As a child (and like most children, I imagine) I used to think conducting an orchestra entailed something like what Bugs Bunny does in this video:
Waving the hands, as conductors frequently do, seemed largely for show. The conductor appeared to me to be more dancing along with the music than actually leading the musicians in any meaningful way. It wasn’t until I married an amateur musician that I actually learned that the conductor could have an important influence on the way an orchestra sounds. But as Greta and I moved from place to place and she joined a variety of different ensembles, I got to hear her explain why some conductors were better than others.
One of the most basic functions of the conductor, I learned, was simply keeping the whole orchestra coordinated, so that all the different musicians started and stopped playing at the right times. One key to this was to express the beat of the music through the movement of the conductor’s baton (or hands). Musicians could then count the number of beats when they were silent (which might number in the hundreds), and begin playing at the right time. Different songs have different rhythms, and so the conductor uses different movements to express the beat depending on the rhythm. This chart shows some of the simpler patterns a conductor might use:
Good conductors, Greta told me, use something pretty close to these patterns, so it’s easy for musicians to follow and start playing at the right time. Bad conductors (often described in more colorful terms than this) are more like Bugs Bunny in the video — so concerned with the “emotions” of the piece that they neglect the basics.
But what exactly are musicians paying attention to as they try to follow a conductor? What is it about the conductor’s motion that makes it easier or more difficult to follow? As you can see from even this simple diagram (or this series of videos), even the basic rhythms aren’t always easy to follow. To make things even more confusing, many conductor’s manuals suggest that the beat is indicated when the conductor’s motion changes direction, while the hand is moving at the highest speed. But simple physics would suggest that a direction-change is accompanied by low speed. The only way to reconcile these two notions is if a conductor’s motion actually traces a wide loop, so that it doesn’t have to change speed as it changes direction.
Geoff Luck and John Sloboda taped a conductor performing the simplest pattern — the one-beat — with a tracking device on his finger (this conductor did not use a baton). They asked him to conduct in three different ways, with progressively wider-radius loops at the bottom of the movement where the beat is supposed to be indicated.
They showed a point-light representation of these movements to volunteers (some musicians, some not), who were supposed to press a button in time with the beat indicated by the conductor. The viewers had some time to practice before the real study began, but they weren’t given a lot of instruction on where the beat was supposed to occur in the conductor’s movement.
So what characteristics of the conductor’s movement matched up with the beats indicated by the viewers? Perhaps what’s most interesting is what didn’t match up: the radius of curvature of the movement. The width of the arc of the conductor’s movement had no impact on the perceived beats. What did have an impact was the velocity and acceleration along the motion trajectory of the conductor’s hand: both were significantly correlated with the viewer’s perception of a beat. Viewers tended to indicate a beat when the conductor’s velocity was high, but acceleration was negative (i.e. slowing down).
So if velocity and acceleration are all that matters, then perhaps simply showing viewers this motion, without any curves, will also produce the same beat. In a second experiment, Luck and Sloboda did just that: the conductor’s velocity and acceleration were replicated along a horizontal line, as if the curve of the hand movement was simply stretched out across the computer display. Now were viewers able to pick up the beat indicated by the conductor? Yes, to a certain extent. Velocity and acceleration were both associated with the beats perceived by views. However, viewers did tend to feel that two beats were produced with the conductor’s motions, instead of the intended single beat.
Finally, the conductor’s motions were shown along the original paths, but with constant speed and acceleration. Once again, the radius of the conductor’s motions had no impact on the perceived beat. So it appears that the velocity and acceleration of the conductor’s motions are the key factors viewers use to decide when the beat should be.
The researchers say that acceleration is the more important of the two factors — that beats are indicated when the conductor is slowing down or speeding up. But they also point out that other aspects of motion were not studied, and that in other, more complex conducting motions, different factors might be involved.
Geoff Luck, John Sloboda (2008). Exploring the Spatio-Temporal Properties of Simple Conducting Gestures using a Synchronization Task Music Perception, 25 (3), 225-239 DOI: 10.1525/mp.2008.25.3.225