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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Timbre is the word that describes the quality you’re describing. While pitch is the frequency of the note, 440 Hz for A, the shape of the sound wave is not a perfect sine wave. The variation in the shape of the wave will contribute to the quality of the sound.
Materials and sound reflection mostly.
With different materials u can get “different” sounds. It’s like the: what weights more? 1 pound of feathers or 1 pound of steel?
It’s the same result but the amount of (in this case how the sound moves through the materials and the shape of the item) is different.
Anytime you play a note on an instrument, you are actually getting many different overtones of that same note, but higher octaves. So, if you play an A (440 hz), you will also get some sound of the next A (880 hz), and so on. The volume of each of these overtones is specific to the instrument played, so pianos have a specific pattern of volumes that we can recognize.
ETA: Here’s a link with some really good pictures of graphs showing what I’m describing: [link](https://vibrationresearch.com/resources/overtone-comparison-obserview/)
It’s physics. Sound is developed by a resonance of an object, or system. A violin resonates along its strings and through its wooden form. A piano similarly resonates along its strings and wooden and metal soundboards. The length and tension of the strings affects the sound, as well as the shape and size of the sound board or body of the instrument.
Any sound can be described as a combination (or sum) of many different pitches (or notes), each with different volumes. We can artificially create a note that is A440 with a sine wave that only requires one pitch to describe (a sine wave at 440 Hz), but most tones aren’t that artificially simple. A440 on a violin is actually described by an infinite number of pitches all resonating together (just that the vast majority of those pitches are imperceptible). We hear it as 440Hz because that is the loudest pitch of them all, but also because the next loudest pitches in that tone are all *harmonics* of 440Hz, which means they reinforce the fundamental (generally the lowest pitch in the harmonic content).
There is also an envelope which affects the sound quality of an instrument. The easiest way to think of this is how you make word sounds with your mouth. Just go “oo-ah-oo-ah” out loud. It’s the same fundamental pitch, but the tone changes depending on the shape of your mouth. The shape of your mouth acts like a filter which dampens or augments certain harmonics of the note you are singing. The shape of an instrument has a similar effect.
The timbre, or sound quality of an instrument is created by the unique harmonic content, as well as its envelope and how that envelope interacts with the harmonic content.
When you play a note on an instrument, the instrument will produce the fundamental frequency, for A, this is 440Hz. But the instrument also produces harmonics. Harmonics are integer multiples of the fundamental frequency. For an A, the 2nd harmonic is 880Hz, 3rd is 1320Hz, etc…
You might also get subharmonics (integer fractions), ie, 220Hz, 110Hz, and maybe even harmonics of the subharmonics, so 660Hz, 1100Hz. Although these usually occur at much much lower amplitudes.
Essentially the relative amplitudes (and phase!) of all of the harmonics together create the specific timber or tonality of the instrument. This is why a violin will sound different from a piano.
Even laboratory sin wave generators cannot produce perfect sin waves, harmonics will always be present, although typically at *very* low amplitude compared to the fundamental.
The overtone patterns that different instruments produce are an important part of the picture. Clarinets and Oboes have very similar sound production, but sound distinctly different because Clarinets are “missing” half of the prominent overtones compared to an oboe.
But the way that the sound changes over time is also very important component. When you pluck a guitar string, the snapping back produces a bunch of random fluctuations, which we interpret as unpitched noise (but only for a few milliseconds). But as the string vibrates, the vibration acts as a filter that dampens overtones, so as the sound decays, it not only gets quieter, but trends closer to a pure sine wave.
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.
If you looked at the sound waves from both instruments, you would see two waves with the same frequency (number of repetitions over time) since frequency controls the pitch of a sound, and maybe even the same amplitude (height of the wave) which controls the volume. However, these are not the only two qualities a wave has: there is also the shape of the wave.
The shape of the wave is what determines everything besides the pitch and volume, and we refer to this as the timbre of the sound. There’s no easy way to tell exactly what kind of sound a certain wave shape will produce, though in general the more jagged the wave is the more harsh the timbre will be.
This is getting a bit technical but this is why: the “purest” shape of wave, in a sense, is a sine wave, the wave you get by measuring the height of something as it moves around in a circle. Any other shape of wave can be represented as a series of sine waves of different frequencies overlapping one another. Thus, if a sound wave is anything other than a pure sine wave, what you are really hearing is a root note with a bunch of higher frequency notes stacked on top of it. These higher frequency notes are called overtones, and our ears magically interpret them all as adding timbre to the root note rather than as their own individual sounds, but you can pick them out some times if you listen closely. Anyway, this is why jagged waves sound more grating and harsh, because the overtones present in those shapes of waves are really really high frequency.
All of this is still assuming that sound waves repeat forever and don’t change over time. Another big reason instruments sound different from each other is the envelope of the sound, or how the sound changes over the duration of a note being played.
They are also made with different materials, and expressed differently. A guitar string is a plucked or strummed metal/nylon string. A piano is a little hammer hitting multiple tuned strings. A cello/violin is often used with a bow, which changes the sound. And we’re not even touching on synthesizers, tuned drums, brass/woodwind and the tons of other ways a single note can be created.
Basically, a note is just a pitch, there can be millions of sounds that can make that same note.
Even on a single guitar, you could play a single note on multiple different places on a guitar, and it will sound different in each spot. Tension of the strings, how you manipulate the string/fretboard (vibrato) and how you pick/strum the string, all make a difference.
A tuning fork comes closest to a pure sine wave. No harmonics or overtones. So all tuning forms should sound the same.
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