INTRODUCTION

THIS article uses theories of African rhythm from ethno/musicology, findings from anthropological research and population genetics, musical analyses based on transcriptions, and computational phylogenetic techniques to compare the intervallic and structural properties of timeline rhythms performed in Pygmy and Bushmen musical cultures. The Pygmy and Bushmen societies considered in this article were, until very recently, semi-nomadic hunter-gatherer people living in sub-Saharan Africa. Pygmy groups (known under a variety of ethnonyms that include Aka, Baka, Efe, Mbendjele,Twa, Gyeli, Bongo and Mbuti) occupy the equatorial forest ranging from Uganda and Rwanda in Eastern-Central Africa across the Democratic Republic of the Congo to Cameroon and Gabon in Western-Central Africa (Olivero et al., 2016). The Bushmen groups (known by ethnonyms that include San, Basarwa, Ju'hoansi, !Kung, Nharo and Khoisan) live in the Kalahari desert straddling Namibia and Botswana, and small numbers also live in South Africa (Lee & Daly, 1999).

Comparative studies of Pygmy and Bushmen musical cultures date back to 1946, when Gilberto Rouget recorded the music of the 'Babenzele' (Mbendjele) Pygmies as part of an expedition to the Ouesso region of the Republic of the Congo. Upon hearing recordings of !Kung Bushmen made by Laurence Marshall in the 1950s, Rouget noted the striking resemblances between Pygmy and Bushmen musics and speculated that they share a common cultural heritage (Grimaud & Rouget, 1956). Since then, numerous anthropologists and ethnomusicologists have documented the relationship between the two musical cultures. The most salient musical characteristics typically cited as common to both groups are the use of ostinato with variations, vocal polyphony, counterpoint, yodelling and singing without words (Frisbie, 1971; Fürniss, 2006; Grauer, 2006, 2009, 2011; Olivier & Fürniss, 1999; Lomax, 1962, 1976).

There is still, however, considerable debate amongst music scholars regarding the connections between Pygmy and Bushmen musics. Some stress the similarities between the two and look to a possible common ancestry, while others place more stress on the differences. Victor Grauer (2009), for example, concludes that Pygmy and Bushmen groups have "many shared stylistic, structural, conceptual, and cultural attributes" and "that both traditions might well stem from a common root, dating to a period deep into the Paleolithic, when the ancestors of both may have formed a single band" (p. 422). By contrast, Susanne Fürniss (2006), when comparing the musical features of Aka Pygmy and Ju'hoansi Bushmen, argues that "although many musical and extramusical features converge and though the acoustic results are very close, the conception that the Jul'hoansi have of their music is radically opposite to the Aka's" (p. 201).

The current study provides a new perspective on this debate by focussing on the analysis of one central musical feature that has received little attention in the literature cited above: timelines 2.

In sub-Saharan African and related musical contexts, timelines have been described by scholars as distinctive and foundational cyclical rhythms (or rhythmic ostinati) that provide the structural and organisational bases for composition and performance, and serve as time-keeping devices for musicians and dancers (Agawu, 2006; Arom, 1991; Kubik, 2010; Peñalosa, 2009). Kofi Agawu (2006) highlights the importance of timelines in research on rhythm in West African ensemble music, arguing that "practically every scholar writing about West African rhythm during the last half century has taken note of time lines" (p. 3). Further, he concludes that "there is, in short, general consensus that time lines are materially real, widely used, and crucial markers of temporal reference in African ensemble music" (p. 3). However, timelines do more than just function as a "temporal reference" for ensembles; they also embody important aesthetic principles. David Locke's (1998) research on the Gankogui timeline rhythm, played on the bell in the performance of West African Gahu music, suggests that the alternating on-beat off-beat structure of this timeline has a powerful "rhythmic potency" that creates "terrific drive" in the music, establishes the "basic rhythmic feel," and adds to the "crucial power of the entire piece" (p. 19). Similarly, David Peñalosa (2009) argues that the clave, a timeline featured in many African-derived musics such as Cuban son, rumba, and salsa, generates a cyclical tension-and-release dynamic: a principle that connects many musics of the Caribbean and South America to their African roots.

Gerhard Kubik (1999) explores this connection further, arguing that timelines are "formidable diagnostic markers for detecting historical connections between certain New World African diaspora musical styles and those of distinctive language zones on the African continent" (p. 56). The reason timelines can be used to reveal the historical connections between related musical styles, Kubik argues, is that their asymmetrical structure is highly resilient to change:

They are immune to all social, cultural, or environmental influences. One can change a time-line pattern's instrumentation, accentuation, speed, starting point, and mnemonic syllables used to teach it, but not its mathematical structure. Any attempt to change that dissolves the pattern (p. 56).

Drawing on Kubik's (1989) work and Arom's (1991) influential theory of rhythmic structures in Central African music, Godfried Toussaint has used computational phylogenetic techniques, typically used by biologists for DNA analysis, to study the evolutionary relationships between sub-Saharan African timelines and those used in a range of musical styles. In numerous publications dating back over ten years 3, his work suggests that phylogenetic analyses can be fruitfully applied in musicological research and that "timelines are effective markers of the structural evolution of rhythms, and their cultural transmission" (Toussaint, Campbell, & Brown 2011, p. 389).

While Toussaint's approach does not consider the relationships between biological and musical evolution, other researchers have used phylogenetic methods to compare the relationships between biological evolution and other cultural phenomena (Mace et al., 2005), such as Turkish textile designs (Tehrani & Collard, 2002), Indo-European folktales (Graca da Silva & Tehrani, 2016), and Hunter-Gatherer marriage practices (Walker et al., 2011). A dedicated comparative study of the structure and phylogeny of timelines used in Pygmy and Bushmen music that considers all of these perspectives (phylogenetic, musical, and cultural) has the potential to provide new insights into the relationship between their musical cultures and the common cultural heritage they may share.

The aim of this article, therefore, is to examine the contemporary and historical relationships between Pygmy and Bushmen musical cultures by drawing on the research of musicologists such as Kubik, Arom, Furniss and Grauer, population geneticists such as Cavalli-Sforza et al. (1994) and Verdu (2014), and others, as well as additional structural and computational phylogenetic analyses of transcriptions of timelines taken from Pygmy and Bushmen recordings. The forthcoming text is presented in four main sections. First, the musical materials, methods, and software used for structural and phylogenetic analyses are detailed. Second, 31 distinct Pygmy and Bushmen timelines are compared in order to quantify the structural similarities and differences between them. This section also examines the connections between the structure of Pygmy and Bushmen timelines and analogous timelines used in other parts of sub-Saharan Africa and beyond. Third, the connections between timelines are considered further by exploring the cultural context in which timelines are performed. The final section makes use of computational phylogenetic analysis of the original 31 timelines as well as research findings from the fields of population genetics and ethnomusicology to uncover possible Pygmy/Bushmen ancestral rhythms.

MUSICAL MATERIALS AND METHODS

A total of 62 timelines were transcribed by the author for analysis in this study. 48 were taken from recordings of Pygmy performances and 14 from Bushmen performances. The transcriptions were made from a mixture of audio and video formats recorded by other researchers in the field. The majority are commercially available on CD and/or online and usually accompany published texts (e.g. Arom, 1991; Kisliuk, 1998). However, one set of recordings of Mbendjele Pygmy music used in this study comes from recent fieldwork by a colleague, Camille Oloa-Biloa, that is not publicly available. In total, I listened to around 1060 individual performances taken from 18 different sets of recordings, which amounts to approximately 45 hours of material, recorded between 1946 and 2014. The cultural groups featured on these recordings were Western Pygmies (BaYaka: Aka, Baka, BaAka, Mbendjele) and Eastern Pygmies (Mbuti) of Central Africa, and San !Kung (Ju'hoansi) and Nharo Bushmen of South Africa 4.

Timelines were selected for further analysis based on the criteria: they were performances by Pygmy or Bushmen groups and not versions performed by neighbouring non-Pygmy/Bushmen; the timelines were reasonably audible within the often dense polyrhythmic texture; the timelines were repeated several times in order to establish a clear cyclical pattern. Through a process of repeated listening/viewing, selected timelines were then transcribed in Western and TUBS (Time Unit Box System) notation 5. Other relevant contextual details (recording date and location, cultural group, region, event, etc.) were also noted, gleaned from CD notes and booklets, websites, publications, and, in the case of Camille's recordings, direct communication with the researcher.

The next step was to identify groups of related timelines from the transcriptions by looking at the number of pulses within each cycle and the number and placement of sounded strokes within that cycle. When an exact match was found, these timelines were treated as a uniform set. Rotation of timelines (the same rhythmic sequence with a different starting point) were retained. This resulted in 31 distinct sets, of which 19 were of Pygmy origin and 12 of Bushmen origin (see Table 1). When comparing the structure of timelines, it was useful to represent each timeline in two additional notational forms: as an interval vector and as a binary sequence. Figure 1 shows the various notational forms used.

The first representation in Figure 1 is Western notation and the second is a commonly-used variant of TUBS where an 'x' represents a sounded stroke and a '.' represents non-sounded pulse. These notational forms were useful when comparing my transcriptions with those in the existing literature. The third representation, an interval vector, is popular amongst some musicologists as it shows the lengths between strokes and indicates intervallic structure (e.g. Arom, 1991; Pressing, 1983). Finally, the fourth representation depicts a rhythm as a binary sequence, used in mathematical and computer-orientated studies of musical rhythm, where a '1' represents a sounded stroke (onset) and '0' a non-sounded pulse (rest) 6.

Binary representations were used in this study for the comparison of timelines in conjunction with the well-known edit-distance or Levenshtein-distance algorithm (Levenshtein, 1966). The edit-distance is defined as the minimum number of edits (substitutions, insertions, and deletions) necessary to transform one sequence of symbols to another. Thus, the edit-distance provides a measure of similarity between the binary representations of two rhythms. While there are many algorithms that could be used to measure the distance and similarity between musical objects (Toussaint, 2013, pp. 247-256), the edit-distance shows a high correlation with human similarity judgments in experimental conditions (Post & Toussaint, 2011; Toussaint, Campbell, & Brown, 2011). The edit-distance model was implemented in MATLAB using existing code (Ahmadzadeh, 2012), yielding a distance matrix for every pair of rhythms (Appendix B, available at: http://hdl.handle.net/1811/85870).

Finally, phylogenetic trees were generated from the distance matrix in the program SplitsTree v4.13.1 (Huson & Bryant, 2006) to provide a visual representation of the distance relationships between timelines and to look for possible ancestral rhythms. The tree was generated from the distance matrix using the BioNJ function, an agglomerative algorithm that accepts a distance matrix and uses a first-order model of the variances and covariances to estimate evolutionary distances. It does this by iteratively picking a pair of taxa (rhythms in this case), creating a new node, which represents the cluster of these taxa, and reducing the distance matrix by replacing both taxa by this node (Gascuel, 1997). The BioNJ function was chosen because it has been used successfully in conjunction with the edit-distance model as an effective measure of rhythmic similarity (Toussaint, Campbell, & Brown, 2011; Toussaint, Matthews, Campbell, & Brown, 2012).

The SplitsTree program also calculates the least squares, or LSFit, which provides a measure of the goodness-of-fit between the distance matrix and the tree. This is obtained by dividing the sum of all approximated distances in the splits tree by the sum of the original distances in the data set (Guastavino et al., 2009; Huson, 1998). If the index is very close to 100%, the tree represents the distance matrix faithfully. Lower fit values represent a poorer correspondence between the tree and the distance matrix. The musical materials and results of this analysis are discussed below.

STRUCTURAL SIMILARITY AND DIFFERENCE

This section examines the structural similarities and differences between Pygmy and Bushmen timelines and how these structural properties might be explained by existing models of rhythm. Table 1 shows the 31 distinct sets of timelines used for analysis, ordered by the cultural group: Pygmy and Bushmen. A further sub-group differentiates between timelines that divide the tactus (primary underlying pulse) into three and those that divide the tactus into two or four, typically referred to by scholars as ternary and binary or simple and compound rhythms (London, 2004, p. 18). However, I make use of the alternative terms triple-pulse and quadruple-pulse in Table 1 as it more accurately reflects the transcriptions used here. Whether a timeline was triple or binary/quadruple was determined primarily by listening to performances and noting the subdivision of the pulse suggested by the placement of the strokes. A secondary source, and means of checking my interpretation, was the transcriptions in the accompanying literature. Scholars such as Arom (1991), Kisliuk (1998), and Olivier (2001) helpfully provide numerous transcriptions in books and articles in TUBS or Western notation that indicate the timeline pulse subdivision, as well as the starting point and rotations of rhythms.

Numbers have been added in the first column to differentiate sets of timelines and provide easy reference. The second column shows the name of the cultural groups that performed the music. Following Lewis (2014, p. 221), I use the term 'BaYaka' to represent the west-central African Pygmy groups Mbendjele, Baka, and Aka who occupy the forest west of the Ubangi River in the Central African Republic, Congo and Cameroon. The term 'Mbuti' is used to represent the Kango-Sua, Efe, and Asua groups that occupy the Ituri forest in the north-eastern region of the Democratic Republic of th Congo (Fürniss, 2014, p. 188). The term 'San' is used to encompass the Ju'hoansi, Nharo, and !Kung groups who live in and around the Kalahari desert in Botswana and Namibia (Lee & Daly, 1999). See Figure 2 below for a map of recording locations. The third column is a transcription of timelines over one cycle in TUBS notation and the fourth is an intervallic representation based on transcription. Column five (n) is the number of timelines transcribed from the recordings with totals for each group and column six (p) is the number of pulse per cycle.

Table 1. 31 distinct sets of Pygmy and Bushmen timelines.

	Pygmy triple-pulse
No.	Cultural Group	Rhythm (one cycle)	Interval Vector	n	p
1	BaYaka	x.x.x.xx.x.x	2221221	6	12
2	BaYaka	x.x.xx.x.x.x	2212221	3	12
3	BaYaka	x.x.x.x.x.x.	222222	4	12
4	BaYaka	x.x.x.x.x..x.x.x.x.x.x..	22223222223	1	24
5	BaYaka	x.x.x..x.x.x x.x.x..x.xx.	223221223212	1	24
6	BaYaka	x.x.x..x.x..	22323	4	12
7	BaYaka	x.x..x.x.x..	23223	1	12
8	BaYaka	x.x.x.xx.x..	222123	1	12
9	BaYaka	x.x.x.x.xx..	222213	1	12
10	BaYaka	x.x.x.x.xx.x.x.x.x.x.xx.	2222122222212	9	24
11	BaYaka	x.x.x.x.x.xx.x.x.x.x.xx.	2222212222212	1	24
12	BaYaka	x.x.x.x.x.xx.x.x.x.x.x.x	2222212222221	1	24
13	BaYaka	x.x.x.x.x.x.xx.x.x.x.xx.	2222221222212	8	24
14	BaYaka	x.x.x.xx.x.x.xx.x.x.x.x.	2221222122222	1	24
	quadruple-pulse		Total	42
15	Mbuti	x.x…x…x.x…	24424	1	16
16	BaYaka	x..x..xx..x.x…	331324	2	16
17	BaYaka	x..x..x…x.x…	33424	1	16
18	Mbuti	x…..x…x.x…	6424	1	16
19	BaYaka	x..x..x.xx..x..x..x.xx..x..x..x.	3321333213332	1	32
	Bushmen triple-pulse		Total	6
20	San	x.x.x.x.x.x.	222222	2	12
21	San	x.x…x.x.x.	24222	1	12
22	San	x.x..x…	234	1	9
23	San	x.x…x..	243	1	9
24	San	x.x.x.x..	2223	1	9
25	San	x..x..x.x…	3324	1	12
	quadruple-pulse		Total	7
26	San	x.x…x…x.x…	24424	1	16
27	San	x.x…x.x…….	2428	1	16
28	San	x…..x.….x…	664	2	16
29	San	……x…x…x.	448	1	16
30	San	x…x…..x…x.….	4646	1	20
31	San	x..x..x.	332	1	8
			Total	7

CULTURAL CONTEXT AND RESILIENCE

PHYLOGENETIC ANALYSIS AND ANCESTRAL RHYTHMS

This section discusses the results of computational phylogenetic analysis on the 31 timeline groups in Table 1. Following the distinction shown in Table 1 between rhythms that divide the tactus into three or four, Figure 4a-c shows three rooted phylogenetic trees. Figure 4a shows just quadruple-pulse timelines; Figure 4b shows triple-pulse timelines; and Figure 4c shows quadruple-pulse and triple-pulse timelines together. The resultant phylogenetic trees provides a visual representation of the hierarchical distance between timelines and their cluster relationships. Each node in the tree is labelled with a "BP," "MP," or "B" to identify BaYaka Pygmy, Mbuti Pygmy or Bushmen timelines, followed by a shortened label (to improve readability), then, for example, 'T12' or 'Q16,' (triple-pulse or quadruple-pulse, and the pattern length/number of pulses per cycle) and the assigned number identifier (in brackets) taken from Table 1. BaYaka Pygmy labels are shown in black, Mbuti Pygmy labels are in red, and Bushmen labels are blue.

Figure 4a-c shows that one of the main distinguishing features that has influenced the cluster relationships in the phylogenetic trees is pattern length or number of pulses per cycle. This is most evident in Figures 4b and 4c. In Figure 4b, the cluster that branches off to the left of the tree contains 24-pulse timelines, the centre of the tree contains 12-pulse timelines, and the cluster to the right contains mainly 9-pulse timelines. Similarly, in Figure 4c, longer 32-pulse and 24-pulse timelines feature in the left-hand branch of the tree, 16-pulse timelines occupy the middle of the tree, and shorter 12-pulse and 9-pulse timelines are found towards the root of the tree.

This clustering makes sense because the edit-distance algorithm used to generate the distance matrix would require a greater number of edits to transform, for example, a 12-pulse timeline to a 24-pulse timeline than timelines of the same length. However, before dismissing the edit-distance algorithm as perhaps too general for fine-grained comparative study, it is worth noting that the distances calculated also depend on the placement of strokes within each timeline being compared as well as the pattern length. Future research, therefore, might use phylogenetic analysis to compare timelines of the same length in order to identify the hierarchical relationships between them and to identify common structural features.

The main goal here however is to identify ancestral rhythms. Each of the trees in Figure 4 show a node labelled 'root' at the bottom of the graph, indicating that the most recent common ancestor is unknown and that there is no clear ancestral timeline rhythm.

Population geneticists have also used phylogenetic models to understand our common ancestry and they provide some important insights. Starting in the 1960s with the work of Cavalli-Sforza and his associates, a body of research has been amassed that has furthered the understanding of worldwide biological diversity patterns and human origins and migrations by analysing the structure of human DNA. The most up-to-date model to emerge from this research (Cavalli-Sforza et al., 1994) suggests that "the current peopling of the world results from serial migrations "Out of Africa" over the past 100,000 years. In this model, mankind expanded throughout the world via a series of migrations increasingly distant from the African source, each migration followed by founding events of new populations" (Verdu, 2014, p. 33). In his review of this body of research, Paul Verdu (2014) concludes that, although the findings are still open to debate, there is an ancient common origin between central African Pygmy and non-Pygmy populations dating to around 70,000 years ago and a likely common origin between Eastern and Western Pygmy groups dating to roughly 20,000 years ago (p. 45).

Drawing on the 'Out-of-Africa' model (Cavalli-Sforza et al., 1994; Chen et al., 2000; Oppenheimer, 2012), as well as studies in archaeology, ethnomusicology, anthropology, linguistics, and his work with Alan Lomax on the Cantometric project, Victor Grauer (2011) argues that eastern Pygmy, western Pygmy, and Bushmen cultural practices are derived from a "Hypothetical Baseline Culture," which represents the core values of a common ancestral group (p. 3) 10. The location of this ancestral group is "unknown" but is possibly the "tropical forest or East African savannah" (p. 57). Fascinatingly, the music, Grauer writes, may have survived from the historical 'moment' when these cultural groups diverged somewhere between 70,000 and 100,000 years ago:

Astonishing as it might sound, by listening to a recording of traditional Pygmy or Bushmen music, we are, in a sense, entering a kind of time warp, hearing the sorts of sounds our African ancestors may well have been making anywhere from 70,000 to over 100,000 years ago (p. 2).

Grauer's emphasis, like many Pygmy/Bushmen comparative studies, is the similarities in song/singing style (vocal polyphony, counterpoint, and yodelling) and not timelines. As Grauer acknowledges, there are also alternative hypotheses that could explain the diffusion of musical elements over a geographical area: independent invention (coincidence) and convergent evolution, "based on the assumption that the tradition represents an adaptation of some sort, stemming from some universal property of the human mind" (p. 72). Nonetheless, his theory is an intriguing one that might explain the timeline data presented above.

It is conceivable that foundational rhythms such as the 3:2 pattern featured in the music of a common ancestral group and the timelines in Table 1 are later adaptations that build on and extend this basic structural theme. If the location of this ancestral group was somewhere in east Africa, as some genetic studies suggest (Cavalli-Sforza & Feldman, 2003), perhaps rhythms containing the 3:2 pattern migrated westwards and southwards from this location and were subsequently adapted by Pygmy and Bushmen groups into the timelines seen in Table 1. Pushing the speculation further, perhaps the widely-used "standard patterns" (2212221, 22323, 33424) found in Pygmy music are later adaptations that migrated to other parts of sub-Saharan Africa and then 'out of Africa' through cultural interactions with their non-Pygmy neighbours.

These are interesting issues to explore but extreme caution is required when reconstructing complex cultural practices such as music that may originate far back in the Paleolithic era. The first problem is the huge time spans in question, since solid documentary evidence of the music played by Pygmy and Bushmen dates from only around 70-100 years ago. We know absolutely nothing of the rhythms played by these cultural groups dating from 70,000-100,000 years ago and how and why they may have developed and mutated since then.

A second problem is that the hypothesis outlined here relies heavily on data from genetic research. Therefore, it is built on the notion that there is a strong correlation between biological evolution and ancestry, and cultural (Mace et al., 2005) and musical evolution (Nettl, 2006). This correlation may exist. Brown et al. (2014) examined the statistical correlations between music, language and genes among nine indigenous populations of Taiwan using "traditional group-level folk songs and mitochondrial DNA" (p. 1). They conclude that "the correlation between music and genes was statistically significant" and that "music – particularly polyphonic group singing – might serve as a useful marker to study human migrations and human origins more generally" (p. 4). In a related study, Rzeszutek et al. (2012) argue that "many useful parallels have been drawn between cultural and biological evolution", but add that "the forces shaping cultural diversity can differ markedly from those that drive the structure of genetic diversity" (p. 1611). A similar note of caution is provided by Savage and Brown (2013). They point out that "it is crucial to remember that music evolution does not necessarily mirror the patterns of language, genes, or any other system" (p. 9). The precise relationship between Pygmy/Bushmen biological and musical evolution remains unknown.

A third, related problem is that "the study of ancient DNA has been extremely contentious" (Olson, 2002, p. 80) and that in the equatorial forests of the Congo Basin, where the majority of Pygmy groups have always lived, the soil is acidic and rapidly decays human bones (Cavalli-Sforza et al., 1994, pp. 160, 180). "Even when fossils between 15,000 and 150,000 years old have been found, linking the bones with existing groups has proved difficult" (Olson, 2002, p. 50). As a result, "biological anthropologists are challenged by a tremendous lack of historical and demographic knowledge, even recent, in central Africa" (Verdu, 2014, pp. 34-35).

Clearly, further study is needed to reliably reconstruct the musical practices of sub-Saharan Africa's ancient (and more recent) past. If indeed such a reconstruction is possible, the data presented above indicates that the comparative study of resilient and foundational musical features, such as timelines, has much to offer such an endeavour.

CONCLUSIONS

In this article, I have used theories of African rhythm from ethno/musicology, findings from anthropological research and population genetics, musical analyses based on transcriptions, and computational phylogenetic techniques to compare the intervallic, cyclical, and structural properties of 31 timeline rhythms performed in Pygmy and Bushmen musical cultures. By utilising these different analytical and theoretical perspectives, some interesting similarities and differences have been brought to light.

Despite variations in cycle length and the number and placement of strokes, Pygmy and Bushmen timelines are highly interrelated. The 'rhythmic oddity' model is useful is explaining the structural connections between timelines used by Pygmy groups from the Western-Central Africa; a generative approach highlights how many Pygmy/Bushmen and African and African-derived timelines feature commonly used rhythmic cells, such as the 3:2 pattern that form their structural and aesthetic bases; and the principle of maximal evenness suggests that Pygmy/Bushmen groups show a preference for timelines that are regular and almost regular. Furthermore, these models highlight important relationships between some Pygmy/Bushmen timelines, especially the well-known "standard patterns," and those used in music in other parts of sub-Saharan Africa, the Caribbean, and beyond that could be explored in future studies.

The accompanying ethnographic data suggests that timelines are multi-purpose musical devices used in various different types of events and social contexts both within and across Pygmy and Bushmen cultures. Moreover, the foundational structure of timelines appear to be resilient to radical change, their basic structure remaining unaltered in old and new musical forms and cultural settings.

Phylogenetic analysis of the 31 timelines revealed that pattern length and the number and placement of the strokes are the factors influencing cluster relationships. Phylogenetics also reveal that no clear Pygmy/Bushmen ancestral timeline comes to the fore.

Future research is needed to shed more light on Africa's complex cultural and musical history, and to formulate a more coherent theory of musical evolution and its relationship to biological evolution. The approach used recently by Brown et al. (2014), which examines the coevolutionary relationships between musical, genetic, linguistic, and geographic distances, is an important step forward but could be expanded to include detailed ethnomusicological research on the structure of the foundational rhythmic features that underpin music making in sub-Saharan Africa. Future studies that aim to map and quantify the generative adaptations of rhythms within Pygmy and Bushmen societies over a period of time, and how they may have changed on their journey to places like Cuba would also provide useful insights into the processes that drive musical evolution. I hope that the current study has shown that timelines are a productive resource in the quest to uncover Africa's intriguing musical history, development, and influence.