We can also ask which pitch within the expressed chord is most likely to be the one played on the beat. For human movers, the lowest-pitched gangly bang we make is usually our footsteps. For music and the rhythmic expression of chords, then, we expect that the pitch played on the beat will tend to be lower than that played between the beats. Indeed, chords are usually caressed starting on the lowest expressed pitch (and often on the chord’s tonic, which in a C major chord would be the C pitch). Chords are, again, like gangly rings, with the lowest pitch ringing on the beat.
Consider yet another attribute of human gait: our gangly bangings can occur simultaneously. Multiple parts of a mover’s body can be clattering at the same time, and even a single bang will cause a ring on both the banger and the banged. So we should expect that the auditory mechanisms evolved for sensing gait would be able to process gait from the input of multiple simultaneous pitches. Consistent with this, the pitches within a chord are commonly played simultaneously, and our brains can make perfect sense of the simultaneously occurring notes. Pitch modulations that are part of the melody, on the other hand, almost never occur simultaneously (as we will discuss later).
The idea that musical chords have their foundation in the pitch combinations heard in the banging gangly sounds of human movers is worth investigating further. However, there are a wide variety of phenomena concerning chords that one would hope to explain, and that I currently have no theoretical insights into how to explain based on the raw materials of our ganglies. The laboratory of Dale Purves at Duke University has carried out exciting research suggesting that the human voice may explain the signature properties of the diatonic scale, and one might imagine persuasive explanations for chords emerging from his work. In fact, people do often vocalize while they move and carry out behaviors, and one possibility is that chords are not about gangly bangs at all, but about the quality of our vocalizations. The advantage of looking to gangly bangs as the foundation for chords, however, is that banging ganglies are time-locked to footsteps, and thus intrinsically note-like. Human vocalizations, however, are not time-locked to our footsteps, and also lack a clear connection to the between-steps movements of our banging ganglies. If chords were driven by vocalizations, we would not be able to explain why chords are so wedded to the rhythm, as demonstrated above. If one can find chords in our ganglies, then it allows for a unified account: our banging ganglies would explain both rhythm and chords—and the tight fit between them.
Chords, I have suggested, may have their origins in the pitches of the complex rings given off by gangly human movers. Later in the chapter, I will suggest that the pitch modulations in melody, in contrast, come from the Doppler shifting of the envelope of those gangly pitches.
Choreographed for You
Choreography is all about finding the right match between human movement and music. I had always figured it wasn’t the music as a whole that must match people’s movement so much as it was just the rhythm and beat. Get the music’s bangs in line with the people’s bangs—that’s all choreographers needed to care about. But I now realize there’s a great deal more to it. A lot of what matters in good choreography is not the rhythm and beat at all. The melodic contour matters, too, and so does the loudness. (To all you choreographers who already know this, please bear with me!)
Why should musical qualities beyond rhythm and beat matter to choreography? Because there are sound qualities beyond our intrinsic banging gangly sounds that also matter for sensing human movers. For example, suppose you and I are waiting for an approaching train, but you are 100 yards farther up the tracks (toward the approaching train) than I am. You and I will hear the same train “gait” sounds—the chugs, the rhythmic clattering of steel, and so on—but you will hear the train’s pitch fall (due to the Doppler effect) before I hear it fall. Now imagine that I am wearing headphones connected to a microphone on your lapel, so that at my position along the tracks I am listening to the sounds you are hearing at your position along the tracks. The intrinsic gait sounds of the train would be choreographed appropriately with my visual perception of the train, because those gait sounds don’t depend on the location of the listener. But my headphone experience of the pitch and loudness contours would no longer fit my visual experience. The train’s pitch now begins falling too early, and will already approach its lowest going-away-from-me pitch before the train even reaches me. The train’s loudness is also now incorrect, reaching its peak when the train is still 100 yards from reaching me. This would be a deeply ecologically incoherent audiovisual experience; the auditory stream from the headphones would not be choreographed with the train’s visible movements, even though the temporal properties—the beat and rhythm—of the train’s trangly bangings are just as they should be.
Real-world choreography pays attention to pitch and loudness contours as well as gait sounds; and, crucially, which pitch and loudness contour matches a movement depends on where the listener is. Choreography for pitch and loudness contours is listener-centric.
The implication for musical choreography is this: in matching music to movement, the choreographer must make sure that the viewpoint is the same point in space as the listening point. Good choreography must not merely “know its audience,” but know where they are. Music choreographed for you, where you’re sitting, may not be music choreographed for me, where I’m sitting. In television, choreographers play to the camera’s position. If movers are seen in a video to veer toward the camera, melody’s pitch must rise to fit the video, for example. In live shows, choreographers play to the audience, although this gets increasingly difficult the more widely the audience is distributed around the stage. (This is one of many reasons why most Super Bowl halftime shows suck.)
Whereas our discussion so far has concerned rhythm and beat, which do not depend on the listener’s position, the upcoming sections concern pitch and loudness, each of which depends crucially on the location of the listener. Music with only a beat and a rhythm is a story of human behavior, but without any particular viewpoint. In contrast, music with pitch and loudness modulations puts the listener at a fixed viewpoint (or listening point) in the story, as the fictional mover changes direction and proximity to the listener. These are the mover’s kinematics, and the rest of this chapter examines how music tells stories about the kinematics.
Motorcycle Music
Next time you’re on the highway at 70 mph next to a roaring Harley, roll down your window and listen (but do not breathe!). I did this just the other day, and was struck by something strange about how the chopper sounded. The motorcycle’s “footsteps” were there, namely the sounds made by the bike’s impacts directly on the asphalt as it barreled over crevices, crags, and cracks. The motorcycle’s “banging gangly” sounds were also present—the sounds made by the bike’s parts interacting with one another, be they moving parts in the engine or body parts rattling due to engine or road vibrations. And the bike’s exhaust pipe also made its high-frequency vroom (not quite analogous to a sound made by human movers). These motorcycle sounds I heard were characterized not only by their rhythm, but also by the suite of pitches among the rings of these physical interactions: the bike’s “chords.” These rhythm and chord sounds informed me of the motorcycle’s “state”: it is a motorcycle; it is a Harley; it is going over uneven ground; it is powerful and rugged; it needs a bath; and so on. Rhythm and beat (and the chords with which they seem inextricably linked), the topics of much of this chapter thus far, are all about the state of the mover—the nature of the mover’s gait, and the emotion or attitude expressed by that manner of moving about.
What, then, was so strange about the motorcycle sounds I heard while driving alongside? It was that the motorcycle’s overall pitch and loudness were constant. In most of my experiences with motorcycles, their pitch and loudness vary dynamically. This is because motorcycles are typically moving relative to me (I never ride them myself), and consequently they are undergoing changes in pitch due to the Doppler effect, and changes
in loudness due to changing proximity. These pitch and loudness modulations give away the action, and that was what was missing: the motorcycle had attitude but no action.
Music gets its attitude from the rhythm and beat, but when music wants to tell a story about the mover in motion—the mover’s kinematics—music breaks out the pitch and becomes melodic, and twiddles with the volume and modulates the loudness. The rest of this chapter is about the ecological origins of melody and loudness. We will begin with melody, but before I begin to defend what I think musical melodic pitch means, we need to overcome a commonly held bias—encoded in the expressions “high” and “low notes”—that musical pitch equates with spatial position.
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.
Doppler Dictionary
In the summer months, our neighborhood is regularly trawled by an ice cream truck, loudly blaring music to announce its arrival. When the kids hear the song, they’re up and running, asking for money. My strategy is to stall, suggesting, for example, that the truck only sells dog treats, or that it is that very ice cream truck that took away their older sister whom we never talk about. But soon they’re out the door, listening intently for it. “It’s through the woods behind the Johnsons’,” my daughter yells. “No, it’s at the park playground,” my son responds. As the ice cream truck navigates the maze of streets, the kids can hear that it is sometimes headed toward them, only to turn at a cross street, and the kids’ hearts drop. I try to allay their heartache by telling them they weren’t getting ice cream even if the truck had come, but then they perk up, hearing it headed this way yet again.
The moral of this story about my forlorn kids is not just how to be a good parent, but how kids can hear the comings and goings of ice cream trucks. There are a variety of cues they could be using for their ice cream–truck sense, but one of the best cues is the truck’s pitch, the entire
envelope of pitches that modulates as it varies in direction relative to my kids’ location, due to the Doppler effect.
What exactly is the Doppler effect? To understand it, we must begin with a special speed: 768 miles per hour. That’s the speed of sound in the Earth’s atmosphere, a speed Superman must keep in mind because passing through that speed leads to a sonic boom, something sure to flatten the soufflé he baked for the Christmas party. We, on the other hand, move so slowly that we can carry soufflés with ever so slightly less fear. But even though the speed of sound is not something we need to worry about, it nevertheless has important consequences for our lives. In particular, the speed of sound is crucial for comprehending the Doppler effect, wherein moving objects have different pitches depending on their direction of movement relative to the listener.
Let’s imagine a much slower speed of sound: say, two meters per second. Now let’s suppose I stand still and clap 10 times in one second. What will you hear (supposing you also are standing still)? You will hear 10 claps in a second, the wave fronts of a 10 Hertz sound. It also helps to think about how the waves from the 10 claps are spread out over space. Because I’m pretending that the speed of sound is two meters per second, the first clap’s wave has moved two meters by the time the final clap occurs, and so the 10 claps are spread out over two meters of space. (See Figure 23a.)
Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man Page 15