Over the past few years, I have been (slowly) learning my way around the guitar, and more recently started playing the piano. As I’ve made my way through countless YouTube tutorials and spare music books lying around the house, I’ve noticed none of them seem to explain the more fundamental aspects of sound and music. To be fair, the physics of sounds aren’t exactly critical to playing music, especially when the instruments are already engineered for our convenience, but my curiosity kept building.
One question, in particular, vexed me the most: if two instruments play the same note in the same octave, what makes them distinct? In this article, I’ll answer that, as well as any other question that pops up along the way.
The first thing I realized when I began researching this topic was that I completely misunderstood (or misremembered?) what a sound wave is. My grade eleven physics teacher would be so disappointed. If you’re like me, the term sound wave evokes the image of water rolling across the ocean, moving up and down as it ploughs forward.
These are called transverse waves, a mechanical wave that oscillates perpendicularly to its direction. The other form of mechanical wave, which I had completely forgotten existed (sorry Mr. Stringer), is called a longitudinal wave. These babies oscillate in parallel with the direction of the wave.
When an object vibrates, it pushes against the air, compressing it into a pocket with higher pressure (seen in red, above). This pocket naturally reverts to its old state (in blue) while compressing the air next to it. This cycle of compression and rarefaction (i.e., decompression) repeats over and over, causing the sound wave to travel.
That may be how sound works, but what about music? To answer that, we need to look at some of its fundamental elements.
Pitch
Pitch (how high or low a sound is) is a result of a sound wave’s frequency. That is, how often the cycle (compression to rarefaction to compression again) repeats. We measure this in Hz (or cycles per second). The frequency is closely related to the sound’s wavelength, the distance between compressed regions. A short wavelength means a higher frequency, since it takes less time to traverse a shorter distance.
In music, we most commonly use the chromatic scale, meaning there are twelve notes before the pattern repeats itself. Why does the pattern repeat itself? Another good question, Mike.
As the frequency of the sound wave increases, so, too, does the pitch. B is a higher note than A, so its cycle repeats more often. If you play A again, but one octave up (A1), it’ll be higher than the original B0, but still sound like the A0. This is because the frequency of A1 is double that of A0, and half of that of A2, up another octave. Our ear recognizes the mathematical relationship between notes of different octaves.
Dynamic level
The dynamic level of a sound (or its loudness, if you’re not trying to be fancy) is determined by the amplitude of the wave. The amplitude of a sound wave is how compressed (pressurized) the air becomes compared to the uncompressed region. This is a measure of how much energy is being transferred through the sound wave.
Given that the dynamic level of a sound is filtered through our perception, there is a little more to it. The human ear can detect frequencies between 20 to 20,000 Hz, but we don’t perceive all frequencies equally. We are most sensitive to sounds between 300 and 3000 Hz which, incidentally, includes most frequencies used in speech. Sounds outside of this range don’t register as well, and end up sounding much quieter, even if they have the same amplitude.
Timbre
The timbre, or colour, of a sound is how it feels different when coming from a guitar versus a trombone or a steel drum, even if they’re playing the same note. The difference originates from the unique set of overtonesthat an instrument produces. Wait! What’s an overtone, Mike? Well, when you play a certain note, its pitch results from the wave’s frequency. Overtones refer to all the other frequencies that you didn’t even know you were playing. I’ll explain.
The simplest example is plucking a string on a guitar.
The string is pulled taught from the rest position to its highest point. Once released, it passes through the rest position to its lowest point, and back. This cycle of high-low-high is repeated at the string’s fundamental frequency, which produces the desired pitch. (For example, if this cycle repeated 440 times per second, it would be an A). However, the vibration of the string is a little more complicated than it first seems, and requires us to think in terms of wavelengths as well as frequencies.
Since the string is fixed on both ends, the wave rebounds on itself, creating a transverse wave that is twice as long as the string. In addition to this primary wave, the string simultaneously produces a wave with half the length of the primary. It also creates waves that are a third, a quarter, a fifth (and so on) of the length, all of which repeat across the string. These harmonics are what produce the overtones, accounting for the timbre of the instrument. The overtones have their own frequencies, and give colour to the sound, without interfering with the pitch. For example, the second wave (half the primary’s wavelength) oscillates at twice the frequency, producing a note exactly one octave above the fundamental. The third is a perfect fifth above the second, and the fourth is another octave above the second. (For example, playing A0 would be complemented by A1, E1, A2, C2…)
These waves can be modified in a number of ways, influencing the resulting timbre. The body of the instrument can act as a filter, amplifying certain frequencies while repressing others. This accounts for the distinct sounds between instruments, and different models of the same instrument. The waves are also influenced by the event that creates them. For example, a piano hammering on strings sounds very different from a harpsichord plucking them, and a violin’s bow is another animal all together. These give certain frequencies more or less amplitude, and can even produce inharmonicity (waves that aren’t multiples of the fundamental).
With all these frequencies being produced, though, why do we still perceive them as single notes? Well, our ears and brain work together to seamlessly integrate these complex patterns into pleasing (or sometimes not so pleasing) music. It’s a good thing, too. I have enough trouble learning my way around the chromatic scale; it’s nice that my brain is making it easier on me. If you add too many frequencies together, that musical sound (with a recognizable pitch) will bleed into noise (with no discernable fundamental frequency).
Well, that took a little more research than I was expecting, but I can finally get back to playing Chopsticks on repeat without that unanswered question buzzing in my brain. I have to capitalize on this before another one inevitably takes its place. I’m sure it’ll be as unimportant as it is annoying, like how do metronomes keep from losing the beat? Wait… how DO metronomes keep from losing the beat…?