’s analysis. The interval between the first and second strokes—that is, the duration of the second pulse in each beat—averages 39% of the beat span. This timing is consistent with the kidi drum, which, according to Locke (1992, 112), often plays a subtle “rubato” and, according to my timing measurements, is based on an uneven beat subdivision with an average duration ratio of 30:40:30. Thus, the kagan and kidi seem to follow a non-isochronous subdivision timing pattern structured short–long–short.

Figure 12. Simplified transcription of basic patterns for Kpegisu (after Locke 1998). 

[26] This stands in contrast, however, with phrasings of the gankogui bell and axatse rattle that do not also adhere to this non-isochronous subdivision pattern. For instance, the rattle’s mean timing pattern is 32:35:33, which is reminiscent of the kagan and kidi’s short–long–short pattern in prinicple, but is too close to an isochronous ternary pulsation to be perceived differently. The bell shows an average timing pattern of 64:67:36:65:66:63:39, which is close to the expectation based on isochrony suggesting 67% and 33% values. Moreover, it does not support the kagan and kidi’s short–long–short pattern because its strongest elongation relative to the isochronous expectation, the last stroke taking 39% not 33.3% of the beat span, falls on the third, not second pulse of the respective beat. It seems, then, that while the kagan and kidi’s pulsation non-isochrony in Kpegisu certainly contributes to the rhythmic feel of the ensemble rhythm, it does not also have the status of a metrical norm affecting the entire ensemble.

[27] To sum up, there is only little evidence of non-isochronous beat subdivision and none of asymmetric nesting in Ewe drum ensemble music. While pulsation non-isochrony certainly adds to the rhythmic feel in Kpegisu, it does not amount to a metric norm in this piece and does not occur at all in the other pieces I examined. 

Asante

[28] Asante (also: Ashanti) music from southern and central Ghana, like Ewe music, falls outside the swing belt hypothesized by Kubik. Studies of Asante percussion music indeed have yielded no indication of pulsation non-isochrony or of asymmetric nesting (Nketia 1963; Anku 1997, 2000, 2007; Meyer 2005). The media I have analyzed to test this state of research are an extensive set of field recordings of two Asante genres, Nwomkoro and Dansuom, kindly provided by Andreas Meyer.⁸ In what follows, I focus on the Dansuom ensemble, which Meyer (2005) describes as consisting of three types of iron bell (firikyiwa, dawuro, nnawuta), a water-resonated calabash drum (koraa), and two types of lead drum (donno, apentemma). 

[29] Dansuom groups play two different styles, Highlife, which uses a quaternary beat subdivision and Adowa, showing a ternary pulse (Meyer 2005). I analyzed recordings of both styles by ear and timing measurements and found evidence of isochronous pulsations only. For example, the three strokes of the dawuro bell pattern in the Highlife style (see Figure 13) relate by a mean timing of 74:74:52 (in percent of the beat span), suggesting an isochronous quaternary subdivision with nominally 25% per pulse. Similarly, the average timing pattern of a typical donno pattern (Figure 13), 25:49:125:52:51:98, consists of values that all are very close to multiples of 25%, again pointing to an isochronous quaternary pulse realized with great precision. While more flexible and divergent timings occur in some of the patterns in some ensemble parts, these phrasings are nowhere near pronounced and stable enough to suggest pulsation non-isochrony.

[30] In summary, my spot analyses corroborate the state of previous research indicating that neither non-isochronous beat subdivision nor asymmetric nesting play a prominent role, if indeed any role at all, in Asante percussion musics. 

Figure 13. Transcription of some patterns for Dansuom Highlife (modified after Meyer 2005). 

Conclusion

[31] A number of projects I have conducted with colleagues since 2010 have shown that various genres of Mande percussion music from Mali exhibit rhythmic structures that do not conform to the concept of pulse (beat subdivision) as assumed in various theories of African rhythm. These structural features include the non-isochrony of beat subdivisions and the asymmetric nesting of binary and ternary layers of such non-isochronous subdivisions. Psychological experiments have confirmed that these structures are perceptually stable and aesthetically relevant for enculturated listeners from Mali. The aim of the current paper has been to empirically explore the possibility of a wider spread of comparable phenomena by comparing the results from Mali with an examination of three genres from Ghana. I found prominent cases of consistent pulsation non-isochrony and asymmetric nesting in the percussion music of the Dagbamba in northern Ghana, but not among the Ewe and Asante in southern Ghana. 

[32] The findings above are consistent with Gerhard Kubik’s suggestion that there is a “swing belt” in the Sahel and Sudanian savannah zones of sub-Saharan Africa. However, it will require many more case studies and a much wider comparative research perspective to test and corroborate or to refute this claim. Kubik (2010, 50) speculated that the existence of swing feeling had been overlooked in Africanist musicology for decades because it does not play a prominent role in the music cultures whose study shaped the field, such as those from southern Ghana. My findings are somewhat consistent with this assumption as I did not find pulsation non-isochrony to feature prominently in drumming genres of the Asante and Ewe peoples from southern Ghana. However, I want to mention two caveats on this topic. First, my findings cannot rule out the occurrence of pulsation non-isochrony in other styles from south of the Sahel and Sudanian savanna zones. Secondly, Dagbamba drumming from northern Ghana, which does feature non-isochronous subdivision, was well represented in key scholarly works and field recordings from two leading theorists of African rhythm, John Chernoff (1979) and David Locke (1990, 2009, 2011). This indicates that in addition to a regional bias, there might be other factors that have contributed to the lack of acknowledgement of the phenomena in question in theories of African rhythm. One such potential factor is the theoretical bias not to question the axiomatic assumption of pulse isochrony as expressed in many theories of African rhythm. This is mere speculation, however, as I do not have any evidence of such a theoretical bias.

[33] Independent of the question of exactly how widely spread pulsation non-isochrony may be, an important contribution of the current paper is the further evidence that it has some spread in some regions of Africa. Such evidence has been accumulated since 2010 and is sufficient to refute the widespread assumption that “African rhythm” in general is based on pulsation isochrony and symmetric nesting. This assumption weakens the plausibility of efforts to represent the rhythmic systems of African musics under a coherent ideal type. Even within the relatively compact and specific subfield of West African percussion music, rhythmic systems evidently exhibit a higher degree of diversity than previous theories have suggested. As a proviso, I should admit the central component of most analytical theories of African rhythm is polyrhythm, of which the narrow focus of the current study, beat subdivision structure, is only one aspect. However, to consider the subdivision structure as an isolated, perhaps secondary aspect that does not make a critical difference would be to seriously underrate its relevance. Pulsation non-isochrony in Malian drumming engenders appealing rhythmic feels that are preferred over alternative ones by experienced listeners (Neuhoff et al. 2017; Jakubowski et al. 2022). This is a lot already, but pulsation non-isochrony does still more than just that. While the isochronous meters of Ewe and Asante music usually operate with very stable tempos, the non-isochronous subdivision-based meters in Mande drumming are typically performed with specific patterns of drastic accelerando (Polak 2017). This frequently involves metric transformations through reduction from quaternary to ternary and/or from ternary to binary subdivision levels (Morford and David forthc.); these density reductions are based on exactly the asymmetric nesting structures illustrated in Figures 2–5. Such tempo-metric transformations are also used to differentiate sections within pieces and thus create musical form (Polak and London 2022). This is to say that pulsation non-isochrony is a fundamental characteristic of Mande music from Mali, and the current paper’s findings suggest that the same also holds for other musics of the wider region, such as Dagbamba drumming from northern Ghana. This makes for a difference between these musics and the genres of Ewe and Asante drumming from southern Ghana, and this difference can be heard and felt, musically analyzed, and empirically measured. In conclusion, I would argue that future Africanist music research should emphasize the diversity of African rhythmic systems more consistently than before, and that possible generalizations from individual case studies to “African rhythm” or African music at large should be based on substantiated arguments rather than intuition alone.

Acknowledgements

I thank Andreas Meyer, James Burns, David Locke, and John Chernoff for providing me with field research materials and for stimulating discussions. Furthermore, I thank Bill Martin, Samuel Horlor, and Thomas Pooley for their help in improving earlier drafts of the manuscript. 

References

Agawu, V. Kofi. 1995a. African Rhythm: A Northern Ewe Perspective. Cambridge: Cambridge University Press.

Agawu, V. Kofi. 1995b. “The Invention of ‘African Rhythm’.” Journal of the American Musicological Society 48(3): 380–395.

Agawu, V. Kofi. 2003. Representing African Music: Postcolonial Notes, Queries, Positions. New York: Routledge.

Agawu, V. Kofi. 2006. “Structural Analysis or Cultural Analysis? Competing Perspectives on the ‘Standard Pattern’ of West African Rhythm.” Journal of the American Musicological Society 59(1): 1–46. 

Agawu, V. Kofi. 2016. The African Imagination in Music. New York, NY: Oxford University Press.

Anku, Willie. 1997. “Principles of Rhythm Integration.” Black Music Research Journal 17: 211–238.

Anku, Willie. 2000. “Circles and Time: A Theory of Structural Organization of Rhythm in African Music.” Music Theory Online 6(1).

Anku, Willie. 2007. “Inside a Master Drummer’s Mind: A Quantitative Theory of Structures in African Music.” Transcultural Music Review (11).

Arom, Simha. 1984. “The Constituting Features of Central African Rhythmic Systems: A Tentative Typology.” The World of Music 26(1): 51–67.

Arom, Simha. 1985. Polyphonies et Polyrythmies Instrumentales d’Afrique Centrale: Structure et Méthodologie. Paris: SELAF.

Arom, Simha. 1991. African Polyphony and Polyrhythm: Musical Structure and Methodology. Cambridge, New York, Paris: Cambridge University Press.

Benadon, Fernando. 2006. “Slicing the Beat: Jazz Eighth-Notes as Expressive Micro-Timing.” Ethnomusicology 50: 73–98.

Burns, James. 2009. Female Voices from an Ewe Dance-Drumming Community in Ghana: Our Music Has Become a Divine Spirit. Burlington, VT: Ashgate.

Burns, James. 2010. “Rhythmic Archetypes in Instrumental Music from Africa and the Diaspora.” Music Theory Online16(4). https://www.mtosmt.org/issues/mto.10.16.4/mto.10.16.4.burns.html

Butterfield, Matthew W. 2011. “Why Do Jazz Musicians Swing Their Eighth Notes?” Music Theory Spectrum 33(1): 3–26. 

Chernoff, John M. 1979. African Rhythm and African Sensibility: Aesthetics and Social Action in African Musical Idioms. Chicago: The University of Chicago Press.

Chernoff, John M. 1991. “The Rhythmic Medium in African Music.” New Literary History 22(4): 1093–1102. 

Clarke, Eric F. 1987. “Categorical Rhythm Perception. An Ecological Perspective.” In Action and Perception in Rhythm and Music, edited by Alf Gabrielsson, 19–33: Royal Swedish Academy of Music.

Clarke, Eric F. 1999. “Rhythm and Timing in Music.” In The Psychology of Music, edited by Diana Deutsch. 2nd ed., 473–500. San Diego: Academic Press.

Corcoran, Christopher, and Klaus Frieler. 2021. “Playing It Straight.” Music Perception 38(4): 372–85. 

Dauer, Alfons M. 1983. “Kinesis und Katharsis: Prolegomena zur Deutung afrikanischer Rhythmik.” In Musik in Afrika: 20 Beiträge zur Kenntnis traditioneller afrikanischer Musikkulturen, edited by Artur Simon, 166–188. Berlin: Museum für Völkerkunde Berlin.

Dittmar, Christian, Martin Pfleiderer, Stefan Balke, and Meinard Müller. 2017. “A Swingogram Representation for Tracking Micro-Rhythmic Variation in Jazz Performances.” Journal of New Music Research, 1–17. 

Friedson, Steven M. 1996. Dancing Prophets: Musical Experience in Tumbuka Healing. Chicago: University of Chicago Press.

Friedson, Steven M. 2009. Remains of Ritual: Northern Gods in a Southern Land. Chicago: University of Chicago Press. 

Gerstin, Julian. 2017. “Comparisons of African and Diasporic Rhythm: The Ewe, Cuba, and Martinique.” Analytical Approaches to World Music 5(2): 1–90.

Jones, Arthur M. 1934. “A Study in the Combination of Rhythms in African Music.” Bantu Studies 8(1): 1–16. 

Jones, Arthur M. 1937. “The Study of African Musical Rhythm.” Bantu Studies 11(1): 295–319.

Jones, Arthur M. 1954. “African Rhythm.” Africa 24(1): 26–47. 

Jones, Arthur M. 1959. Studies in African Music. London: Oxford University Press.

Kaufmann, Robert. 1980. “African Rhythm: A Reassessment.” Ethnomusicology 24(3): 393–416. 

Koetting, James. 1970. “Analysis and Notation of West African Drum Ensemble Music.” Selected Reports in Ethnomusicology 1(3): 116–146.

Kubik, Gerhard. 1972. “Transcription of African Music from Silent Film: Theory and Methods.” African Music 5(2): 28–39.

Kubik, Gerhard. 1983. “Musikgestaltung in Afrika.” In Musik in Afrika: 20 Beiträge zur Kenntnis traditioneller afrikanischer Musikkulturen, edited by Artur Simon, 27–40. Berlin: Museum für Völkerkunde Berlin.

Kubik, Gerhard, ed. 1988. Zum Verstehen afrikanischer Musik: Ausgewählte Aufsätze. Leipzig: Reclam.

Kubik, Gerhard. 1994. Theory of African Music, Vol. I. Wilhelmshaven: Florian Noetzel.

Kubik, Gerhard. 1999. Africa and the Blues. Jackson: University Press of Mississippi.

Kubik, Gerhard. 2010. Theory of African Music, Vol. II. Chicago: The University of Chicago Press.

Locke, David. 1982. “Principles of Offbeat Timing and Cross-Rhythm in Southern Ewe Dance Drumming.” Ethnomusicology 26(2): 217–246.

Locke, David. 1990. Drum Damba: Talking Drum Lessons. Crown Point, IN: White Cliffs Media.

Locke, David. 1992. Kpegisu: A War Drum of the Ewe. Tempe, AZ: White Cliffs Media.

Locke, David. 1998. Drum Gahu: An Introduction to African Rhythm. Tempe, AZ: White Cliffs Media. 

Locke, David. 2009. “Simultaneous Multidimensionality in African Music.” African Music 8(3): 8–37.

Locke, David. 2010. “Yewevu in the Metric Matrix.” Music Theory Online 16(4). https://www.mtosmt.org/issues/mto.10.16.4/mto.10.16.4.locke.html

Locke, David. 2011. “The Metric Matrix: Simultaneous Multidimensionality in African Music.” Analytical Approaches to World Music 1(1): 48–72.

Lortat-Jacob, Bernard. 1980. Musique et Fêtes au Haut-Atlas. Paris, La Haye, New York: Mouton Éditeur.

Merriam, Alan P. 1982. “African Musical Rhythm and Time Reckoning.” In African Music in Perspective, edited by Alan P. Merriam, 443–61. New York, NY: Garland Publ.

Meyer, Andreas. 2005. Überlieferung, Individualität und Musikalische Interaktion: Neuere Formen der Ensemblemusik in Asante/Ghana. Frankfurt: Peter Lang

Morford, James B. 2023. “When One Plus One Doesn’t Equal Two: Implications of Pulsation Non-Isochrony for Debates in African Musicology.” AAWM Special Topics Symposium 2023: Theoretical, Analytical, and Cognitive Approaches to Rhythm and Meter in World Musics, NYC, June 1-2 and 8-9, 2023.

Morford, James B., and Aaron M. David. (forthcoming). “Metric Modes and Fluid Meter in Mande Drumming Music.”Music Theory Online 29(3).

Neuhoff, Hans, Rainer Polak, and Timo Fischinger. 2017. “Perception and Evaluation of Timing Patterns in Drum Ensemble Music from Mali.” Music Perception 34(4): 438–51. 

Nketia, Joseph H. Kwabena. 1963. Drumming in Akan Communities of Ghana. London: Thomas Nelson.

Nketia, Joseph H. Kwabena. 1974. The Music of Africa. New York, NY: Norton.

Nzewi, Meki E. 1997. African Music: Theoretical Content and Creative Continuum. The Culture-Exponent’s Definitions. Oldershausen: Institut für Didaktik populärer Musik.

Polak, Rainer. 1998. “Jenbe Music in Bamako: Microtiming as Formal Model and Performance Practice.” Iwalewa-Forum 2: 24–46.

Polak, Rainer. 2010. “Rhythmic Feel as Meter: Non-Isochronous Beat Subdivision in Jembe Music from Mali.” Music Theory Online 16(4). https://www.mtosmt.org/issues/mto.10.16.4/mto.10.16.4.polak.html

Polak, Rainer. 2017. “The Lower Limit for Meter in Dance Drumming from West Africa.” Empirical Musicology Review12(3­­–4): 205–226. 

Polak, Rainer. 2022. “Non-Isochronous Metre in Music from Mali.” In The Oxford Handbook of Time in Music, edited by Mark Doffman, Emily Payne, and Toby Young, 252–274. Oxford: Oxford University Press.

Polak, Rainer, and Justin London. 2014. “Timing and Meter in Mande Drumming from Mali.” Music Theory Online20(1). https://mtosmt.org/issues/mto.14.20.1/mto.14.20.1.polak-london.html

Polak, Rainer, and Justin London. 2022. “Tempo, Meter, and Form: An Analysis of ‘Dansa’ from Mali.” In Trends in Word Music Analysis, edited by Lawrence Shuster, Sam Mukherji, and Noe Dinnerstein, 143–159. London: Routledge.

Polak, Rainer, Nori Jacoby, and Justin London. 2016. “Both Isochronous and Non-Isochronous Metrical Subdivision Afford Precise and Stable Ensemble Entrainment: A Corpus Study of Malian Jembe Drumming.” Frontiers in Neuroscience 10:285. 

Polak, Rainer, Nori Jacoby, Timo Fischinger, Daniel Goldberg, Andre Holzapfel, and Justin London. 2018. “Rhythmic Prototypes Across Cultures: A Comparative Study of Tapping Synchronization.” Music Perception 36(1): 1–23.

Pooley, Thomas Mathew. 2018. “Continental Musicology: Decolonising the Myth of a Singular ‘African Music’.” African Music 10(4): 177–193.

Waterman, Christopher A. 1991. “The Uneven Development of Africanist Ethnomusicology: Three Issues and a Critique.” In Comparative Musicology and Anthropology of Music: Essays on the History of Ethnomusicology, edited by Bruno Nettl and Philip V. Bohlman, 169–186. Chicago: The University of Chicago Press.

Waterman, Richard A. 1948. “‘Hot’ Rhythm in Negro Music.” Journal of the American Musicological Society 1(1): 24–37. 

Waterman, Richard. 1952. “African Influence on the Music of the Americas.” In Acculturation in the Americas, edited by Sol Tax, 207–18. Chicago: University of Chicago Press. 

Discography and online media collections

Burns, James. 2004. Ewe Drumming from Ghana: The Soup Which is Sweet Draws the Chairs in Closer. London: Topic Records TSCD 924 (British Library Sound Archive) [CD].

Chernoff, John M. n.d. A Drummer’s Testament: Dagbamba Society and Culture in the Twentieth Century. Accessed May 28, 2023. www.adrummerstestament.com/

Chernoff, John M., and Alhaji Ibrahim Abdulai. 1992. Master Drummers of Dagbon, Vol. 1. Cambridge, Mass: Rounder [CD].

Koetting, James. n.d. “The James Koetting Ghana Field Recordings.” Accessed May 25, 2023. http://library.brown.edu/cds/koetting/

Ladzekpo, Seth K. 1969. Music of the Ewe of Ghana. New York City: Folkways AHM 4222 [LP]. 

Locke, David. n.d. Dagomba Dance Drumming. Accessed May 25, 2023. https://sites.tufts.edu/dagomba/

Locke, David. 1992. Kpegisu: A War Drum of the Ewe. Tempe, AZ: White Cliffs Media [Accompanying CD].

Locke, David. 1998. Drum Gahu: An Introduction to African Rhythm. Tempe, AZ: White Cliffs Media [Accompanying double CD]. 

Lortat-Jacob, Bernard, and Hassan Jouad. 1979. Berbères du Maroc: Ahwach. Paris: Chant du Monde LDX 74705 [LP].

Meyer, Andreas. 2005. Überlieferung, Individualität und Musikalische Interaktion: Neuere Formen der Ensemblemusik in Asante/Ghana. Frankfurt: Peter Lang [Accompanying DVD].

Rakhra, Vijay, and Inusah Hamidu Jawula. 2003. Dagbamba Masters: Traditional Drumming from Tamale, Ghana. Vijay Rakhra Productions [CD].

Rakhra, Vijay, and Ghana Dance Ensemble. 2006. Dance-Drumming of the Anlo-Ewe: An Instruction. Vijay Rakhra Productions [DVD].

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1. Some of the latter grant the fast pulse a status that is fully independent of a metric beat (e.g., Koetting 1970); this is a minority position, however. A more widely argued view is to see the fast pulse as a form of beat subdivision that is contingent on the diverse beats which are available simultaneously to a listener’s experience in situations of metric ambiguity. David Locke has elaborated this view under the concept of “metric matrix” and argued it is a hallmark of African rhythm (e.g., Locke 2009, 2010, 2011). ↩︎
2. I first came across the term “pulsation non-isochrony” in a conference talk by James Morford (2023). ↩︎
3. My use of the term “composition” here is inspired by Meki Nzewi’s (1997) concept of “performance composition,” which emphasizes the conventional binding of individual and situational improvisation and performance practice to the specific musical structures of particular repertoires. ↩︎
4. Polak (2022) includes an analysis of a traditional djembe piece (Wolosodòn) based on the interleaving of binary (long–short) and ternary (short–medium–long) pulsations, as shown in Figure 2. The video of this piece is freely accessible at https://vimeo.com/178581785. ↩︎
5. A summary of these studies is provided in Polak (2022). ↩︎
6. The website A Drummer’s Testament (Chernoff n.d.) offers a wealth of information on Dagbamba (Dagomba) music, history, and culture collected by Chernoff in collaboration with master drummer Alhaji Ibrahim Abdulai and a team of elders and translators. It also provides ethnographic field recordings of Dagbamba drumming. The website Dagomba Dance Drumming (Locke n.d.) contains recordings of the basic ensemble parts in isolation as well as ensemble recordings, written analyses and transcriptions, plus information about the Dagbamba people, their drum pieces, and Locke’s principal teacher, research partner, and player of the recorded samples, Abubakari Luna. ↩︎
7. Recordings I have used include Locke 1992, 1998; Burns 2004, 2009; Rakhra & Ghana Dance Ensemble 2006; Ladzekpo 1969; and Koetting n.d. ↩︎
8. Some of this material is published on the DVD accompanying Andreas Meyer’s 2005 book on tradition, individual creativity, and improvisational interaction in “neo-traditional” Asante percussion ensembles. ↩︎