Dimensions In Rhythm

Adding Metric Multi-Dimensionality to Your Perception, Concept and Playing (Not Just for Drummers!)

Excerpt from, “The Harmonic Perspective of Rhythm.”

Harmonic Rhythm: Toro’s Approach

For the development of an experiential perspective to go along with these concepts, I will now look at the core of (Percussionist and Theorist Efrain) Toro’s method. Broadly speaking, Toro approaches the development of single player multi-dimensionality from at least two perspectives: one in his first instructional book, For Your Hands Only, and another in his treatise on odd metres, The Odd in You. For Your Hands Only is about hand technique but concentrates throughout on the development of independent[1] motions between the two hands (or any other combination of limbs or digits to which one may wish to apply it). That approach is covered in more detail in the section, “Linear Modalities” (page 153, or here on this blog: Part 1. Part 2. Part 3).

The concepts reviewed above and the discussion of a harmonic conception of rhythm relate more to the approach taken by The Odd in You. This is the approach in mind in the following discussion. In order to create an experience of the harmonic series in the rhythmic realm of frequency, a musician would practice hearing and playing these frequencies on their lap, on a table, or on an instrument of choice. First, a long one; then, in the same space of time, one would play and/or say, ‘one, two,’ for as many repetitions as it takes to be thoroughly comfortable (perhaps even on the edge of boredom, or when the mind starts to wander but the rhythm does not), then, ‘one, two, three,’ and so on. It would be a good idea to keep the one with the feet and also an external timing device, depending on the practitioner’s experience with keeping steady time.

This is preliminary practice and should be mastered first. However, the idea is not to only hear these separate metres in sequence, but simultaneously. The first exercise in The Odd in You is to keep two and three with the feet and play the other metres, one to nine, with the hands. As suggested in the previous paragraph, this is a goal that needs to be broken down into a number of intermediate steps according to one’s experience, enthusiasm and aptitude. For example, two and three can be played with the hands for a good while first. Many musicians know how to do this already, and a bit of practice while concentrating alternately on each metre, counting each out loud, etc., may be all that is needed. Even in such a case, however, a short discussion of the relationship between these two and about linear versus harmonic conceptions of that relationship is in order.

Two and Three: The Foundation

Two and three have a unique relationship that can be easily derived and worked with in a linear way. The easiest approach is to count in three, as this way the second articulation of the two metre occurs with the upbeat/offbeat/’and’ of beat twoin the three metre.

Figure 1. Two from Three.

Audio Example 1. Two from Three (CD Track 11).

Thus, we say, ‘One, two and three…’ Some people find a mnemonic phrase helpful such as, ‘Pass the butter,’ or ‘Red beans and rice.’ Indeed these devices, though less than rhythmically explicit, can be helpful to jog the memory concerning the ‘melody,’ or rhythmic interplay between the two parts, especially in more difficult relationships when counting becomes tedious.

A second approach is to count in two; in this case each beat must be divided into triplets, and the relationship to the beat is thus a bit more complex, landing on each of the triplet partials in leapfrog fashion instead of on a downbeat or upbeat.

Figure 2. Three from Two.

Audio Example 2. Three from Two (CD Track 12).

Here we would count, ‘One, -, let, two, trip, -,’ maintaining of course the spaces for the missing syllables. Alternatively, we could rather count all and accent or tap those syllables. Though more involved than the previous approach counted in three, still it is not extremely difficult to grasp with a bit of practice. The reader will note that I previously dismissed this approach as overly complex, but it does have its place. Thinking linearly and deriving the polymetric relationship of two and three is a very helpful way to get started with this mode of dual metric perception, but as suggested in the hands-on instructions above, the goal is to move past hearing two metres as components of the same line, and hearing them as two co-existing lines, occupying the same temporal space (i.e., they are the same length). As we shall see later, Toro’s method makes use of the aforementioned linear relationship—the dotted note—as a cornerstone for the development of rhythmic perspective.

Two and three are near the foundation of the harmonic perspective of rhythm (or, as in Figure 2 from The Harmonic Perspective of Rhythm Revisited, at the top); in addition, their relationship is uniquely simple, as it requires the beat to be divided only in half. Other metric relationships are more complicated, with finer divisions. It is a bit like cutting a cake into threes: It is do-able, but what about fives? We do not usually do that (not very accurately), or, we use another measuring stick. Have you ever seen an evenly sliced pizza in any number but eight? What is more, this example is out of time and visual. Music is not. We can take our time to slice our pizza or tart into seven equal pieces if we want to. Notation can make rhythm, including complex relationships, more visual, and that can be helpful; but if we get into five with seven or even five with three, the notation will not tell us how the two rhythms sound together without some quick and complex calculations, as previously described. And, though the notation can provide a helpful visual approximation of the relationships involved, it must first be prepared, preferably with a ruler and calculator to spatially represent the correct ratios, or with the aid of computerized score writing software.

But, we can count to five or seven, and conceive of them aurally. We then make the articulations even—that is, we entrain them as a constant stream—but filling the space of one. This may take a few tries, but it is much easier than the counting and simultaneous re-grouping of subdivisions. In this way, we use an internal measuring stick (entrainment to a metre (London 2004)) that the body/mind system is adept at, much more so than the counting and regrouping exercise. But, to be able to let two or more metres happen in the body at the same time, familiarity with the preceding and following two and three exercises is essential.

The Building: Adding a Third Metric Reference

To continue outlining the first exercise in The Odd in You, we would next play the two and three with our feet, then add the two with the hands together and then separated (one hand playing count one, the other count two). Next the hands switch to the three, i.e., they play with the other foot. From here it gets a bit more difficult, as the hands play four (double the two), six (double the three) and, with only the one and its offbeat for reference, five and seven. Eight and nine tend to come easier, as they can be derived and felt as multiples of what is being played by the feet. To manipulate the whole sequence might take several weeks or months of practice but with some work it is achievable. Playing through these different time values in an unbroken sequence produces in me a feeling of open, multi-dimensionality; each change creates a feeling akin to that triggered by a psychologically abrupt change of scene in a movie, an abrupt change of key in music, or perhaps, the change from sleeping to waking consciousness and back again. The hands on two and then three with the feet present mild coordination challenges but from four up the challenge becomes perceptual and dimensional.

Audio Example 3. The Odd in You, First Exercise (CD Track 13).

Below is part of a conversation I had with Toro which sheds some light on the powerful feelings alluded to above when hearing and playing multiple metric references and/or switching from one rhythmic perspective to another. Here we were dealing with superimposition of the dotted note, and comparing the feeling to that generated by spiritual transcendence:

And you give yourself. And that becomes a religious experience. And that’s why the act of being in rhythm becomes a religious experience. You see? You just described what a religious experience is. It’s the act of letting go to rhythm. And it takes you…and you’re lost…because there’s no…now. There’s just this…or, you could say there is this now, that is carrying you, every second. But you have no control. And so, what I do is both. I start playing…I just had a religious experience. I’m doing this (hip hop groove) …I go (dotted note)…I’m in! I’m there… (still on dotted note, looks at hi hat with old tempo, plays more, then goes back to it). You see? I’m in two different worlds. And I go to that, and all of the sudden, this (ride cymbal with new, dotted, tempo) …seems to be in slow motion. And I…now I hear this (hi hat) …and this is a triplet. A clear triplet. And the whole gravity changes. See? The gravity’s different. You’re there (waves toward ride cymbal side), you’re connected. You’re in a different world. But consciously! And this is better than being unconscious. And this is my point. That’s my educational point. How to be connected to this heavy stuff…how to connect…and yet be…conscious of it. The Hindus have this stuff. But someone else has to keep time. Here, you’re keeping time yourself. (Toro 2012l)

Harmonic Rhythm in Practice: A Few Examples

Thus two and three, played together, are accessible both linearly and harmonically; they form the foundation and introduction to the harmonic pyramid, and to the development of harmonic perception. Perhaps this is why the two/three complex can be found at the base of AT/Musics the world over (Toro 1995). As partial proof of the veracity of this rather bold statement, we can turn to the literature supporting this point of view vis-a-vis the African repertoire.

In a recent article for Music Theory Online, James Burns presents six rhythmic archetypes and presents numerous examples from Africa and its Diaspora (Zimbabwe, Haiti, Cuba, Ghana, Benin, Congo, Mande Djembe and Bala) for each one, showing how it is used in the pieces in question. He concludes that his presentation, “forcefully demonstrates the presence of a deep-structural grammar, which can generate countless surface variations wherever Africans get together to make music.” (Burns 2010, 89) All of his archetypes but two (one using all the offbeats, or ‘UPS’, as he calls them, and the other creating uneven phrases stressing three out of four main beats) are direct manifestations of the three and two harmonic combination at various levels of the beat hierarchy. All are in a primarily ternary feel. Novotney makes a strong case that the three and two relationship is the generative foundation of West African ternary timelines. (Novotney 1998) Peñalosa argues, in a fashion similar to the reasoning presented in this thesis, that this three and two foundation extends to binary pieces as well, by means of a quantized three. (Peñalosa and Greenwood 2009)

Kubik gives six general concepts he applies to all African music, the first three are:

Concept 1—The overall presence of a mental background pulsation consisting of equal spaced pulse units elapsing ad infinitum and often at enormous speed[2]. These so called elementary pulses…function as a basic orientation screen. They are two or three times faster than the beat, or gross pulse, which is the next level of reference.

Concept 2—Musical form is organized so that patterns and themes cover recurring entities of a regular number of these elementary pulses, usually 8, 12, 16, 24, or their multiples, more rarely 9, 18, or 27 units. These are the so called cycles and the numbers we call form or cycle numbers.

Concept 3—Many of the form or cycle numbers can be divided or split in more than one way, thus allowing for the simultaneous combination of contradictory metrical units. For example, the number 12 which is the most important form number in African music, can be divided by 2, 3, 4, and 6. (Kubik 2010, 42)

Thus, he is outlining the conditions—primarily in a ternary base of 12 pulsations—through which ‘contradictory metrical units’ are derived. To the above can be added the previously cited observations of Chernoff and Jones as to the consistent multi-dimensional nature of African music, based in twos and threes.

It should be now fairly clear that this two and three foundational principle is indeed operating in at least a wide range of African Diaspora repertoire. Bold, all-inclusive statements, i.e., that all ethnic music is based on a simultaneous two:three foundation, would be difficult to maintain with scholarly rigour; it is left to the reader in his or her own experience to make or refrain from such judgements. However, to further assist the development of this perceptually and experientially based point of view, we must consider two other rhythmic structures: Binary metres and linear repertoire such as one finds in Indian rhythmic practice.

[1]   Some musicians, including Toro, think this term is misleading, preferring others such as interdependence.

[2]   Polak and Gerischer, however, among others, argue that these pulse units are not always equally spaced. This subject will be taken up in the discussion of rhythmic ‘feel’. (Polak 2010; Gerischer 2006)

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