Why Pitch Seems Spatial

Something is falling from the sky! Quick, what sound is it making? You won’t be alone if you feel that the appropriate sound is one with a falling pitch (possibly also with a crescendoing loudness). That’s the sound cartoons use to depict objects falling from overhead. But is that the sound falling objects really make, or might it be just a myth?

No, it’s not a myth. It’s true. If a falling object above you is making audible sounds at all (either intrinsically or due to air resistance), then its pitch will be falling as it physically falls for the same reason passing trains have falling pitch: falling objects (unless headed directly toward the top of your head) are passing you, and so the Doppler effect takes place, like when a train passes you. Falling objects happen to be passing you in a vertical direction rather than along the ground like a train, but that makes no difference to the Doppler effect. Because falling objects have falling pitch, we end up associating greater height with greater pitch. That’s why, despite greater sound frequencies not being “higher” in any real sense, it feels natural to call greater frequencies “higher.” Pitch and physical height are, then, truly associated with one another in the world.

But the association between pitch and physical height is a misleading association, not indicative of an underlying natural regularity. To understand why it is misleading, let’s now imagine, instead, that an object resting on the ground in front of you suddenly launches upward into the sky. How does its pitch change? If it really were a natural regularity that higher in the sky associates with higher pitch, then pitch should rise as the object rises. But that is not what happens. The Doppler effect ensures that its pitch actually falls as it rises into the sky. To understand why, consider the passing train again, and ask what happens to its pitch once it has already reached its nearest point to you and is beginning to move away. At this point, the train’s pitch has already decreased from its maximum, when it was far away and approaching you, to an intermediate value, and it will continue to decrease in pitch as it moves away from you. The pitch “falls” or “drops,” as we say, because the train is directing itself more and more away from you as it continues straight, and so the waves reaching your ears are more and more spread out in space, and thus lower in frequency. (In the upcoming section, we will discuss the Doppler effect in more detail.) An object leaping upward toward the sky from the ground is, then, in the same situation as the train that has just reached its nearest point to you and is beginning to go away. The pitch therefore drops for the upward‑launching object. If rocket launches were to be our most common experience with height and pitch, then one would come to associate greater physical height with lower pitch, contrary to the association people have now. But because of gravity, objects don’t tend to launch upward (at least they didn’t for most of our evolutionary history), and so the association between physical height and low pitch doesn’t take hold. Objects do fall, however (and it is an especially dangerous scenario to boot), and so the association between physical height and “high” pitch wins. Thus, greater height only associates with “higher” pitch because of the gravitational asymmetry; the fundamental reason for the pitch falling as the object falls is the Doppler effect, not physical height at all. Pitch falls for falling objects because the falling object is rushing by the listener, something that occurs also as the train comes close and then passes.

Falling objects are not the only reason we’re biased toward a spatial interpretation of pitch (i.e., an interpretation that pitch encodes spatial position or distance). Our music technology–our instruments and musical notation system–accentuates the bias. On most instruments, to change pitch requires changing the position in space of one’s hands or fingers, whether horizontally over the keys of a piano, along the neck of a violin, or down the length of a clarinet. And our Western musical notation system codes for pitch using the vertical spatial dimension on the staff–and, consistent with the gravitational asymmetry we just discussed, greater frequencies are higher on the page. The spatial modulations for pitch in instrument design and musical notation are very useful for performing and reading music, but they further bang us over the head with the idea that pitch has a spatial interpretation.

There is yet another reason why people are prone to give a spatial interpretation to melody’s “rising and falling” pitch, and that is that melody’s pitch tends to change in a continuous manner: it is more likely to move to a nearby pitch than to discontinuously “teleport” to a faraway pitch. This has been recognized since the early twentieth century, and in Sweet Anticipation Professor David Huron of Ohio State University summarizes the evidence for it. Isn’t this pitch continuity conducive to a spatial interpretation? Pitch continuity is at least consistent with a spatial interpretation. (But, then again, continuity is consistent with most possible physical parameters, including the direction of a mover.)

We see, then, that gravity, musical instruments, musical notation, and the pitch continuity of most melodies conspire to bias us to interpret musical pitch in a spatial manner (i.e., where pitch represents spatial position or distance). But like any good conspiracy, it gets people believing something false . Pitch is not spatial in the natural world. It doesn’t indicate distance or measure spatial position. How “high” or “low” a sound is doesn’t tell us how near or far away its source is. I will argue that pitch is not spatial in music, either. But then what is spatial in music? If music is about movement, it would be bizarre if it didn’t have the ability to tell your auditory brain where in space the mover is. As we will see later in this chapter, music does have the ability to tell us about spatial location–that’s the meaning of loudness.

But we’re not ready for that yet, for we must still decode the meaning of melodic pitch. My hypothesis is that hiding underneath those false spatial clues lies the true meaning of melodic pitch: the direction of the mover (relative to the listener’s position). It is that fundamental effect in physics, the Doppler effect, that transforms the directions of a mover into a range of pitches. In order to comprehend musical pitch, and the melody that pitches combine to make, we must learn what the Doppler effect is . We take that up next.