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    Hi, i'm a maths student and have recently learnt about Fourier transforms. I know that all instruments have an associated timbre. I was wondering if it was possible to remove the timbre and emit just a pure note.

    Would this pure note sound different in different media (air, water, ... )? If yes, what would the pure note sound like if you were to divide the waveform by the Fourier transform of the 'air pure note' Would this produce an even more pure note?

    If this has been looked into before which I expect is highly likely. Please could you link me to any information as I can't find anything :/ Playable music files would be best.

    Thanks, Ben
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    As you might know, analogue synthesisers used to do this in reverse, start off with a fundamental note, a sine wave, and mix in higher frequency harmonics in varying proportions until it sounded like a rather naff version of an instrument. Then you'd apply an envelope to replicate the attack and sustain characteristics of an instrument, slow attack for a bowed violin, fast for a xylophone.

    Going the other way there's an device called a vocoder which started out as a form of lossy analogue data compression , these get some use when people want an 'angelic' or 'robotic' vocal effect.
    If you're interested in hearing some, there's synths and vocoder on the soundtrack to the film 'clockwork orange' and probably plenty of other places too. You can *probably* download a vocoder effect for your pc.
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    (Original post by bencrossley1)
    Hi, i'm a maths student and have recently learnt about Fourier transforms. I know that all instruments have an associated timbre. I was wondering if it was possible to remove the timbre and emit just a pure note.

    Would this pure note sound different in different media (air, water, ... )? If yes, what would the pure note sound like if you were to divide the waveform by the Fourier transform of the 'air pure note' Would this produce an even more pure note?

    If this has been looked into before which I expect is highly likely. Please could you link me to any information as I can't find anything :/ Playable music files would be best.

    Thanks, Ben
    A "pure" note would be a sine wave. No real musical instrument produces one but a tuning fork gets very near. A signal generator produces a sine wave which, if passed through a loudspeaker, generates a "perfect" tone. (Assuming it isn't distorted by the speaker.)

    All musical instruments emit notes which contain various amounts of higher harmonics added to the fundamental (lowest) frequency. This is, as you say, what gives instruments their characteristic timbre.

    I don't quite understand why you would want to remove these higher harmonics to produce a sine wave. If you want a sine wave it is easier to just get a signal generator and generate one.

    The simplest way to remove the higher harmonics, if you really want to, is to electronically pass the sound through a low-pass filter. A low-pass filter removes or attenuates higher frequencies. If your note is, say, 400Hz, then the next harmonic is at 800 Hz, so just set the filter to cut in at between 400 and 800Hz and you have just the fundamental left. (In theory.)
    This is old technology and is (was) the way the old analogue synthesizers worked. In addition to what Joinedup has said, these instruments had oscillators which produced square and triangular waves as well as sine waves. Square and triangular waves contain higher harmonics, and by mixing these all together, and using a low pass filter, you could produce quite a range of different timbres.

    Just do a search on analogue synthesis, low and high pass filters.
    Then try FM synthesis, which was the later version as pioneered by Yamaha's DX7 synth back in the 80s. In this system (rather simply put) sounds are produced by modulating one waveform with another. It's all fascinating stuff but you need to do a bit of searching.
 
 
 
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