Imagine a single musical note, just one, and then envision an instrument playing that note. Think about all the ways that note might differ from another that the same instrument can play. Volume is one difference. Almost all instruments can vary the volume of the notes they produce, and most instruments can also alter the tone, allowing you to produce bright, open sounds or darker, more closed ones.
I expect that the first variable you imagined was pitch. A musical instrument's ability to produce different pitches is nearly always its greatest strength. Pitch lets us sing melodies, strum chords, and create four-part barbershop-style harmony if that's what we want to do. But what exactly is pitch, and what are the ways it can be used, manipulated, and honed in any musical production to make each piece of music unique?
We tend to think about music as an arts subject, but when it comes to pitch, it helps to think in terms of science. You might have heard the term "A440," and you may even know that this is a specific pitch used by orchestras when tuning up before a concert or produced by a tuning fork. If you strike it against a surface to get it resonating, A440 refers to the note A and its fundamental frequency, which is 440 Hz. Hertz, abbreviated as Hz, means cycles per second and refers to how many times in one second a waveform shape is produced, or how many times it oscillates through a full cycle, equating to its pitch.
It doesn't matter whether the note is produced by a violin, a trumpet, a sawtooth wave, an electric drill, or even a tuned analog snare drum. If the fundamental frequency of a pitch oscillates 440 times per second, the note you'll hear is an A. So let's explore the term fundamental frequency.
This is the loudest, most recognizable pitch within any sound. If you can sing back a note that someone sings to you, that is the product of your brain latching onto a fundamental frequency, hearing it as the loudest portion of the note, and then your vocal cords reproducing it. When I say the loudest portion, I mean that pitch is complicated. In addition to hearing the fundamental frequency, whenever we hear a note being played, we also hear a multitude of harmonics or overtones triggered on top of that fundamental frequency.
Imagine a piano, a violin, and a trumpet all playing the same note, which we might call A clearly. The pitch of those notes is the same in all three instruments, yet violins, trumpets, and pianos sound very different. That's because the harmonics, triggered by those instruments, are different. One instrument might have more harmonics, for example, or the volume of those harmonics might differ from the harmonics of another instrument.