Distant Beat

As I write this I am on the (inner) window ledge of my office at RPI, overlooking downtown Troy and the Hudson River. I’m on the fifth floor (of the city side of the building), with a steep, sloping hill at the bottom, so everything I hear is either fairly far away, or very far away. Because of my extreme distance from nearly everything, I end up hearing only a small sample of the sounds occurring in the city. Mainly, I hear the very energetic events. If a sound were not very energetic, then it would be inaudible by the time the sound waves reached me. I can see a tractor dumping rocks, but I hear only the boom of a particularly large one, missing out on the sounds of the many smaller rock hits I can see but cannot hear. Generally, when something makes complex sounds, whether it is a car, a washing machine, or a tornado, some of the noises composing the whole are more energetic than others. If it is far away from you, then you will only hear the most energetic parts of the sound. But if you are close, you’ll be able to hear the full panoply of sounds.

As with most complex sound makers, human movers make sounds of varying energy and frequency. The most energetic sounds tend to be our footsteps. Accordingly, the first thing we hear when someone is approaching from afar tends to be their footsteps. The other gait‑related sounds from clanging limbs are difficult to hear when far away, but they get progressively more audible as the mover nears us. That is, as a mover gets closer to us and the loudness of his gait sounds thereby rises, the number of audible gait sounds per footstep tends to increase.

If music has culturally evolved to sound like human movement, then we accordingly expect that the louder parts of songs should have more notes per beat (i.e., more fictional gangly bangs per step). Do they? Do fortissimo passages have greater note density than pianissimo ? Caitlin Morris, as an undergraduate at RPI, set out to test this among scores in An Anthology of Piano Mu sic, Vol. II: The Classical Period , by Denes Agay (New York: Music Sales America, 1992), and found that this is indeed the case. Figure 43 shows how the density of notes (the number of notes per beat) varies with loudness over 60 classical pieces. One can see that note density increases with loudness, as predicted. Music doesn’t have to be like this. Music could pack more notes in per beat in soft parts, and have only on‑the‑beat notes for the loud parts. Music has this louder‑is‑denser characteristic because, I submit, that’s a fundamental ecological regularity our auditory systems have evolved to expect for human (and any) movers.

This result is, by the way, counter to what one might expect if loudness were due not to spatial proximity but to the energy level (or “stompiness,” as we discussed in the Chapter 4 section titled “Nearness versus Stompiness”) of the mover. Louder stomps typically require longer gaps between each stomp. “Tap, tap, tap, tap, tap” versus “BANG! . . . . . . . . BANG!”

Now that we have expanded on rhythm, we will move on to further evidence that melodic contour acts as Doppler pitch.

Figure 43 . Data from 60 pieces in Denes Agay’s An Anthology of Piano Music, Vol. II: The Classical Period showing that louder portions of music tend to be packed with more notes. Each of 234 contiguous segments of constant loudness were sampled, counting the total number of notes and beats; averages are over these 234 segments. Data collected and analyzed by Caitlin Morris. (Standard errors shown.)