So if an A is 440hz, why does a piano playing an A sound different than a violin, a guitar, or someone’s voice making that same A 440 note? It’s obvious that the pitch is the same on each instrument but each instrument has a distinct sound. I’ve never heard an A on a piano and thought, is that a piano or a cello. Why can we distinguish between instruments?
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Mainly two things: harmonics and temporal characteristics.
When you play a note on an instrument, you never get a pure frequency. Instead, you get the frequency of the note plus a bunch of *harmonics* that are multiples of that frequency. The harmonics are always less powerful than the fundamental frequency, but how powerful each harmonic is differs across instruments. The unique mixture of harmonics is part of what defines an instrument’s characteristic sound.
This is not the whole story, though. Harmonics mainly influence how a note sounds in its sustained phase. But there are also differences in how the notes played on different instruments begin and end. Broadly speaking, you can divide the sound made by an instrument into an *attack*, *sustain* and *decay* phase. The *attack* is the way the sound begins. For instance, a note played on a piano starts with the percussive action of a hammer striking one or more strings. That hammer strike makes its own noise that is different from the vibration of the strings. After the hammer strike comes the *sustain* phase, which on a piano is just the strings vibrating. How the note *decays* depends on the use of the sustain pedal. If the pedal is depressed, the strings just keep vibrating while gradually losing energy, so the sustain and decay phase basically merge into one another and the decay is very long and gradual. If the sustain pedal isn’t used, then when the piano key is released, a damper makes contact with the strings and quickly ends the sound. A sustained piano note thus sounds a bit like a harp string, while a *staccato* piano note (played by quickly pressing and releasing the key) makes a sound somewhat more similar to a xylophone.
Other instruments can have very different attack and decay qualities. Guitar strings are plucked or strummed with fingers, finger nails or a metal or plastic pick, rather than hit with a hammer. Flutes derive their attack properties from the characteristics of human breath, and have no decay to speak of – a note played on a flute is sustained as long as the player keeps blowing, but ends pretty much immediately after. And so on and so forth.
It’s much easier to recognize an instrument if you don’t just hear the sustain phase but also the attack and decay of its notes. Harmonic profiles can often be more similar (though still unique) between instruments. Interestingly, harmonic profiles are also easier to imitate. You can do this using electronic synthesizers, but the “OG synthesizer” was the pipe organ. Pipe organs are pretty unique instruments in that they can produce nearly perfect sine waves – single-frequency sounds with almost no harmonics (if you’ve ever heard a perfect sine-wave tone, perhaps it reminded you of a pipe organ – this is why it did). But each key on a pipe organ is connected to multiple pipes. By opening or closing “stops”, the organ player can control which pipes the air flows through (and how much) when a key is depressed. One pipe will be the note’s fundamental frequency, while other pipes are – you guessed it – harmonics of that frequency. Thus, the organ player can use stops to alter the harmonic profile of the organ, and thus *somewhat* imitate different instruments. Of course, you can only imitate the sustain phase this way – it’s not possible to emulate the attack and decay of other instruments that have totally different mechanisms for producing sound. So a pipe organ will never sound anything like a guitar, but it can sound a bit like a bassoon or trumpet, for instance.
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