Dimensions In Rhythm

Harmonic Feel, Part 2

Excerpt from, “The Harmonic Perspective of Rhythm”

Part 2 focuses on a typical Afro-Caribbean feel. Stay tuned for a post I hope to write soon about various feels typical of Mandeng Jembe music. That post may or may not disagree with some of what is said in this one! Until then, the feel described herein could be labeled a, ‘front heavy’ or ‘front swung’ quaternary feel. That is, the subdivisions in the first part of the beat are squashed together somewhat. For Part 1, with an intro and discussion of Afro-Brazilian feel, go here.

Afro-Caribbean Feel

(Efrain) Toro’s concept of Afro-Caribbean feel—that of the folkloric music of Cuba and Puerto Rico especially—is likewise based on the interaction of binary and ternary subdivisions In this case, however, he says that it is interaction of the first two triplet partials with the offbeat sixteenth notes that describes the characteristic feel:

Figure 1. Toro’s Afro-Caribbean Feel Formula.

Audio Example 1. Computer Generated Afro-Caribbean Feel Formula (CD Track 36).

To Cuba…Almost

In order to test this model, I first turned the work of Olavo Alén, (Alén 1995) who did timing measurements on Tumba Francesa rhythms in the regions of Santiago de Cuba and Guantanamo in the Eastern part of Cuba. However, as he did not include his raw data in the published paper, and since he worked primarily in rhythms conceptualized in a ternary metre[1], I decided to produce data of my own. I used the introduction of a recording of Los Muñequitos de Matanzas, called “Oyelo de Nuevo.” (Los Muñequitos de Matanzas 1994) My reasons for this are the following: 1) When talking of Afro-Caribbean feel (Toro’s preferred terminology, though many would say Afro-Cuban), the music of Cuba has been at the heart of that broadly inclusive traditional landscape, both historically, and stylistically; 2) the Cuban Rumba is widely considered one of the most influential genres in Afro-Caribbean folkloric music and popular music; 3) the Rumba is characterized as having an ‘in the cracks’ feel; (Hernandez 2000; Toro 1993a; Peñalosa and Greenwood 2009; Goines and Ameen 1993) 4) Los Muñequitos has been one of the premier recording Rumba groups since their debut in 1956; 4) the beginning of a Rumba often includes the three conga (in Spanish, tumbadora) players demonstrating the sixteenth note feel in unison with a rocking, ‘heel-toe’ motion of the hands; this introduction is not obligatory but seems to be a call to group acknowledgement of the underlying feel before the separation into the several parts that fit together rhythmically to create, with vocals and other small percussion instruments, the overall Rumba sound. Such is the case with the beginning of “Oyelo de Nuevo[2].” This rocking sixteenth motion is reminiscent of the way Toro showed the feel to me, as well as my own experiences with folkloric Rumba from the early 1990s onward; it is the basis of the segundo, or middle drum, accompaniment in the Matanzas style.

As Cuban Rumba was not the primary focus of this study, it was not feasible to travel to Cuba or some other location where an ‘authentic’ Rumba group could be found. Such a recording would make for a larger data sample, more easily processed through multi-track recordings, with different input from each instrument. Nevertheless, I was able to gather timing data on the basic feel as indicated by the players in their introduction. It should be clear from the aforementioned discussions that it is not my objective to ‘prove’ Toro’s theory about feel, for the theory itself is built on the a priori assumption that human musical activity is by its very nature not in conformance to certain quantitative parameters; it is, in Toro’s view, imperfect, like nature. (“But nature doesn’t happen by subdivision.” (Toro 2012j)) My intention here is to evaluate his archetypal model in light of some sample material to see what observations this process might generate.

Data Collection and Analysis

I imported the recording into the Pro Tools platform, and, using a combination of listening, knowledge of the music, and visual waveform data, put markers at each subdivision as articulated in the introductory section described above. I then exported the timing data, with the marker names (Clave 2, Beat 1.2, etc.) and put it into a spreadsheet where I calculated subdivision and cumulative timings as with the Brazilian data. I chose to work this time in percentages, rather than NUTs, similar to approach taken by Polak. (Polak 2010) In this way, the articulations can be compared as percentages of the total beat, both for individual subdivision length or cumulative position within the beat, rather than fractions of 400 NUTs. The data remained in millisecond accuracy, up to the calculations of percentages.

The length of the extract was about 10 seconds, or about five clave cycles, until the entrance of the voices and separate drum parts would make determination of individual subdivision strikes impossible.

As with the Brazilian data, I found that the Afro-Caribbean harmonic timing model seemed to offer the right shape, but with extremes of timing variation that act more like points of gravity, competing with the gravity of even sixteenth timing.

Figure 2. Los Muñequitos Intro Marcha, Average Timing.

I think it is reasonable to assume that even sixteenth timing is the conceptual model offering the backdrop from which the performers operate, but that it is warped by the ternary pull. This is likely a result of the performers’ experience with more clearly ternary-based music, whether the influence is motional, aural, or a combination of the two. Much Afro-Cuban folkloric music, both sacred and secular, operates from a primarily ternary feel, as do its West African root styles. Although not usually cited as a direct root of Cuban music, of the Mandeng jembe rhythms discussed earlier, in Keïta’s and Billmeier’s choice of 62 rhythms 61% were presented and transcribed in a ternary feel. In my personal experience with Congolese folkloric, and Yoruba Dundun drumming, both cited as primary influences on the music of Cuba, (Malabe and Weiner 1990; Hernandez 2000; Peñalosa and Greenwood 2009; Mauleón 2011) there was also an approximately even split between binary and ternary feels.

Similar in Conception, Slightly Different in Execution

But are these just wobbles in the accuracy of the timing or do they confirm the influence of the harmonic conception according to Toro’s model? Other research of this sort indicates that, although there are clear individual and stylistic differences, the patterns of variation from the mechanical norm demonstrated regularity and by extension, intentionality. (Polak 2010; Gerischer 2006; Alén 1995; Benadon 2006; Bengston 1977) Likewise the data presented in this study has also shown each beat to have similar patterns of variability about the mid-line representing mechanical or metronomic timing. As for the relevance of Toro’s models, I decided to compare the two to decide if there appears to be a better fit between each model and the data from its relevant culture area.

Figure 3. Harmonic Models and Empirical Data.

Although difficult to take in at first, by looking at the lines in pairs—red and green, yellow and puce—it is clear that the data and the models match in relative shape. That is, the highs and lows occur in nearly the same positions on the horizontal axis. Interestingly, the data lines—Los Munequitos and pandeiro (green and puce)—also match quite well; better, in fact than either does with its relevant model. Each shows short durations on the second subdivision (‘e’), as do both models, and longer durations for the last subdivision (‘a’), as does the Brazilian model. They differ, however, for durations of the first, and especially the third (‘&’). This third position is where the models are also farthest apart in their predictions, well above and below the middle line. Examining them once again, it appears that indeed the Afro-Caribbean model has a very long middle subdivision, more than 33%[3], a whole triplet partial, and the Brazilian model, conversely, a very short one:

Figures 4 and 5. Afro-Caribbean and Afro-Brazilian Harmonic Models Reference.

Looking at the cumulative timing values, as before, we see a similar trend:

Figure 6. Cumulative Average Timing Values Comparison.

Here, from another perspective, it can be seen that the data lines—green and puce—are similar in form but that where separate, each is nearer to its respective model—green near red and puce near yellow. Also, both data lines peak considerably below the 75% mark; each one has a short subdivision earlier in the beat which pulls everything back and leaves a gap at the end which manifests as a long, near triplet last subdivision. Looking at figure 7.70 again and comparing to the middle, mechanical timing line, we see that both sets of data have near sixteenth note first subdivisions, relatively short second subdivisions, as both models predict, relatively long and short third subdivisions for the Afro-Caribbean and Brazilian lines, respectively, as the models predict, and relatively long last subdivisions for both, as one of the models predicts. Though the Afro-Caribbean model predicts even timing for the last subdivision and the data showed they were longer, the Brazilian data showed still longer final subdivisions—more toward its model.

The Ears Have It

What all this means to me is that Toro’s ears and his intuition are relatively correct. The data sets are too small to make grand pronouncements about the nature of these two rhythmic feels, from these two large culture areas. Likewise, the variability is such that I have avoided statistically powerful terminology like ‘correlation’, and ‘degrees of certainty’. In fact, Toro’s conception is so broad, and flexible, it is hard or impossible to evaluate ‘scientifically’. However, I still find it significant because we are concerned not with exactness but with perspective. When approaching a new or ‘slippery’ feel then, these two models, or others developed by other theorists and/or performers for other feels, can indeed offer a foothold or a foundation from which to explore the more particular nuances. This ‘nuance level’ of comprehension will always be grasped by the finer capacity of the senses (or the computer, through recording and data analysis).

From this framework will our understanding be richer? Our potential more? Although a basic poly-metric grid will never approach the detailed interpretation possible to a sensitive aural specialist (as we all are, to some degree), conceptual engagement might also help and encourage us to preserve what might otherwise be lost in a world increasingly predominated by a linear aesthetic.

The sound of music is unique to that culture and it is perceived in the 4 and 6 frequencies because 2 and 3 are too big. Here is where all the cultures make their own sound. For practical purposes the space between 4 and 6, how close or how loose they are played in the specific style of music, defines its sound.

Ethnic musicians don’t know what they are doing. They do it because they grew up doing it but they don’t have a point of view about what they are doing.

If you don’t know what you do then you can only play the patterns you’ve learned!

This is the way we all learned things and once in a while there is (a) Picasso, Einstein, Feynman, Debussy but one in a million… because they know what’s happening they can play around with it. (Toro 2011b)

Click here for Part 1

[1]   The formula in question applies to a binary feel, but others have shown various ternary feels to also be non-isochronous. (Polak 2010; Alén 1995; Benadon 2006; Bengston 1977)

[2]   This approach is similar to that of Polak, who, working with Jembe players in Mali, used the ‘echauffement‘ (‘heating up’) section of the soloists’ performances to gather and hypothesize about timing data. This section likewise consists of all main beats and subdivisions played throughout several iterations of the metric cycle. (Polak 2010)

[3]   In fact it is 42%, the difference between the 33% of the second triplet subdivision and 75% of the last sixteenth.

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