Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man (19 page)

The speed of sound is a couple hundred times faster than the two-meter-per-second speed I just pretended it was, but the same principles apply: when I move toward you my pitches are upshifted, and when I move away from you my pitches are downshifted. The shifts in pitch will be much smaller than those in my pretend example, but in real life they are often large enough to be detectable by the auditory system, as we will discuss later. The Doppler effect is just the kind of strong ecological universal one expects the auditory system to have been selected to latch onto, because from it a listener’s brain can infer the direction of motion of a mover, such as an ice cream truck.

To illustrate the connection between pitch and directedness toward you, let’s go back to our generic train example and assume the track is straight. When a train is far away but approaching the station platform where you are standing, it is going almost directly toward you, as illustrated in Figure 24i. This is when its pitch will be Doppler shifted upward the most. (High and constant pitch is, by the way, the signature of an impending collision.) As the train nears, it gets less and less directed toward you, eventually to pass you by. Its pitch thus drops to an intermediate, or baseline, value when it reaches its nearest point to you and is momentarily moving neither toward nor away from you (see Figure 24ii). As the train begins to move away from you, its pitch falls below its intermediate value and continues to go lower and lower until it reaches its minimum, when headed directly away (see Figure 24iii). (If, by the way, you were unwisely standing on the
tracks
instead of on the platform, then the train’s pitch would have remained at its maximum the entire period of time it approached. Then, just after the sound of your body splatting, the train’s pitch would instantaneously drop to its lowest pitch. Of course, you would be in no condition to hear this pitch drop.)

Figure 24
. Illustration that the pitch of a mover (relative to the baseline pitch) indicates the mover’s directedness toward you. When the train is headed directly toward the observer, pitch is at its maximum
(i)
, and is at its lowest when headed directly away
(iii)
; in between the pitch is in between
(ii)
.

As a further illustration of the relationship between pitch and mover direction, suppose that a mover is going around in a circle out in front of you (not around you). At (a) in Figure 25 the mover is headed directly away, and so has minimum pitch. The mover begins to turn around for a return, and pitch accordingly rises to a baseline, or intermediate, level at (b). The mover now begins veering toward you, raising the pitch higher, until the mover is headed directly toward you at (c), at which point the pitch is at its maximum. Now the mover begins veering away from you so as not to collide, and pitch falls back to baseline at position (d), only to fall further as the mover moves away to (a) again.

Figure 25
. The upper section shows a mover moving in a circle out in front of the listener (the ear), indicating four specific spots along the path. The lower part of the figure shows the pitch at these four spots on the path.
(a)
When moving directly away, pitch is at its minimum.
(b)
Pitch rises to baseline when at the greatest distance and moving neither toward nor away.
(c)
Pitch rises further to its maximum when headed directly toward the listener.
(d)
Pitch then falls back to baseline when passing tangentially nearby. The pitch then falls back to its minimum again at
(a)
, completing the circle.

From our experience with the train and looping-mover illustrations, we can now build the simple “dictionary” of pitches shown in Figure 26. Given a pitch within a range of pitches, the figure tells us the pitch’s meaning: a direction of the mover relative to the listener. In the dictionary of nature, pitch means degree of directedness toward you.

Figure 26.
Summary of the “meaning” of pitch, relative to baseline pitch. (The actual mapping from direction to pitch is non-linear, something we discuss later in the upcoming section.)

This pitch dictionary is useful, but only to a limited extent. Doppler pitches tend to be fluctuating when you hear them, whether because movers are merely going straight past you (as in Figure 24), or because movers are turning (as in Figure 25). These dynamic pitch changes, in combination with the pitch dictionary, are a source of rich information for a listener. Whereas pitches above and below baseline mean an approaching or receding mover, respectively,
changing
pitch tells us about the mover’s turning and veering behavior. A
rising
pitch means that the mover is becoming
increasingly directed
toward the listener; the mover is veering more toward you. And
falling
pitch means that the mover is becoming
decreasingly directed
toward the listener; the mover is veering more away from you. One can see this in Figure 25. From (a) through (c) the mover is veering more toward the listener, and the pitch is rising throughout. In the other portion of the circular path, from (c) to (a) via (d), the mover is veering
away
from the listener, and the pitch is
falling
.

To summarize, pitch informs us of the mover’s direction relative to us, and pitch
change
informs us of change of direction—the mover’s
veering
behavior. High and low pitches mean an approaching and a receding mover, respectively; rising and falling pitches mean a mover who is veering toward or away from the listener, respectively. We have, then, the following two fundamental pitch-related meanings:

Pitch
:
Low pitch
means a
receding
mover.
High pitch
means an
approaching
mover.

Pitch change
:
Falling pitch
means a mover veering more
away
.
Rising pitch
means a mover veering more
toward
.

Because movers can be approaching or receding and
at the same time
veering toward or away, there are 2 × 2 = 4 qualitatively distinct cases, each defining a distinct signature of the mover’s behavior, as enumerated below and summarized in Figure 27.

(A) Moving away, veering toward.

(B) Moving toward, veering toward.

(C) Moving toward, veering away.

(D) Moving away, veering away.

Figure 27
. Four qualitatively distinct categories of movement given that a mover may move toward or away, and may veer toward or away. (I have given them alphabet labels starting at the bottom right and moving counterclockwise to the other three squares of the table, although my reason for ordering them in this way won’t be apparent until later in the chapter. I will suggest later that the sequence A-B-C-D is a generic, or most common, kind of encounter.)

These four directional arcs can be thought of as the fundamental “atoms” of movement out of which more complex trajectories are built. The straight-moving train of Figure 24, for example, can be described as C followed by D, that is, veering away over the entire encounter, but first nearing, followed by receding. (As I will discuss in more detail in the Encore section titled “Newton’s First Law of Music,” straight-moving movers passing by a listener are effectively veering away from the listener.)

These four fundamental cases of movement have their own pitch signatures, enumerated below and summarized in Figure 28.

(E) 
Low, rising pitch
means
moving away, veering toward
.

(F) 
High, rising pitch
means
moving toward, veering toward
.

(G) 
High, falling pitch
means
moving toward, veering away
.

(H) 
Low, falling pitch
means
moving away, veering away
.

Figure 28
. Summary of the movement meaning of pitch, for low and high pitch, and rising and falling pitch. (Note that I am not claiming people move in circles as shown in the figure. The figure is useful because all movements fall into one of these four categories, which I am illustrating via the circular case.)

These four pitch categories amount to the auditory atoms of a mover’s trajectory. Given the sequence of Doppler pitches of a mover, it is easy to decompose it into the fundamental atoms of movement the mover is engaged in. Let’s walk through these four kinds of pitch profiles, and the four respective kinds of movement they indicate, keeping our eye on Figure 28.

(A) The
bottom right
square in Figure 28 shows a situation where the pitch is low and rising. Low pitch means my neighborhood ice cream truck is directed away from me and the kids, but the fact that the pitch is rising means the truck is turning and directing itself more toward us. Intuitively, then, a low and rising pitch is the signature of an away-moving mover noticing you and deciding to begin to turn around and come see you. To my snack-happy children, it means hope—the ice cream truck might be coming back!

(B) The
upper right
square concerns cases where the pitch is higher than baseline and is rising. The high pitch means the truck is directed at least somewhat toward us, and the fact that the pitch is rising means the truck is further directing itself toward us. Intuitively, the truck has seen my kids and is homing in on them. My kids are ecstatic now, screaming, “It’s coming! It sees us!”

(C) The
top left
square is where the pitch is still high, but now falling. That the pitch is high means the truck is headed in our direction; but the pitch is falling, meaning it is directing itself less and less toward us. “Hurry! It’s here!” my kids cry. This is the signature of a mover
arriving
, because when movers arrive at your destination, they either veer away so as not to hit you, or come to a stop; in each case, it causes a lowering pitch, moving toward baseline.

(D) The
bottom left, and final,
square of the matrix is where the pitch is low and falling. This means the truck is now directed away, and is directing itself even
farther
away. Now my kids’ faces are purple and drenched with tears, and I am preparing a plate of carrots.

Figure 28 amounts to a second kind of ecological pitch-movement dictionary (in addition to Figure 26). Now, if melodic pitch contours have been culturally selected to mimic Doppler shifts, then the dictionary categorizes four fundamentally different meanings for
melody
. For example, when a melody begins at the bottom of the pitch range of a piece and rises, it is interpreted by your auditory system as an away-moving mover veering back toward the listener (bottom right of Figure 28). And if the melody is high in pitch and falling, it means the fictional mover is arriving (upper left of Figure 28). At least, that’s what these melodic contours mean if melody has been selected over time to mimic Doppler shifts of movers. With some grounding in the ecological meaning of pitch, we are ready to begin asking whether signatures of the Doppler effect are actually found in the contours of melody. We begin by asking how many fingers one needs to play a melody.

Only One Finger Needed

Piano recitals for six-year-olds tend to be one-finger events, each child wielding his or her favorite finger to poke out the melody of some nursery rhyme. If one didn’t know much about human music and had only been to a kiddie recital, one might suspect that this is because kids are given especially simple melodies that they can eke out with only one finger. But it is not just kindergarten-recital melodies that can be played one note at a time, but nearly all melodies. It appears to be part of the very nature of melody that it is a strictly sequential stream of pitches. That’s why, even though most instruments (including voice, for the most part) are capable of only one note at a time, they are perfectly able to play nearly any melody. And that’s also why virtually every classical theme in Barlow and Morgenstern’s
Dictionary of Musical Themes
has just one pitch at a time.

Counterexamples to this strong sequential tendency of melody are those pieces of music having two overlapping melodies, or one melody overlapping itself, as in a round or fugue. But such cases serve as counterexamples that prove the rule: they are
not
cases of a single melody relying on multiple simultaneous notes, but, rather, cases of
two
simultaneously played single melodies, like the sounds of
two
people moving in your vicinity.

Could it be that melodies are one note at a time simply because it is physically difficult to implement multiple pitches simultaneously? Not at all! Music revels in having multiple notes at a time. You’d be hard put to find music that does not liberally pour pitches on top of one another—but not for the melody.

Why is melody like this? If chords can be richly complex, having many simultaneous pitches, why can melodic contour have only one pitch at a time? There is a straightforward answer if melodic contour is about the Doppler pitch modulations due to a mover’s direction relative to the listener. A mover can only possibly be moving in a
single
direction at any given time, and therefore can have only a single Doppler shift relative to baseline. Melodic contour, I submit, is one pitch at a time because movers can only go in one direction at a time. In contrast, the short-time-scale pitch modulations of the chords are, I suggested earlier in the chapter, due to the pitch constituents found in the gangly bangs of human gait, which
can
occur at the same time. Melodic contour, I am suggesting, is the Doppler shifting of this envelope of gangly pitches.

Human Curves