Dimensions In Rhythm

Harmonic Feel, Part 1

Excerpt from, “The Harmonic Perspective of Rhythm”

Part 1 focuses on a typical Afro-Brazilian 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, ‘back heavy’ or ‘back swung’ quaternary feel. That is, the subdivisions in the second part of the beat are squashed together somewhat. Enough said for now! For Part 2, which looks at Afro-Caribbean feel, go here.

Feel

What about music that works with one primary rhythmic line? In music that does not feature the juxtaposition of separate parts that are (hypothetically) generated from different metric conceptions, does the harmonic perspective of rhythm still apply? One way that it does, according to Toro, falls in the realm of feel. Feel, as the word suggests, seems to be best communicated not by analysis but by exposure and awareness. The literature, starting with Keil, has long suggested that the analytical approach embodied in the process of notating rhythm falls short of producing music with the range of nuance that is demanded from a good performer.

‘Perfection’ is no Ideal

“Music, to be personally involving and socially valuable, must be, ‘out of time’ and ‘out of tune.’” (Charles Keil 2005, 96)

Keil coined the term, “Participatory Discrepancies” to indicate that music played by people, as opposed to the idea of music represented by notation and its implied conceptual framework, is full of ‘discrepancies’, or variations from the notated idea. (Charles Keil 2005, 1995)

The Long and the Short(er) Roads

The usual method to learn to reproduce a particular kind of groove for a particular style or piece of music is rooted in lots exposure and imitation of that music. The downfall of complete reliance on this method is the time required for the comprehension of a particular groove. Writers in both academic and instructional fields have suggested that the way to intellectually grasp grooves that do not neatly line up with standardized subdivisions as represented in musical notation, particularly in African and African diaspora music contexts, is to think of the subdivisions of the beat as somewhere in between binary and ternary. (Hernandez 2000; Billmeier and Keïta 2004; Schepers 2005; Spiro and Ryan 2006; Toro 1995)

This perspective does not offer a precise temporal orientation. It is rather a prescription for the development of an experiential perspective. By learning to alternate between binary and ternary subdivisions while playing, one develops a felt sense of the space between the strict metric interpretations of those subdivisions. In this way, it is supposed that the musician develops and refines a sense of elasticity in music which helps to be able to articulate various ‘in between’ or ‘in the cracks’ feels while never losing a strong sense of the larger metric cycle.

Toro (Percussionist Efrain Toro) goes farther than most, however, in attempting to define the actual metric interactions that produce several exemplary feels, thereby differentiating the approaches allegedly driving those cultures to favour their particular feel, as well as attempting to define a shortcut to get ‘in’ without years of exposure.

There are as many potential feels as there are cultural music traditions or even as many as there are individual exponents of those traditions. Therefore, once again, I will not attempt to produce an exhaustive or statistically significant list but rather deal with two that Toro defines. I will also look at some of the literature that has attempted to measure those feels and see if the two corroborate.

Bridges of Understanding

For Toro, whereas compositional material in rhythmic music emanates mostly from the interaction of two and three at the metric level of beat markers, feel is generated by the interaction of two and three within beats, that is, at the subdivision level. Looking at the harmonic series again, if the metre is generated by two main beats to a cycle, along with three, the feel is established by the way that four and six interact. This is akin to combining, or superimposing the ternary and binary structures discussed in the previous section. In fact, several theorists including Toro suggest that this is indeed close to the real generative perspective, at least in some very elastic feels such as that found in the Cuban Rumba. (Toro 1993a, 1; Hernandez 2000; Peñalosa and Greenwood 2009, 228–29)

Still, there is usually a clear guiding structure; Rumba Columbia feels mostly ternary whereas Rumba Guaguanco mostly binary. However, Polak complains that in his early experience in Mali, finding himself at a loss to understand whether a piece in question was binary or ternary, he resorted on several occasions to transcribing it both ways. (Polak 1998) Although several have suggested it is in between these two that many feels lie, no one else to my knowledge has offered concrete, theoretical prescriptions to generate them. Toro himself admits there is really no way to accurately notate feel, but his methods promise a quicker road to acquisition bridged by understanding.

The Feel of Brazil

Toro considers Brazilian[1] feel to be the product of the interaction of the second two notes of a triplet with the second note of a duplet, or group of two, along with the beat itself. This is simply the two and three sub-divisional groups together, but heard as one line, without unison strikes. This timing, applied to the interpretation of sixteenth notes and with the proper accents, allegedly gives the classic Brazilian feel. The accents come at several different levels, but from the same concept, namely that the offbeat is accented. Toro claims that all ‘ethnic’ music in the world is accented on the offbeat. (Toro 2012d) So, heard in two, the second beat is accented. In a Samba, this would usually be played by the lower Surdo or bass drum. At the level of duplet subdivisions, the second is accented, and at the level of triplet subdivisions, the second is also accented.

Figure 1. Toro’s Brazilian Feel ‘Formula’.

Audio Example 1. Computer Generated Brazilian Feel Formula (CD Track 35).

This could be conceived, of course, as the linear two and three described earlier, counted in three as, ‘one, two and three,’ or in two as, ‘one, (trip), let, two, trip, (let), but at a faster pace than indicated previously; now this happens within each beat, and most certainly must be ‘felt’, not counted.

From a linear point of view, we are replacing this decidedly mechanical interpretation:

with this:

Figures 2 and 3. Sixteenth Substitution from a Linear Perspective.

Commodification Antithetical to Depth?

Conceptually, however, the first interpretation is more potent as it implies, as discussed throughout this thesis, that even a single line, without sequential variations that refer to other metric structures, is nevertheless representative of a harmonic conception of time through this element of feel. This feel then becomes the backdrop against which and from which all the music is interpreted. Toro is insistent that this perspective, whether conceptually informed or not, is key to understanding and performing a given AT/Music, but that this point of view is lost in the marketplace and pedagogy of many performers and institutions. According to Toro:

The sound of the music is not in the pattern (or the instrumentation), it’s in the music (the feel). If you buy books to get patterns of music, you are wasting your money. People talk about independence in music, it’s nuts; the more dependent you are in the music (working within the feel grid), the more you can move around. That’s what you practice (the grid). You don’t practice anything else. Whatever pattern you learn, you can make it sound Brazilian…with that. Don’t look for patterns. Look for the sound. The sound is a composite of many different elements. The composite is more than its elements.” (Toro 2012e)

Quantitative Analysis

But is it possible to prove the validity of Toro’s proposition? I decided to look at the work of Gerischer, as she is the only author I know of who has published work that attempts to quantitatively evaluate feel in Afro-Brazilian music. (Gerischer 2006) She measured timing placements for various instruments in several ensembles and chose to use Jairazbhoy’s ‘Nominal Units of Time’ (NUTs) system to evaluate her results. (Jairazbhoy 1983) This system proposes a measurement system of 100 units, comparable to Ellis’ system of musical cents used to measured pitch. (Ellis 1885) Gerischer applied the 100 unit measurement to each sixteenth note articulation so that, hypothetically, one beat would contain 400 units, one measure 1600 units. The pieces are in notated in 4/4 time using the TUBS (Time Unit Box) system. (Koetting 1970)

For the first piece, a samba da roda performed by a group from São Félix, Bahia, she found the following average timing values:

Table 1. Samba da Roda Average Timing Values. (Gerischer 2006)

By dividing a beat of 400 NUTs into three and then dividing the second of those beats in half, we should get Toro’s predicted, ideal timing values.

Figures 4 and 5. Straight and Harmonic Model Timing, NUTS.

Competing Influences

At first glance, the figures don’t seem to agree with Toro’s model. Looking at Gerischer’s graphs of the data, however, and her interpretation, Toro’s idea starts to hold more weight. She describes the feel as, ‘medium’ (~100), ‘short’ (~80), ‘medium’, and ‘long’ (~120), noting that the especially long timing of the last note was a characteristic feature in all the Bahian Samba music analysed. The theoretical harmonic model predicts long-short-short-long, which can be construed as the same general shape, with longer timings for the first and last subdivisions. The data is close to the standardized 100 NUTs; this is why it is still heard as a binary piece. But it has a shape that corresponds to Toro’s predictive model, as we can see in the following chart.

Figure 6. Samba da Roda Average Timing Values.

The red line represents the mechanical timing indicated by standard notation. Although the lines representing the average timing for the other instruments don’t ever reach the predicted values from the harmonic model, their shape indicates an influence. It is as if each timing paradigm exerts its own sort of gravity on the players and they do their best to compromise. The timing lines point toward the high and low timing values in the harmonic model, while zigzagging around the mechanical sixteenth note line.

Cumulative Values: Position Within the Beat

Also notable in this graphic portrayal is that each instrument crosses the red line very near to the ‘and’ (&) or the middle of the beat, as the harmonic model indicates. This is true for every beat. These are average timing lines, representing length of articulations, not placement within the cycle. Given that the on-beat strikes had values close to 100 and that the first subdivision or ‘e’ strikes were all considerably lower (as predicted by the harmonic model), the middle or ‘and’ strikes would also fall short of the dead-centre 200 NUTs mark. This idea begs an analysis of cumulative timing values, to see where each instrument and each model strikes within the beat, rather than just looking at their lengths. I added Gerischer’s timing values which, as the NUT analysis concept would specify, total approximately 400 for each beat. As with Polak’s study in Mali (Polak 2010), Gerischer notes that the timing of the beats themselves is very consistent, so I will not concern myself with variation at that level, but rather the cumulative timing values within each beat. The data now looks like this.

Table 2. Samba da Roda Cumulative Average Timing Values, per Beat.

The values now start on the ‘e’ and end on the first strike of the next beat, as I felt this was easier to understand and visualize. Now each value indicates the relative position within the beats themselves, so we can see, for example, at a glance that all three instruments played their middle or ‘&’ strokes in the 180-190 NUT range, earlier than the middle of the bar or 200 NUTs, as predicted by the two models. Graphically, the data now looks like this:

Figure 7. Samba da Roda Cumulative Average Timing Values, per Beat.

One Beat at a Time

I will assume from this graph that the relative behaviour for each of the instrument/player combinations is similar through the course of each beat. Here is beat 1 by itself, to get a clearer view.

And again as a bar graph:

Figures 8 and 9. Cumulative Timing, Beat 1.

This perspective has made the original data clearer to me. The second strikes (note the first strike in this cumulative timing analysis is the beginning of the beat, with a timing value of zero, and the beats are assumed to have accurate, that is, even, timing as discussed elsewhere) were about the same as a mechanical sixteenth note, not the triplet timing predicted by Toro’s model, though the triangle and pandeiro notes were slightly longer. The third subdivisions were short in length, as Toro’s model would predict, but the strikes not quite at the middle of the beat as both models predict. The last strokes, however, as shown by their proximity to the green harmonic timing lines in the previous two graphs, are close to the timing of the harmonic model; that is, they are near to being one triplet subdivision’s length from the next beat (or, a cumulative timing value of 267 NUTs). This characteristically elongated note was noted by Gerischer as a consistent feature in all the recordings of music she made in Bahia.

So it seems as if the ‘medium-short-medium long’ timing that Gerischer found in the Samba da Roda as well as other examples she analysed could be construed as: a first subdivision suggesting even, sixteenth notes; a second subdivision shortened considerably, advancing the whole cycle; the third subdivision again about an even sixteenth in length, but striking early in the beat, having been started early because of the previous short note; this leaves the fourth and final strike about as early as the last subdivision of a triplet. The last, characteristically Brazilian accent is close to a triplet, the others close to sixteenths except for the second which is shortened so there is room at the end for that loping, triplet sized feel heading back to the beat. Toro also says he conceives of the standard Brazilian bass pattern for the drum kit as being more like a triplet figure than a sixteenth figure, and compares it to a shuffle, switching between the two without stopping or losing continuity. He says this approach makes is easier to execute technically and sounds more musical. (Toro 2012i)

Brazilian Accents

Toro mentions the accents being key to the feel as well. Perhaps the quick movement from subdivisions two to three, with accents on both, feels like the interaction between the second triplet subdivision and the halfway point, the primary upbeat, or the third sixteenth. Indeed at faster tempos these can have near to a ‘flam’, or ‘crushed’ effect, as if one is falling into the other, thus standing out in the overall sound. Gerischer notates the accents of the Samba da Roda piece on the first and last subdivisions of each beat for the reco reco scraper, as well as a “stressed” slap note on the pandeiro just before beats two and four. These are normally considered the standard accents in the Afro-Brazilian feel, usually played most prominently by the surdo bass drums, or by the bass drum in standard drum set adaptations. Toro also lists many combinations of this bass drum pattern with different high hat and ride cymbal patterns in his book on Latin playing, 2/3 or not 2/3: A Musical Textbook in Latin Style. (Toro 1993a) In a lecture at UKZN, however, he disputed the importance of this point. “A Brazilian bass is not, ‘Badoom, badoom, badoom, badoom.’ Actually, it has nothing to do with that. The idea is of short and long notes.” (Toro 2012e)

Interestingly, though she does not name them as accented, Gerischer notates the triangle rhythm for the Samba da Roda, which plays every subdivision in question, as, ‘damped, open-stroke, open-stroke, damped.’ So, considering the open strokes to have the quality of accentuation within the rhythm, these are the accents Toro prescribes, as well as the same method of accentuation used by the surdo drums to bring out the even numbered main beats (beats two and four in a four-beat metric scheme)—by playing open strokes amongst muffled ones. It seems to me that the Brazilian feel has both accents on subdivisions one and four, and on subdivisions two and three, but played by different timbres. Usually one and four are low instruments like bass drums, or thumb strokes on the pandeiro, and the two and three accents on higher pitched instruments (those with timbres favoring higher frequencies) like triangle, pandeiro jingles, or sticks on the high hats. This argument is not considering timeline patterns that were the main focus of the “Proximate Three” section (page 100) but rather simpler, time-keeping, feel generating patterns such as those mentioned. Gerischer’s other data produced similar results.

Bodies in Motion

Finally, note that each instrument’s average timing values and corresponding lines vary in very similar fashion through the theoretical one bar cycle (in fact they are average values taken from 20 to 30 seconds of recorded material. (Gerischer 2006)) This suggests that the patterns played and the instruments on which they are played affects the timing. Likewise, so would the bodies (and minds) of the people who play them. These ideas indicate Toro’s emphasis on the concept of motion as the cornerstone of his theoretical and practical philosophies. It also harks back to the observations of early ethnomusicologist Erich von Hornbostel, that African music proceeds from motion, as discussed by Blacking (Blacking 1955).

Indeed, closer to the material at hand, Gerischer’s informant Tustão observes:

I think it also generates suingue when you liberate your body. You don’t play only with your hands but with your body. Playing is a form of liberating one’s body. If you do it, you will learn to swing. If you dance, you understand the rhythm. Rhythm is a context thing. When you play, you understand everything around it. It’s a very broad thing, this suingue. If you want to learn Bahian rhythms, you have to go there, walk there, understand the people and then you will learn what you want to learn, because suingue is experience and living (Gerischer 2006, 102).

Toro would also argue that the feel in question is not obtainable by conceptual models; it is something that must be listened to, played and absorbed. To portray two rhythmic ideas simultaneously is at the core of the harmonic concept, but the ambiguity seems to extend beyond the mere execution of two perfectly performed metric references. To refer to many ideas, concepts or archetypes without clear preference for either is a feature of many artistic disciplines, for it is on this liminal ground that perception is freed from a linear, analytic approach, the mind forced to reconcile not with an answer but with simultaneous layers of meaning. In the words of Gerischer’s Brazilian informant Tustão again:

The suingue is the precision of the preciseness, it is a crazy thing, because it’s an oscillation between the almost correct. It doesn’t work exactly correctly; for example, if you use a drum machine it would be hard. The suingue is exactly that oscillation, which is neither wrong nor exactly correct…A percussionist uses false notes or leaves things out to create silences, and works out the form that way. He’s not entirely precise (i.e., metronomic), because everywhere in music there is a lot of personal interpretation, which makes this nuance, such that you feel this small oscillation, that makes you dance, that you don’t stay still. This is called suingue, the swing is this oscillation within a rhythm. (Gerischer 2006, 103)

And from Gerischer herself:

Though the microrhythmic phenomena described here seem to be based on an underlying microrhythmic structure, and seem significantly regular, one should not forget that all the phenomena depicted are tendencies in the time-relations of a performance. There are neither regular exact values, nor exact repetitions of the given periods of time. The articulations vary from cycle to cycle and also between musicians and groups. Musicians, in my conversations with them, repeatedly stressed the abundance of playful variations of familiar patterns, and the importance of distinctive interpretations by individuals and bands within various styles. Though microrhythmic phenomena occur with regularity and seem to be crucial to the rhythmic feeling and drive, they do not have the precision implied in the equidistant time-values of standard notation (Gerischer 2006, 110–11)

When Prescriptions Don’t Work, the Power of Suggestion

Thus Toro’s multi-dimensional perspective regarding Brazilian feel can be seen as a pedagogical crutch, a signpost, or the suggestion of a different paradigm for the understanding of the phenomenon. It does offer a relatively accurate starting point from which to understand and interpret the feel concept. It is not a precise prescription, and, if it were, and if it were popular enough, the music would surely evolve new levels of complexity in response. Perhaps we are only now attempting to analyse these micro-rhythmic phenomena after many generations of such an evolutionary process toward ever greater complexity.

Continue to Part 2…

[1]   Brazil is of course a vast country with a vast musical and cultural landscape. This is a general discussion covering Afro-Brazilian feel.

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