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Acoustics is the study of sound and its transmission.
you pluck a string of an acoustic guitar to initiate a tone, here’s what
string vibrates really fast. Hundreds of times per second. So fast that your eye
can’t follow the movement.
• The vibrating string connects to the body of the guitar via the
bridge. This enables the vibrating string to set the body of the
guitar flexing back and forth at the same frequency (number
of vibrations per second) as the vibrating string.
• When the guitar body flexes one way, it compresses the air
molecules that surround it (compression). When it flexes the
other way, the air pressure drops (rarefaction). As the guitar
body flexes back and forth, the compression and rarefaction
of the surrounding air particles repeats itself over and over.
And over and over. Really fast.
a result, spherical pulses—pressure waves—of air particles radiate
outward in all directions from the flexing guitar body. Really fast. These
pulses—not the air itself!—move through the atmosphere at 743 miles an hour, the speed of sound.
(In Canada, that’s 1,188 km per hour, which seems faster than in America,
probably because of the cold, crisp Canadian air.)
• The tone travels as a pressure wave through the air until it
hits your ear drum. At that point, it transmogrifies into
mechanical motion, setting your ear drum vibrating, just like
the diaphragm inside a microphone.
then those three teeny bones in your middle ear get into the act. Remember the
“hammer, anvil, and stirrup” from elementary or middle school? Smallest
bones in your body.
• Finally, your inner ear transduces the vibrations into nerve
impulses. The nerve impulses then travel to a number of
different parts of the brain, each specialized to analyse a
specific element of the sound, some related to pitch (tones,
intervals, chords), some to time (beat, pulse, tempo meter,
At this point, your brain interprets your original plucking of the
guitar string as a tone. Or, if you’re British, a note.
The whole process happens so fast it seems instantaneous. You
pluck the guitar string, you hear the corresponding tone or note
you’re listening to a song, depending on how well crafted the tune is, you may
then experience an emotional reaction as your brain processes the music.
Being a parallel processor, your brain easily and automatically
handles all the different sound processing tasks simultaneously.
brain may look up tones in a neural dictionary. The cortex of marmoset monkeys
contains pitch-sensitive neurons, that is, neurons that actually code for pitch.
These nerve cells respond to specific frequencies, which means that if the same
holds true for humans (it’s likely), then the human brain stores a vocabulary or
dictionary of different pitches, the way the brain stores a vocabulary of words.
HOME, AND A
So, that’s what
happens when you hear a tone (or note).
Or is it?
distinct from sound—begins, not with tones, but with something called harmonics or overtones (these two terms mean the
same thing) and their role in the construction of scales (the subject
of Chapter 4).
you play the note “Middle C” on the guitar (B string, first fret), the string
vibrates 261.6 times per second (assuming you’ve tuned your guitar), or 261.6 cycles per second. Also called 261.6
Hertz, after physicist and wave theory pioneer Heinrich Rudolf Hertz.
Also abbreviated 261.6 Hz.
The vibrating string sets the body of the guitar pulsing at the
same frequency, 261.6 Hz.
When you play the same note, Middle C, on the piano, a hammer
hits some strings attached to the sound board inside the piano,
which starts vibrating at the same frequency, 261.6 Hz.
You hear the same note, Middle C, on each instrument. Yet, you
can easily tell the sound of the guitar from the sound of the piano.
answer has to do with tone color. The technical term for tone color is timbre
(pronounced, TAM-ber, unless you know proper French). It’s a function of
harmonics, or overtones.
Try this little experiment:
your guitar again. Acoustic or electric, it doesn’t matter. If it’s electric,
plug it into an amp and crank it a bit. If you’re a keyboard player, borrow a
you don’t know how to play guitar, that’s okay—you don’t have to know how to
play to do this:
the high “E” string down to “C” (Middle C). (Never mind why Middle C is called
Middle C. Or why it vibrates at 261.6 Hz instead of some nice round number like
250. That’s coming up in a bit.)
• Now pluck the string. When you do this, you set the whole
string vibrating at 261.6 Hz.
• If you look closely, you can observe the string blur,
immediately after you pluck it. The blurring becomes less
intense as the note dies away.
you realize it or not, when you pluck the string, at the same time as the string
vibrates at 261.6 Hz, the string also automatically divides itself in half. The
two halves vibrate at exactly twice the frequency, 523.2 Hz. You can’t see
this—the string vibrates way, way too fast for the naked eye to see. You observe
only a blur.
This secondary high-speed vibration, at a frequency of 523.2 Hz,
also produces a tone, of course. But that tone has a considerably
higher pitch than Middle C. The secondary tone is called a harmonic
A harmonic or overtone has two properties:
higher in pitch than the original (261.6 Hz) tone, and
way softer in volume than the original (261.6 Hz) tone.
Now, with overtones in the picture, the original tone needs a
name to distinguish it from the overtones. That name is the
fundamental. You can think of the fundamental as the primary tone, and
the overtone as secondary, because it’s softer.
overtone is so soft that the much louder sound of the full-length string
vibrating at 261.6 Hz, the fundamental, drowns out the overtone. (In a few
situations—when playing an electric bass, for example—an overtone can sound
louder than the fundamental. But that’s the exception to the rule.)
Now things finally start to get interesting from a musical perspective.
That vibrating string, at the same time it divides itself in half, also
divides itself into thirds. And quarters. And fifths. And sixths. And so
on, and so on, and so on. All at the same time.
In other words, the string vibrates in a complex way. The
secondary vibrations happen much too fast for the eye to see.
Each of the string-subdivisions produces a different,
soft, high-pitched overtone. The comparatively loud fundamental drowns out all
of them. So it seems that you don’t even hear the overtones. But you do. Your
brain does process them (coming up in just a moment).
summarize: a single vibrating string (or other vibrating thing—such as a pair of
vocal folds) simultaneously divides itself many times and produces a whole
series of soft, high-pitched overtones. Dozens.
If you have the right equipment, you can identify and measure all the
overtones present when you pluck a single guitar string and produce
Middle C. The frequencies of all the dozens of overtones turn out to
be simple whole-number multiples of the fundamental.
Taken together, the fundamental and all the overtones are called
the harmonic series or the overtone series (these two terms mean
the same thing).
4 below shows the frequencies of the first 15 overtones of Middle C. It’s
important that you sit down right now and memorize every single number in the
wait! It’s not important.)
Fundamental and First 15 Overtones of the “Middle C” Overtone Series
f x 2
f x 3
f x 4
f x 5
f x 6
f x 7
f x 8
f x 9
f x 10
f x 11
f x 12
f x 13
f x 14
f x 15
f x 16
are just the first 15 overtones—they continue on and on, ever higher in pitch,
ever softer. The next overtone in the series above would be the 16th overtone, with a frequency 17 times that of
the fundamental, or 4,447.2 Hz.
Although you think you only hear Middle C, (the fundamental, at
261.6 Hz), your brain sort outs all the overtones. Automatically.
Without the slightest conscious effort on your part. A miraculous feat
of naturally-selected engineering.
Any note you play on any musical instrument is named for the
fundamental, even though each note comes with a bunch of
Your brain has evolved mechanisms to identify harmonic
relations. It breaks a tone into its various harmonics or overtones,
analyses them, then puts them back together to identify the sound
as a specific tone (as opposed to random noise).
Because the separate harmonics are related to each other in
simple frequency multiples (Table 4 above), the brain understands
that a single soundmaker must be producing them. The necessity of
identifying soundmakers probably drove the evolution of the brain’s
naturally-selected ability to parse a tone into its overtones. In Palaeolithic
times, having the capacity to tell the difference between an owl’s hoot and a
lethal predator’s growl would have saved you from getting eaten.
The harmonic series is sometimes known as the chord of nature,
because it’s not cultural in origin; it’s a phenomenon of nature. Any tone,
whether coming from a musical instrument or not (e.g., pinging a wine glass),
consists of a fundamental plus a batch of overtones that are always related to
the frequency of the fundamental as integer multiples of the fundamental.
Homing in on the Human Hearing Range
The range of human hearing spans roughly 20
Hz at the low end to 20,000 Hz at the high end.
That means your brain does not respond to
tones or overtones with frequencies lower than
20 Hz or higher than 20,000 Hz.
Of all the common acoustic musical instruments
in the world, the piano has the widest frequency
range. Its 88 keys span a range of 27.5 Hz to
What do you hear when you plink that last,
highest key of the piano? You hear the
fundamental tone at 4,186 Hz, and your brain
also picks up and processes the first few
overtones. But only the first few.
Recall that overtone
frequencies are always whole-number multiples of the fundamental. So the first
overtone of the highest note on the piano has a frequency of 8,372 Hz. The
second overtone, 12,558 Hz. The third overtone, 16,744. Your brain probably does
not process the fourth overtone—it’s too high.
The highest key of the piano actually produces
dozens of overtones, but your brain does not
react to any of the ones with pitches higher than
about 20,000 Hz.
Suppose, by accident
or disease, your hearing became restricted to, say, 5,000 Hz at the high end.
Would you still be able to hear every note on the piano? Yes, you would. But the
instrument would sound muffled, lacking in treble. That’s because your brain
would not be able to process the rich array of overtones in the 5,000 to 20,000
Roedy Black’s Musical Instruments Poster,
the pitch ranges of more than 70 musical
instruments and six vocal ranges. The Musical
Instruments Poster organizes the information by
note and by frequency, including the frequencies
of each of the 88 notes of the piano.
Normally, you do not hear overtones directly, the way you hear
fundamentals. But you can hear for yourself what overtones sound
this (if you’re a guitar player, you probably know how to do this):
you’re right-handed, pluck the guitar string—the one you tuned to Middle C a few
minutes ago—with your right hand. At the same time, with any finger of your left
hand, lightly touch the vibrating string just over the 12th fret (over the metal
fret itself, not the space between frets).
you now hear is a high-pitched note. You have “exposed” the sound of the first
overtone by damping (“killing”) the sound of the fundamental. You have
effectively cut the string in half, and you can hear both halves vibrating at
the same frequency. What you’re hearing is the first overtone of Middle C,
vibrating at double the frequency of Middle C.
• The point at which you damped (muffled) the fundamental
using your finger is called a node. You can clearly hear the
overtone, even though it sounds softer than the fundamental
was before you damped it.
the string again, but this time, lightly stop the string over the seventh fret.
Now you hear a completely different overtone. It’s even higher-pitched than the
first one. And it’s softer. It’s the second overtone.
• Pluck the string again. This time, lightly stop the string over
the fifth fret. Yet another, even softer overtone. So soft, you
can barely hear it. The third overtone.
You can keep doing this, teasing out even higher, fainter overtones.
Another Way of Exposing Overtones
Next time you have access to an ordinary acoustic piano (upright or grand), try
Lightly press down on Middle C, and also on the E and G immediately above
Middle C—so lightly that the hammers do not hit the strings.
Hold down the three keys. The strings associated with Middle C, E, and G are
now undamped and free to vibrate.
With your left hand, hit the note C below Middle C. Give that key a short,
hard, quick, unsustained “bonk.”
The vibrating strings of C below Middle C cause the sound board to vibrate only
for the brief duration of the “bonk.” However, the C-below-Middle-C bonk sets
the open strings of the three keys you are holding down into sympathetic
vibration. This causes the soundboard to vibrate and produce sound waves at the
same frequencies as some of the overtones of C below Middle C. So that’s what
you hear—a series of faint harmonics of C below Middle C.
When you play a single note on any musical instrument, the note
consists of a fundamental tone plus a whole series of simultaneous
overtones. No matter what the instrument is. Not only that, it’s the
same group of simultaneous overtones, regardless of the musical
if it’s the same group of overtones, why does a guitar sound different from a
piano when you play Middle C on each instrument?
Because the loudness (volume) of each individual overtone is
different for each type of instrument, depending on the instrument’s
shape, size, construction, etc.
brain’s evolved music-processing modules instantaneously analyse the varying
loudness levels of the overtones and accurately sort out which overtone series
belongs to which instrument.
instrument produces its own “overtone signature”—its own characteristic array
of relative loudness levels of each overtone. That’s what gives rise to an
instrument’s unique tone color or timbre. And that’s why you can instantly
differentiate the sounds of numerous musical instruments.
Your brain can do this for all manner of different sound sources,
not just musical instruments. Practically any source of sound. They
all produce overtones, each with its own characteristic overtone
voice and all other human voices have unique overtone signatures. You can easily
tell different human voices apart, even when you can’t see who’s talking or
singing. This capability of the human brain makes possible industries such as
radio broadcasting and sound recording.