It might not be something you’ve ever really thought about, but if I were to pose the question “why does that piano sound so different to my harmonica?” what would be your answer? We all know and recognize a large number of different sounds and instruments, but the reasons for this are not as clear as you’d think.

There are three main principals in the recognition of a sound, the Transient or Attack, the Overtone series, and the Flux.

First, I need to point out that it’s common for us to represent sound waves as transverse, it just looks better and is more easily understood; The problem with this is that sound is not a transverse wave, it’s a longitudinal wave:

Changes in air pressure vibrate the tympanic membrane in our ear, which goes on to create an electrical signal that our brain interprets as sound (If a tree falls in the woods and nobodies there to hear it, it does NOT make any sound, because sound is only produced by something that can interpret it as such).

What we hear as pitch is related to the frequency of the waveform, represented in Hz, or cycles per second. What we hear as loudness is related to amplitude, the distance between the resting point of the wave and it’s peak. You should remember that the terms are not interchangeable, the frequency and amplitude of a wave can be measured, but the pitch and loudness are our interpretations of them, and as such are different from person to person.

When we play a note on the guitar, the string vibrates (A transverse wave), which moves the air molecules around it (Longitudinal) — Here comes the tricky part, what we hear is not a single note, the string does not vibrate in one form.

The note we play is known as the fundamental frequency/tone, or the first harmonic, which is the vibration of the whole string in a single wave form; yet the string also vibrates in a number of other forms, such as in half (2nd harmonic/1st overtone), in thirds (3rd harmonic/2nd overtone) and so on. It’s the relationship between the fundamental tone and the overtones that give each instrument it’s unique sound, it’s timbre — while a violin and guitar can both play a middle C, each string will react slightly different in regard to these higher frequencies. The result is a complex waveform that consists of a number of different frequencies playing altogether, some stronger and more present than others.

If we play a note at a single frequency, without the overtones, we’d have a simple sine wave:

When we play a note on a guitar or other instrument, the result something more like this:

That’s not the only dimension to this question however — it’s been shown that if we take the initial attack or transient away and only play the remaining tail of the audio, the instrument is very difficult to determine. That means that if I were to pluck a guitar string but somehow silence that initial hit, you would have a harder time telling what instrument I was playing.

The attack is an essential part of the audio, but it’s not like the rest of the sound—it’s not a simple series of overtones like we’ve seen previously, it’s actually a large mess of different harmonics and frequencies all at once, it’s only after this initial transient that the sound settles into its ‘comfort zone.’

Once the initial strike settles and the overtones become more apparent, we reach the flux stage. At this point, the sound begins to change over time, the overtones don’t maintain the same relationship with the fundamental frequency all the way through, some will die off while others will become stronger—this is more present in some instruments (gong, cymbals) than in others (A trumpet is rather steady).