Restoring the Practice of Subdivision

Version 2Imagine you are going to build a deck for your home. We’ve all heard the adage, “measure twice, cut once.” So you take out your measuring tool, and measure out your lumber. But in my example, there’s a catch. Your measuring tool only has feet marked on it. You need a piece cut to 7 feet, 5 1/2 inches. The best you can do is eyeball it, and pretty much guess where that 5 1/2 inch spot is. You mark your board, then to be sure, you measure again. This time when you eyeball the 5 1/2 spot, it is in a slightly different place, so you measure a third time. Again, it is in in a different place, because the best you can do is guess; you have only feet marked on your tool. Meanwhile, you partner is doing the same thing, also with a measuring tool with only feet marked on it. He too gets differing results for the same reason. Eventually, you decide to take the midpoint between the extremes of your different measurements, and go ahead and make that cut. You and your partner continue cutting lumber until the needed number of pieces is done. You go to assemble your deck floor and are dismayed that none of it fits together properly, and that none of the boards are the same length.

This scenario is not unlike how students often perform rhythms in an ensemble. Each child has only a conductor’s beat “marked,” and each student guesses at how divisions of the beat should be played. If a student has learned rhythms solely with rhythm syllables without learning how those syllables relate to a pulse, then they can only guess at where to place those beat divisions as they perform. Every students will do it a little different, and the result when they all sing or play together is that the performance is rhythmically messy and inaccurate.

Every rhythm is a product of durations performed to a pulse. Gordon has called that pulse a macro beat, and others have called it an ictus. Conductors and students alike work very hard to communicate and follow, respectively, that ictus, given by the conductor’s time-beating motion. But “watching the stick” is simply not enough. Those following the conductor must be able to accurately perform what comes between those conductor beats. Noted band conductor Frank Battisti once said that a conductor’s responsibility is what happens on the beat, a players responsibility is what happens between the beat. How do we teach our students to handle that responsibility? The answer is that we must teach them to be keepers of two kinds of beats simultaneously: the macro beat and the micro beat, the latter of which is the first division of the macro beat. In common time, there are usually two micro beats (two eighth notes) for every macro beat (a quarter note). In so-called compound meters such as six-eight, there are usually three micro beats (three eighth notes) for every macro beat (a dotted quarter note). As students “watch the stick,” they must also be audiating even eighth notes (micro beats) in order to play what comes between the beats accurately.

It has been my observation that conductors do not bring this up until a difficult rhythm is encountered. Only then will they tell their students that they must “subdivide” in order to play accurately. While this is a sound remediation, the fact is that subdivision should be going on all the time. It is part of fully understanding and perceiving any piece of music. It helps groups of musicians play quarter notes together as surely as it helps them play intricate divisions of the beat. What’s more, it doesn’t require much teaching or practice to be able to subdivide. All a conductor needs to do when he or she hears the rhythmic stability start to falter is to begin conducting or tapping out the subdivision, and usually the accuracy will snap into much greater precision. The ability to subdivide, or to audiate micro beats is innate. It is drawn from how the various durations in music are naturally organized by our brains into patterns that are subdivided. Our job as music educators is to give our students as much experience with a variety of rhythms as possible.

Earlier, I mentioned the importance of associating rhythm syllables to a pulse. Rhythm syllables that are merely recited phonetically without regard to an ongoing pulse will not bring about effective rhythmic learning. Simply calling a pair of eighth notes ti-ti in the absence of an audiated ta will not transfer to music literacy. Similarly, trying to explain rhythm by telling students something to the effect that eighth notes or ti-ti’s go twice as fast as quarter notes or ta’s leaves the questions of how fast is twice as fast, and twice as fast as what, unanswered. With the syllables ti-ti, the first ti is the macro beat, and both together are the micro beat. One must hear the first ti in each pair as the ictus, and the second as what is going on between the beats, placed exactly even between the preceding ti and the following one. This is why I prefer syllables that differentiate between notes that are macro beats and those that are not. It helps the student maintain an understanding of what he or she is doing throughout. In Gordon’s system, for example, instead of ti-ti, there is du-de. Du is always the macro beat, and du-de is always the micro beat. Students know that no matter if there is an eighth note following the ictus or not, that ictus is always du and the eighth note that follows is always de; two different sounds for two different rhythmic functions.  (For a further explanation of rhythm syllable systems, see my articles on the subject elsewhere in this blog.)

With “what happens between the beats” firmly in the mind’s eye, students will quickly become more accurate in their rhythm performance. Subdivision should be a constant and ongoing operation for all musicians, not just an occasional remedial strategy. Subdividing while listening to music also enhances enjoyment and understanding, because the rhythmic structure of the music to which students are listening is revealed to them through the accurate realization of duration to beat relationships, and resulting patterns of strong and weak beats which constitute meter. Subdividing fosters greater musical success and enjoyment.

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