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The Science Behind Musical Instruments (Part One)

In Which We Look at How Sound Works in Stringed, Woodwind, Brass, and Percussion Instruments

Image courtesy of akvaMarinka

I was cleaning my room yesterday and amidst the clutter found a presentation I did for my high school physics class that taught students about the sound in musical instruments. I always say I'd like to get back into music, and this could be a great opportunity to re-introduce myself to it by writing out my old script with edits. This will be part one of two, in which I discuss how sound works in stringed, woodwind, brass, and percussion instruments. In the next part, I'll talk about keyboards, electronic and technological instruments. 

To start, the sound that musical instruments make respectively is actually quite complex. The technical descriptor for it would be the infinite sum of sine waves of different frequencies, but we'll break this down into more simpler terms. 

We have the fundamental frequency, which is characterised by what we hear—the pitch. The tone, meanwhile, is made up of harmonic frequencies that are integer multiples of the pitch. The reason why we hear it as a single pitch is because the fundamental frequency is much louder than the harmonics. 

Next, we can look at overtones and harmonics in more depth. As discussed, harmonics are the integer multiples of a vibrating object's pitch—making up the tone. Overtones are any resonant frequencies above the pitch, which may or may not be harmonics. 

When we talk about the instruments themselves, there are reasons why they aren't all played the same way, and it all starts from the fact that they are made in different sizes and from different materials. Since all instruments produce varying harmonic frequencies, they each also produce unique tones.

Since I'm a violinist, I'd like to start with stringed instruments—characterised by, of course, strings. They, along with woodwind instruments, produce pitch and tone. Their overtones are harmonic, though woodwind instruments tend to produce even-integer harmonics. 

Vibrating strings are what provide sound in these instruments. Depending on the instrument, the musician can make the strings vibrate in one of multiple ways: plucking (e.g. the harp, the guitar, and the mandolin), bowing (the violin family), hitting (e.g. the hammered dulcimer and the piano), and blowing (the Aeolian harp, which uses wind to move its strings). 

It is interesting to note that the guitar is the only instrument that has a dying volume and frequency. This happens when a guitar's string is plucked, and its length increases as it reaches its extreme points. The tension here will be more when compared to what will happen a few oscillations later, when the frequency dies down with the volume. 

The violin, for instance, is also capable of this to a degree, but it depends on the bowing speed and force. Regardless, it will always have a constant volume and frequency. 

The pitch of a given stringed instrument depends on its length, thickness, tension, and density. Strings that are longer, thicker, denser, and looser will all vibrate more slowly than shorter, thinner, less dense, and tighter strings. A slower vibration contributes to a lower pitch, while a faster vibration leads to a higher pitch. There are two ways to obtain pitch on a stringed instrument, either by having many strings of different lengths (e.g. on a harp), or by stopping the vibrating length of strings at different points (e.g. on a violin or a guitar). 

Stringed instruments can also produce wave overtones. The first harmonic is determined for a waveform with either one antinode—the middle of a string—or two nodes—the two ends of a string—when there is resonance in a string being pulled. The antinode experiences the greatest change in amplitude, while the two nodes don't experience any vibration. Thus, the length of the resonating structure represents one half of a full wavelength.

We then move on to my second favourite family—the woodwinds. There was a time when most woodwinds were actually made of wood. Now, we mainly consider them wind instruments that aren't played by buzzing the lips together.

For the most part, woodwinds are tubes, and their sound vibrates through air columns from inside the tube. Depending on the instrument, musicians can make sounds in one of multiple ways, by: blowing across an edge (e.g. in a flute, recorder, whistle, or root beer bottle), blowing between a wooden reed and a fixed surface (e.g. in a clarinet or saxophone), or blowing between two wooden reeds (e.g. in an oboe, bassoon, sousaphone, or bagpipes). 

A woodwind pitch is dependant upon the volume of air that vibrates. The pitch is lower when a larger volume vibrates more slowly, and the pitch is higher when a smaller volume vibrates more quickly. For most of these instruments, the musician can change pitch by opening and closing holes along the instrument's body. The more keys there are, the more complex the instrument is in terms of fingering. 

When there is a break, which occurs when the blowing pressure is increased past a certain point, that air column resonates at a higher harmonic and raises the pitch by a large interval for many woodwinds. This is usually called an octave, with the exception of the clarinet, in which case it is called a twelfth. This is how woodwinds are able to achieve range regardless of minor variations.

Like stringed instruments, woodwinds can also produce wave overtones. Here, the first resonant frequency has only a quarter of a wave in the tube, which means the first overtone is the first "allowed" harmonic above the pitch. Since woodwind instruments have two different ends, the closed end is a node and the open end is an antinode, the latter part being the area experiencing the greatest amplitude while the former experiences none. 

Now, let us look at the family that often gets confused with woodwinds—brass. Western European-based brass instruments really are made of brass, but there are also many other brass instruments made from wood, horn, shell, and other materials. 

Brass instruments share only one commonality with woodwinds, that being the sound, which comes through a vibrating air column from inside the tube. The difference here is that the air column vibrates in correspondence with the musician's vibrating lips through a mouthpiece, producing a raspy sound.

The pitch of a brass instrument is dependant upon the volume of air vibrating as well as the speed at which the musician's lips vibrate. The musician can actually cause the air in the tube to resonate at different harmonics depending on how quickly or slowly they buzz their lips on the mouthpiece. The volume of air, meanwhile, depends on the tube's length. A longer tube means a larger volume of air and a lower pitch.

With a single-length tube, we can only play notes found in bugle calls. If we want to hit all twelve notes of the chromatic scale, then we need to change the tube's length (e.g. trombone) or play through different tubing lengths (e.g. brass instruments with valves). Brass instruments, unlike woodwinds, tend to produce odd-integer harmonics.

I'll finish this part off with the family that's the easiest to explain—the percussions. Frankly, these instruments are anything that can be beat with the hands or a stick. 

With percussion instruments, the sound is either a vibrating membrane (membranophones) or a vibrating piece of solid material (idiophones). Percussionists usually produce vibrations by hitting these instruments, but there are other instruments that can be played by shaking or rubbing them, among other ways of producing vibrations. 

The way in which sound vibrates in percussion instruments is quite complex, so many of them don't really have a definite pitch. The majority of them that do are idiophones. Regardless, the pitch will always depend on the amount of material that is vibrating. In other words, percussions must have a different vibrating body for each note (e.g. xylophone bars, chimes, bells, and tuned gongs of a gamelan orchestra). 

The pitch of a membranophone—like a drum—depends on the thickness and tension of its drumhead. Kettledrums are the only membrophones with definite pitch. These instruments in general may produce resonant frequencies that are not whole number multiples of their pitch, meaning that they have non-harmonic overtones. 

This is a lot of information to take in, so this is where we'll stop for now. Thank you for joining me on this musical trip down memory lane, and we'll shift gears with more complicated as well as streamlined instruments in the second part.

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