Saturday, June 28, 2014

What is sound?

The following is a translation into English of the chapter on instrument-making in our recently-published textbook in Spanish on the folk stringed instruments of Puerto Rico: Cuerdas de mi Tierra [Strings of my Land]


      Variations in air pressure against the eardrum, and
their subsequent interpretation by the brain, create the
experience of sound.
      The sounds that we recognize as musical are periodic
or regular variations. Those we recognize as noise are
random, or non-periodic.
      Musical sounds, like all other sounds, radiate outward
from their vibrating source in the form of energy waves
that travel through a medium such as air, water, or dense
      The simplest case is a single sound, called a "pure
tone." It is very rare to hear single, or "pure" tones in
the natural environment. Most sounds we hear are complex
tones, sounds made up of many tones happening together.
      When two or more different sound waves occur together
they interact: their pressure variations variously
reinforce and cancel each other to create a single, more
complex sound wave.  Our brain can still isolate the
individual simpler components of those complex sound waves
in order to recognize their source. Thus we can recognize,
without seeing, whether it was the sound of a pencil
falling on a carpet, or a spoon falling on a marble floor.
Also, our brain can decode the various components of the
sound in order to react appropriately: whether to ignore
the sound, whether to pay attention, whether to be alarmed,
whether to be soothed.

The Harmonic Series

      Every individual tone component of a composite
acoustic pressure wave has two distinguishing
characteristics: the frequency of the wave's rise-and-fall
and its amplitude or power. The frequency and amplitude of
the components of most ordinary sounds we hear--a door
shutting, water dripping from a spigot, someone sneezing--
are random.
     However, among all the sounds we can hear, there is an
extraordinary subset: those composed of frequencies that
line up in precisely numerical order. In these complex
sounds, the first component, usually the most predominant,
is the "fundamental" frequency; the next is twice the
frequency of the first; the next is three times the
frequency of the first; the next is four times the
frequency of the first; and so on until the frequencies
become too fast to perceive. Each of these components are
called "partials" or "harmonics."
      This ordered sequence is called the Harmonic Series.
Sounds whose component tones correspond to a Harmonic
Series are perceived as musical and are called musical
sounds. They sound like a musical note because its
fundamental provides us with its pitch and its ordered
series of accompanying partials, occurring at different
amplitudes, provides us with that tone's "color," or
recognizable distinctive sound.
      Sounds that are not ordered in this way, rather are
made up of random frequencies, we perceive as noise. It is
interesting to note that at one end of the spectrum, sounds
with random components like an explosion; a frying pan
falling to the floor; or a door slamming cause us alarm;
but sounds with components that are numerically ordered,
like the whistling of the wind; or the sound of a bird, or
the twang of a plucked string, bring us delight--and we
yearn to repeat the experience over and again, if we can.
It is as if we have an ancient, ingrained need for these
ordered sounds, sounds that are "musical" to our ears.

The stretched string 

Strings are truly magical: that nothing more than an stretched 
elastic fiber could produce so complex a series of hierarchically 
ordered tones has historically placed strings in the realm of 
extraordinary, mystical objects. The ancient Greeks, and later, 
the Early Church considered the harmonic content of a stretched 
string as nothing less than proof of the existence of God.    
         History has yielded up to us strings made of many different
materials: strings made of strips of animal hides, sinews
or intestines, nylon polymer and drawn metal wire. What
makes them all able to produce musical tones is that they
possess, to a high degree, three qualities: elasticity,
tensile strength and uniformity. This is what allows them
to behave as musical strings. In fact, how closely their
tone approaches a perfect Harmonic Series--and thus how
"musical" they sound--depends directly on the degree to
which they posses these three qualities. The history of the
string-making craft is marked by the quest to create ever
more uniform, ever more elastic and ever stronger strings.
      Strings made up of different materials differ,
however, in the amount of tension they impose on the
instrument and the “color” of the sounds they naturally
produce. The maker must be aware of and account for the

The string's signal

      When we stretch a string we charge it up with energy,
like a battery. The stretched string then exerts a
constant, static tension force on the instrument while at
rest. When we pluck that string, we disturb its static
state and release the stored-up energy in the form of a
complex, periodic vibration. The pulsating string create
tiny changes in the tension that it exerts on the
instrument’s neck and soundboard. These evanescent tension-
changes are the string's signal. Encoded within this signal
is the product of all the components of the Harmonic Series
the string is producing. The string-pulses set all the
instruments' surfaces--and the air inside of the soundbox--
into corresponding motion.
      Those distinct regions of the instrument that are able
comply with specific frequency components in the string
signal begin to vibrate in response. This is the phenomenon
called resonance. But there are many components of the
string signal that the instrument simply cannot comply with
and resonate. Those wave components stay bound up in the
string. Those that are matched are “sucked” out of the
string and their energy is what drives the resonances in
the instrument. So we can say that each instrument
“chooses” it’s own distinctive portion of the signals that
the string is feeding it. This is why a guitar sounds
different from a cuatro, or a violin, or a mandolin, even
though they all have similar vibrating strings. This also
explains the differences in sound between one cuatro and
another. Each instrument chooses which particular string
components to respond to and which to ignore.
      The difference in the sounds of two similar
instruments, or two completely different instruments, is due
to differences in their individual physical form and
structure. If one instrument has slightly thicker walls, or
if the soundbox is deeper or wider in size, or if its wood
is softer or harder, it will draw out of its moving strings
a slightly different combination of distinct frequency
components than the other can.
      So the sound of the instrument comes from its strings,
but what determines the portion of the string’s sound we
actually get to hear is the result of how it’s made, what
it’s made of and its physical shape and size.
      We must keep in mind that most instrument makers are
or were usually not engineers or acousticians, but instead
specialized craftsmen more familiar with wood than with
acoustics. Their stock in trade is not wave motion but the
capacity to recreate acoustic devices whose form was
derived from a specific historical, cultural and aesthetic
tradition. Instrument makers lack the ability to actually
see acoustic waves or perceive the wood surfaces vibrating
in all their daunting complexity. Their skill is solely
that of recreating cultural artifacts and transforming them
into tools that a musician can use to create art.
      Their sound and form is thus predominantly dictated by
history and tradition, rather than acoustical knowledge. As
Luciano Berio explained,

"They are concrete depositories of historical continuity. And
like working tools and buildings, they have a memory: 
they carry with them traces of the conceptual and social 
changes through which they were developed and transformed."
The first stringed instruments

      Evidence of how deep, primitive and compelling the
power of musical sounds is, is how early it was when
musical instruments arrived in the course of human
evolution. Evidence exists that musical instruments go back
as far as when the first humans hunted with bows and
arrows. Indeed, the first stringed instrument is thought to
be the actual hunter's bow.
      Undoubtedly, a hunter was once distracted by
rhythmically plucking the string of his bow, eliciting its
soothing sound. Soon he found that he could vary the sound
by flexing the bow, changing the strings tension and thus
the perceived pitch of its sound.
      The basic components of the hunter's bow are: the string--
elastic strips of rawhide, usually twisted to enhance its
uniformity-and a curved, elastic wooden rod. By virtue of
its elasticity, its tensile strength, and particularly by
its uniformity, the stretched string, once set into motion
by plucking, creates an ordered chorus of sounds. The bow
keeps the string in tension, and vibrates in response to
the dancing string--allowing the hunter to hear it. But not
very efficiently: the thin bow, while enabled by its form
to propel an arrow over a great distance is not very good
at converting the kinetic energy of the stretched string
into acoustic energy. But improvements followed.
      As time went by, the bow--originally a purely
utilitarian implement--became transformed by culture into a
specialized artifact of musical craft. This must likely
occurred after these early hunters placed the bow against
the cheek and discovered that the twanging sound could be
modulated, or changed in its harmonic content, by changing
the shape of the mouth. This is what the North American
Plains Indians did when they created their Mouth Bow. The
hollow cavity of the mouth became the first musical
resonator or soundbox.
      Later, certain indigenous tribes coupled the bow to
hollow gourds, further increasing the instrument's musical
efficiency. Examples of these are still found in Brazil and
Paraguay, with the Berimbau and Gualambao. These can even
be heard in Brazilian pop music today.
      Over the millennia those extraordinary objects,
capable of creating ordered and compelling sounds, evolved
from Africa and traveled to the Mideast. There they became
the earliest members of what became known as the lute
family. The musical bow’s rawhide strips became twisted
animal gut; the bow itself was transformed into the neck,
and the cheek or gourd became the resonant sound box.
Formally speaking, string instruments composed of a
soundbox with a neck attached at one end, over which
strings are stretched are members of what organologists
call the Lute Family.
      That family includes the Puerto Rican cuatro, as well
as its other native stringed instruments. But that is not
to say that the cuatro was derived from the lute. The word
"lute" has over the centuries been used to loosely describe
a myriad instruments from many different countries and
different cultures, each with distinctive shape and
stringing. So while our modern cuatro derives some of its
characteristics from the New Spanish Lute (Nuevo Laúd) of
the 19th century, it is in fact significantly different in
history, culture, form, size and stringing from the French
lute or the German or English lute. The only thing we can
say is that the cuatro is a member of the lute family
because it shares with the Spanish, English, German and
French lutes its neck and soundbox configuration. In turn
this form links them all back to the the Arab/Persian lutes
of great antiquity.
      The earliest examples of instruments from the lute
family were most likely crafted by early agrarian societies
with the same simple tools, available materials and
rudimentary techniques they used to make other implements
of their daily lives: the spoons, bowls, furniture, kitchen
tools, and farming implements.

Guild techniques
      The craft aspects of Latin American stringed
instruments point to an interesting social phenomenon. For
centuries, the manufacture of instruments made for the
elites and the bourgeoisie was overseen by ancient craft
societies known as the Guilds. The Guild system propelled
the refinement of the musical crafts to the greatest
heights ever known. They embodied an ancient tradition of
rigorous training and of strict standard-setting that
precipitated a flowering of the decorative arts over
hundreds of years, up until the system faded in the 19th
century with the advent of the Industrial Revolution.
      The highest technological advancements of their times
were utilized: treadle-powered machinery like bandsaws and
drills were introduced and edge tools and handsaws of the
best steel available were utilized. The finest exotic
hardwoods were imported from around the world.
      The strings themselves were the product of highly
specialized guilds, originally an offshoot of the nautical
cordiers or rope-makers. The ability to create strings of
unsurpassed uniformity--the principle requirement for the
most musical-sounding strings--was their stock in trade,
and a set of strings alone could cost more than several
      The Guilds were closed shops, that is, you could only
be born into them or at best, be invited in by existing
members. If your standards flagged or your work turned too
far afield you could be punished. Penalties for displeasing
the Guild masters included banishment from the profession,
banishment from the region, and even incarceration.
      Guild craftsmen developed the technique of sawing
plates thinly and planning them accurately so that they
could be curved with judiciously applied heat and moisture
into light, resonant, fancifully-shaped soundboxes.
Instruments made this way produced velvety-smooth,
sustaining notes that were appropriate for the refined
parlors and drawing rooms of the day. Often laden with
semi-precious stones and other rare inlay materials, they
served as presents to state officials from status-climbers,
or gifts of state between noblemen and kings.

The enterizo technique
      Because of their cost, instruments produced by the
Guilds were largely unavailable to the common folk.
      Folk musicians could only turn to local woodworkers,
rustic but resourceful craftsmen who brought to their task
slabs of local lumber and a sparse kit of tools that
included little more than knives and hatchets, scrapers,
hammers and awls. They lacked the technology and resources
for making saws that are required to slice wood into
bendable, thin sheets. Thus country folk in the Spanish
colonies, as their counterparts all over Europe, had to
make instruments in what they called enterizo or "whole"
way. The enterizo technique consisted of hewing the entire
body of the instrument: headstock, neck shaft, heel, sides
and back to shape from a single, continuous slab of solid
wood. A soundboard was then fashioned by chopping and
scraping a flat plate of softer wood, often with the bridge
carved out integrally as an rectangular lump on its
surface. The enterizo or unitary construction was an
ancient way of making instruments, dramatically different
from the way the Guilds did, building instrumentos de
piezas, that is, sawing thin sheets of wood into thin
plates, bending the sides and curving the plates,
assembling them into a complex soundbox by glueing them
together with small individual blocks, braces and grafts.
      Pablo Nassarre, theorist and organist of the Royal
Convent of San Francisco of Zaragoza, (1664-1730) described
the enterizo instruments of his day in his book, "Escuela
de Musica, segun la practica moderna" [Musical Method,
following the modern practice], Zaragoza, 1724, Book IV,
Chapter XVI in the section titled "de las proporciones" [on
the proportions].

"The form of this instrument is pyramidal, its lower extreme 
having a semicircular form. It was ordinarily made entirely 
of one piece (except the top) hollowed away in concave 

      To this very day, the enterizo method of making
musical instruments is common among many of the members of
the plucked-instrument family that evolved in Latin
America, notably the folk instruments families of Mexico,
Panama and Puerto Rico. The consequences of utilizing this
unique acoustical architecture with metal strings is a
loud, piercing tone--ideal for outdoor festivities and
community gatherings, be they secular or religious.
The enterizo technique in Puerto Rico
      Puerto Rico was a nation of carvers. As the prominent
Puerto Rican instrument maker Luis Acevedo Flores put it:

“ because the Puerto Rican artisan was eminently a wood 
carver, naturally, it occurred to him to carve his 
instruments, because that is what he knew. He was a great 
carving artisan: he carved his farm implements, he carved 
his kitchen implements, he carved the yokes for his oxen, 
he carved his mortars and pestles, he carved the beaters to 
shell coffee beans, to shell rice. So it would not be odd 
for them to take a piece of wood, hollow it and make a 
concave shape. And all that was left was to put on a top 
and play. Well that is what they did with the cuatro.

“ When we studied the furniture that was made in the past 
in Puerto Rico, we noted that they were generally carved 
furniture, where the finish work was always carved. And I 
can?t imagine, in any way, that in Puerto Rico the 
technique of wood bending was known. I don't think that 
wood bending techniques were known. I believe that 
craftsmen never used them because even pieces used in 
agriculture that appeared to be bent were actually cut from 
a solid piece of wood. They were never bent. And for me, it 
is difficult to imagine that if they knew bending 
techniques, they wouldn't use them when making instruments.
"When you observe someone who works in wood, you would 
definitively think it most logical to bend, from a 
structural point of view, because of the wood’s strength. 
Because that’s when the wood’s fibers are kept in their 
longest and most complete form. When we carve a curve we 
end up with “short grain” which is fragile and easy to 

“I honestly understand that perhaps it is conceivable that 
some people would know bending techniques, some coastal 
craftsmen who would work in shipbuilding, that had to bend 
the wood, and had to bend them cold, not with steam. By 
then in Spain, steam bending was known for a long time. But 
we don’t see that in Puerto Rico."