Figure 38. A notation system in which vertical position indicates intensity, and pitches are shown along the bottom. This is the same excerpt from J.C.F. Bach as in Figure 37 but here the notation schemes for pitch and loudness have been swapped. This is not a good way to notate music because most of the note-to-note modulations are in pitch, not in loudness, which means an overabundance of pitch labels along the bottom, and little use of the vertical dimension within the horizontal bars. (To read the pitches along the bottom, “E5,” for example, is the E pitch at the fifth octave. When the octave is not labeled, it is presumed to be that of the last mentioned octave.)
The reason this alternative music notation system is so bad is, in one sense, obvious. In music, pitch typically varies quickly, often from note to note. Loudness, on the other hand, is much less variable over time. As exemplified by the excerpt in Figure 37, pitch can change at very short time scales, such as a 16th or 32nd note, but intensities typically persist for many measures before they change. To illustrate this, consider the fictional piece of music shown in Figure 39 (using standard music notation). In this example, pitch hardly ever changes, and loudness is changing very quickly. Music is never like this, which is why the standard notation system is a good one. The standard music notation system is so useful for music because it gives the quickly varying musical quality—pitch—the spatial metaphor, and relegates to the glossary the musical quality that stays much more constant: loudness.
Figure 39. An alternative kind of music that never happens (shown in regular notation). If music were often like this, then the alternative notation system in Figure 38 would be sensible. (This fictional music was created by taking J.C.F. Bach’s piece in Figure 38, keeping the notes as in that reverse notation system, but then pretending they represent pitches, as in normal notation (“f4” means “ffff ”).
To get a more quantitative measure of how quickly pitches and loudnesses change over time, Sean Barnett measured the distribution of time spent on a pitch before changing (Figure 19, earlier), and Eric Jordan measured the distribution of time spent at a given level of loudness before changing (Figure 40 below). One can see that pitches typically switch after about half a beat to a beat, whereas intensities change after about 10 beats.
Figure 40. Distribution of time spent at a loudness level before switching. One can see that loudness durations tend to be about 10 beats, and very often as long as 30 or more beats. This is more than an order of magnitude greater than the time scales for durations at the same pitch, which tend to be about a half a beat to a beat. These data were measured from Denes Agay’s An Anthology of Piano Music, Vol. II: The Classical Period.
While it is obvious why the standard notation system is smarter than my hypothetical “reverse” one for music, it is not obvious why music is like this in the first place. Why does music have “fast pitches” and “slow loudnesses”? If music sounds like movement, and loudness modulations are selected to sound like those due to spatial proximity, then the answer is straightforward. In order to significantly change loudness, the mover must move some distance through space. Melodic pitch, on the other hand, is about directedness toward the listener. In contrast to movement through space, which takes a relatively long time, a mover can “turn on a dime.” In a single step, a mover can turn about 45 degrees with ease (and typically does), which would translate to a fourth of the tessitura width (on average). Melodic pitch changes more quickly than loudness in music simply because human movers can change direction more quickly than they can change their proximity to the listener. That’s why music never sounds like the fictional piece of music in Figure 39, and that’s why our Western musical notation system is an efficient one. The comparative time scales of loudness and melodic pitch are what we should expect if music sounds like human movers, with loudness modulated by the spatial proximity and melodic pitch by the direction of the depicted mover.
In addition to the time scale for loudness modulations being consistent with that for changes in proximity, additional evidence for proximity as the meaning of loudness is provided in four Encore sections:
Encore 4: “Distant Beat” I will discuss how the nearer movers are, the more of their gait sounds are audible, and how this is also found in music: louder portions of music tend to have more notes per beat. (This was also mentioned earlier in this chapter as we finished up our discussion of rhythm, because it concerns the interaction between rhythm and loudness.)
Encore 6: “Fast Tempo, Wide Pitch” I discuss how, as expected from theory, music with a faster tempo has a wider pitch range for its melody. This Encore section also shows, however, that—as predicted—the range of loudnesses in a piece is not correlated with tempo.
Encore 7: “Newton’s First Law of Motion” This Encore section takes up a variety of predictions related to the inertia of moving objects, on the one hand, and the asymmetry between pitch rises and pitch falls, on the other. We will predict, and data will confirm, that this asymmetry changes as a function of loudness: when music indicates (by high loudness level) that the mover is close, the probability rises of long pitch runs downward.
Encore 8: “Medium Encounters” This Encore section concerns regularities in how movers distribute themselves in distance from a listener, and makes predictions about how frequently music makes use of various loudness levels.
Summary
In this chapter and the previous chapter, we have covered a great deal of musical ground (and we will cover still more in the Encore chapter). In Chapter Three, we presented general arguments for the music-is-movement theory, clearing three of the four hurdles for a theory of music: why we have a brain for music, why music should be emotionally moving, and why music should elicit movements in us. In this chapter, we have addressed the fourth hurdle, explaining the structural features of music. As I hope readers can see, there is a wealth of suspicious similarities between music and the sounds of people moving—42 suspicious similarities—which are summarized in the table below.
ection
uman movers
usic
. Drum Core
ootsteps areregularly repeating.
he beat is rgularly repeating.
. Drum Core
ootsteps arethe most fundamental auditory feature of human movement.
he beat is te most fundamental quality of music.
. Drum Core
ootsteps ten to be around one to two per second.
eats tend tobe around one to two per second.
. Drum Core
ootsteps usully are not as regular as a metronome.
eats are oftn looser than that of a metronome.
. Drum Core
eople’s foottep rates lower prior to stopping (ritardando).
he number ofbeats per second lowers prior to musical endings (ritardando).
. Gangly Nots
ootsteps areusually higher-energy collisions than between-the-step bangs.
n-beat notesusually have greater emphasis than off-beat notes.
. Gangly Nots
n addition t footsteps, people’s gangly limbs make sounds in between the footsteps.
n addition t notes on the beat, music has notes in between the beats.
. Gangly Nots
he between-te-steps gangly bangs are time-locked to the steps.
he between-te-beats notes are time-locked to the beat.
. Gangly Nots
he pattern o steps and between-the-steps gangly bangs is crucial to identifying the mover’s behavior.
he pattern o on-beat and off-beat notes (the rhythm) is crucial to the identity of a song.
0. Gangly Noes
uman-mover git sounds (steps and between-the-steps banging ganglies) have rings, and often pitches.
usical notesoften have pitches.
1. The Lengt of Your Gangly
eople typicaly make about zero or one between-the-step bangs.
usic typicaly has about one off-beat note per beat.
2. Backbone
ootsteps canbe highly variable in intensity, and we perceptually sense a step even when inaudible.
eats are fel even when no note occurs on a beat.
3. Backbone
t is not merly the temporal pattern of gait sounds that identifies a mover’s behavior. It matters which sounds are on the beat.
he feel of amusical rhythm does not depend solely on the temporal pattern, but on where the listener interprets the beats to be.
4. The Long nd Short of Hit (Encore)
eople are liely to make a between-the-steps gangly bang near the middle of a step cycle.
ff-beat note most commonly occur near the middle of a beat cycle.
5. The Long nd Short of Hit (Encore)
eople are moe likely to make a between-the-steps gangly bang just before a step than just after. (“Long-shorts” are more common.)
ff-beat note more commonly occur in the second half of a beat cycle (just before the beat) than in the first half (just after the beat).
6. Measure o What? (Encore)
atterns of fotstep emphases are informative as to the mover’s behavior.
ime signatur matters to the identity of music.
7. Gangly Chrds
ait sounds hve temporal patterns and pitch patterns (due to the pitches of the constituent ganglies).
usic typicaly has rhythm chords.
8. Gangly Chrds
mover’s temoral pattern of hits is matched to the pitch pattern (because the pitches are due to the constituent gangly bangs).
hords (e.g.,as played with the left hand on the piano) have the same time signature as the rhythm.
9. Gangly Chrds
ootsteps ten to have lower pitch than other gangly bangs.
or chords, te pitch played on the beat tends to be lower than that played off the beat.
0. Gangly Chrds
he pitches aong gangly bang sounds can occur simultaneously (unlike Doppler shifts, see below).
hords are ofen struck simultaneously.
1. Fancy Foowork (Encore)
hen people trn, they tend to have more complex gangly bangings.
hen melodic ontour rises or falls, the rhythm tends to be more complex.
2. Distant Bat (Encore)
eople that ae nearer have more audible gangly bangs per step.
ouder music as more notes per beat.
3. Choreograhed for You
oppler shiftpitch contours and loudness contours matter for the appropriate visual-auditory fit of a human mover.
elodic contors and loudness contours (not just rhythm) are relevant for choreographers in creating visual movements to match music.
4. Why PitchSeems Spatial
oppler pitchs change continuously over time.
elodic contor tends to change fairly continuously.
5. Only One inger Needed
mover is ony moving in one direction at any moment, and thus has only one Doppler shift for a listener.
elodies are nherently one pitch at a time.
6. Home Pitc (Encore)
or a mover a constant speed, Doppler shifts are confined to a fixed range, the highest (lowest) corresponding to heading directly toward (away from) the listener.
elodies tendto be confined to a fixed range of pitches called the tessitura.
7. Home Pitc (Encore)
eople tend t move in all directions relative to a listener, and to fairly uniformly sample from Doppler pitches within the Doppler range.
elodies tendto sample fairly uniformly across their tessitura.
8. Home Pitc (Encore)
itches at th top and bottom of the Doppler range tend to have longer duration (due to trigonometry).
elodies tendto have longer-duration notes when the pitch is at the top or bottom of the tessitura.
9. Fast Temp, Wide Pitch (Encore)
aster movershave a wider Doppler pitch range.
aster tempo usic tends to have a wider tessitura.
0. Fast Temp, Wide Pitch (Encore)
aster moversdo not have a wider range of proximity-based loudnesses.
aster tempo usic does not tend to have a wider range of loudness.
1. Human Cures
eople take aout two steps to make a right-angle turn.
usic takes aout two beats to traverse the top or bottom half of the tessitura (which corresponds to a right-angle turn).
2. Musical Ecounters
he most geneic kind of human encounter is the Hello–HowAreYou–Good-bye, involving a circling movement beginning when a mover headed away begins to turn toward the listener. The Doppler pitch contour is that of a hill, with flatter slopes at the bottom and top.
elodies in msic have a tendency to be built out of pitch hills.
3. Musical Ecounters
he generic ecounter tends to be around eight steps (two steps per right-angle turn).
he constituet pitch hills in melodies tend to be roughly eight beats long.
4. Newton’s irst Law of Music (Encore)
hanging Dopper pitches have little or no tendency to continue changing, consistent with Newton’s First Law of Motion (inertia).
hen melodic ontour varies, there is little or no tendency to continue changing.
5. Newton’s irst Law of Music (Encore)
ore subtly, oppler shifts possess “momentum” only when falling by a small amount.
ore subtly, elodic contours possess “momentum” only when falling by a small amount.
6. Newton’s irst Law of Music (Encore)
mall Dopplerpitch changes are more likely downward, and large pitch changes more likely upward.
mall melodiccontour changes are more likely downward, and large changes more likely upward.
7. Newton’s irst Law of Music (Encore)
xtended segmnts of falling Doppler pitch are more common than extended segments of rising Doppler pitch (due to passing movers).
ownward meloic runs are more common than upward melodic runs.
8. Newton’s irst Law of Music (Encore)
ore proximal and thus louder, movers are more likely to undergo large downward Doppler pitch runs.
ouder portios of music are more likely to feature large pitch runs downward (compared to upward).
9. Slow Loudess, Fast Pitch
eople can tun quickly, and can thus change Doppler pitch quickly (i.e., half a tessitura in about two steps). But people cannot typically change loudness quickly, because that requires actually moving many steps across space.
elodic contor changes quickly, but loudness changes at much slower time scales.
0. Medium Enounters (Encore)
ncounters wih a person have an average distance, spending more total time at near-average distances than at disproportionately near or far distances (in contrast to the fairly uniform distribution of Doppler pitches).
ost pieces hve a typical loudness level (e.g., mezzo forte), spending most of their time at that loudness level, and progressively less time at loudness levels deviating more from this average (in contrast to the fairly uniform distribution of melodic pitches).
1. Medium Enounters (Encore)
n any given ncounter, a person is more commonly more distant than average than more proximal (because there’s more “far” real estate than “near”).
he distributon of times spent at each loudness level is not only peaked, but asymmetrically disfavors the louder loudness levels.
2. Medium Enounters (Encore)
earer-than-aerage portions of a mover’s encounter tend to be shorter in duration than farther-than-average portions.
ouder-than-aerage segments of music tend to be more transient than softer-than-average segments.
Conclusion
So What Are We?
You can’t catch a cat with a carrot. Unless you fashion the carrot into the spear tip of a harpoon and have good aim, you’ll have better luck luring the cat with tuna fish. Even though cats didn’t evolve eating 500-pound tuna, the meaty odor and
taste taps into what cat noses and tongues like. If you keep up a daily dose of fish—and a wee bit of water—you’re likely to have caught yourself a cat. Add a litter box next to your toilet and this cat will quickly become no more likely than you to stain the carpet. With these two simple steps, and only $39 in supplies, you’ll have quickly transformed a wild animal with hundreds of millions of years of evolutionary design into a toilet-trained, self-cleaning vermin remover.
Unlike dogs, who have changed their brains and bodies for hundreds of thousands of years to suit man—that is, they’ve become domesticated—cats are notoriously not domesticated. Cats may be our occasional friends and usefully serve as clean critter catchers, but they think they are wild cats, and they do what wild cats tend to do. They fit into our lives not because they have evolved for us, but because we’ve shaped our houses—and it doesn’t take much shaping—so that cats behaving like cats naturally leads to a function fulfilled for us.
Cats are harnessed, not domesticated—their innate talents redirected, with little or no training, in ways evolution didn’t intend. And the fundamental trick behind our harnessing cats is so simple we hardly appreciate it; in fact, I’ve already mentioned it. Tuna, not carrots, and kitty litter, not a bidet. Although tuna is not what cat ancestors ate, tuna is sufficiently meat-ish in odor and taste that it fits right into a cat’s finicky diet disposition. And although kitty litter is a strange and unnatural concoction, it mimics the loose soil in which cats prefer to bury their feces. Tuna and kitty litter are simulacra of nature, and thus successfully harness cats, turning them into good pets.
Harnessed: How Language and Music Mimicked Nature and Transformed Ape to Man Page 19
