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Why does the same frequency sounds differ?

  1. Feb 24, 2013 #1

    I am trying to generate tones using computer software. I generated a sine wave tone for a frequency of 261.63 Hz, corresponding to middle-C key on a keyboard/piano. But this sound produced is completely different from when I generate it on the instrument.

    Shouldn't all the sounds of same frequencies sound the same? :grumpy:

    Could the difference be because of the specific software I am using (and not something wrong with naturally occurring sound waves :biggrin:) ?
  2. jcsd
  3. Feb 24, 2013 #2
    Not all (sound) waves are sinusoidal
    Look up waveforms
  4. Feb 24, 2013 #3
    The difference in sound is not because of your software. It is because most "real" sounds are composed of more than just one frequency. What you have generated is only the fundamental tone of the note middle C. The timbre of a piano--its distinctive sound--is a sum of many harmonics of that pure sine wave you made, as well as some effects due to the physics of the piano's strings and its geometry. To be able to create an authentic piano sound you would probably have to model it with techniques from signal processing.
    Last edited: Feb 24, 2013
  5. Feb 24, 2013 #4


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    cwilkins is correct. A synthesized pure frequency sounds very dull. The rich sound of real instruments is precisely because there is a broad spectrum of other sounds besides the pure frequency.

    If you listen to synthesizers in the 80's when they first became popular you can easily hear the very artifical sounding tone. This is precisely because the computers of the time were limited and could produce tones with only a very few harmonics, if any. As computer power progressed, more harmonics could be added, making synthesized tones be further and further from an ideal pure tone and closer to natural tones.
  6. Feb 24, 2013 #5
    All you need to do to get zillions of harmonics is amplify your tones until they overload the amplifier.
    But real instruments have startup and decay transients and tremulo and vibrato (oft caused by the inevitable coupling between the vibrations of one string and another and the ELIPTICAL motion of precessing strings.
    Many string instruments use 2 or 3 strings per note especially to enhance this effect
    Due to temperature changes (speed of sound) a reed organ pipe goes out of tune with the other pipes of the same organ - giving beats.
  7. Feb 24, 2013 #6
    This is really interesting. They should have a 'music physics' course in every university.
  8. Feb 24, 2013 #7
    Thanks for the replies.

    If I get it correctly.. then you mean to say that the piano sound of middle-C contains all the harmonics of the fundamental frequency 261.63 Hz.

    But that should not be the case... since the 'C' of all the octaves are harmonics of each other. (261.63, 523.25, 1046.5, 2093, 4186 Hz).

    If the middle-C contains all the harmonics of the fundamental frequency, then, e.g., playing middle-C alone, should be indistinguishable from playing it with the C of the higher octaves... But there is an observable difference..

    What am I missing?
  9. Feb 24, 2013 #8


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    The harmonics are softer than the main note.
  10. Feb 24, 2013 #9
    We talk of the "timbre" of a piano. Thus we recognise it from how it sounds.

    Middle C on the piano starts with anharmonic "noise" for a millisec or so while the higher anharmanic frequencies die out
    But pretty soon the "interference" between waves on the string leaves behind only SLOWLY decaying harmonics of intensities depending WHERE on its length the string was struck and how HARD it was struck and how quickly the hammer lay in contact with it before it bounced off.

    The ear is HORRIBLY nonlinear and the brain (TWO WAY communication real-time with the cochlea!!!) does a marvellous job of sorting it out to our satisfaction (acting as both judge, jury and audience!!).
    Among many other things the brain SUPPLIES the fundamental tone if perchance in the "real world" it be absent!
  11. Feb 24, 2013 #10


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  12. Feb 25, 2013 #11
    It is the same note or tune. If not, your instrument needs tuning. The note (tune) is determined by the frequency and will be recognised as such. The actual sound is different as you have noticed. A piano, guitar and singer can all follow the same tune yet sound different.

    The octave thing you asked in a later post (where C4 and C5 have different frequency yet are said to be the same note) is just to do with the arbitary definitions of western music. We call it the same note but 1 octave higher, but only because the guy who taugt us called it that, and he the guy before him, back until whenever it was defined.
  13. Feb 26, 2013 #12


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    how boring music would be if all instruments sounded the same
  14. Feb 27, 2013 #13


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    I think it's a shame that you guys always forget to mention the fact that real instruments generate Overtones and not Harmonics. Overtones of distributed mechanically oscillating systems are not necessarily exactly harmonically related to the fundamental - because of end effects and the finite width of air columns etc.. This means, for instance, that brass instruments with conical bores will sound markedly different from the equivalent instrument with cylindrical bores (Trumpet vs Cornet etc.). Synthesising overtones is a lot harder than sysnthesising harmonics and there's no point in sampling instruments and scaling up and down to produce different notes because the relationships between overtones and harmonics will vary over the scale. You can't fool an experienced ear'ole.
  15. Feb 27, 2013 #14
    Real instruments? I am out of here before the electro/synth/whatever lynchmob turns up. They are musicians after all. How can you say it's not a "real" instrument? I don't like synth pop stuff but I can play a guitar and I would never say that wasn't real music or wasn't a real instrument.

    It really bugs me how electric violins sound like saxophones.
  16. Feb 27, 2013 #15
    Sophiecentaur that is a good point. Edit: In a real piano tone there will be some bandwidth (frequency spread) on the harmonics.

    For anyone who is curious, I have attached a Fourier spectrum of a piano being struck on the note C3, which has a fundamental frequency of approximately 130 Hz. The solid (unshaded) curve on top depicts the frequency content of the the tone after it has just been struck. The solid orange plot is the frequency content of the sustained note after the transients have decayed (≈200ms). The horizontal axis is in Hz and the vertical axis is in increments of 6 dB. (The top of the plot is -24 dB.)

    Link to the picture: http://www.ocf.berkeley.edu/~cwilkins/piano_sustained_c2.png
    Link to the piano tone: http://www.ocf.berkeley.edu/~cwilkins/piano_c2.wav
    Last edited: Feb 27, 2013
  17. Feb 27, 2013 #16


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    An electric guitar has strings which have overtones and not harmonics (albeit at nearly the same frequencies a harmonics). Any non linear amplification will produce harmonics too, of course. The more 'fuzzy', the more the harmonics will dominate.

    I don't think those plots show that the overtones are exact harmonics. The spectrum analyser has a finite bandwidth and cannot distinguish between the two ( which are close for strings). Your ear will be able to spot beats between harmonics (ear generated) and overtones (from the strings), which will give the 'pianoness' of what you hear.

    A harmonic is an exact multiple of a fundamental and is formed when a single tone hits a nonlinearity. Where is the nonlinearity in a gently struck string? The Overtones correspond to the natural modes of the string. The difference will be small or large, depending upon the instrument but it is fundamental (no pun intended).

    I am amazed that the clear distinction is not acknowledged more widely. But, in a world where the term Fourier is bandied about very casually, it is hardly surprising.
  18. Feb 27, 2013 #17
    Looks like a harmonic to me: 130-260-390-540 etc are integer multiples above the base of 130
  19. Feb 27, 2013 #18
    I see what you are saying. To be clear, my point is that the piano does follow a "sum of modes" model, and that the highest-amplitude frequencies present are those at integer multiples of the fundamental tone. There's a certain amount of bandwidth on the harmonics; I am not saying that the sound is only composed of those pure frequencies. For the sake of this argument I will agree that they are not harmonics in the strictest sense.
  20. Feb 28, 2013 #19


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    It "looks to me" that the accuracy of the frequency measurement is in question - as in all things. Can you (and the measuring equipment) really resolve those frequencies to that degree of accuracy? If it is a digital system then all results are quantised, in any case and the apparent bandwidth in those photos is significant (which it has to be as the sample time is pretty short for an 'struck' and decaying note). The point I am making is that those frequencies come from the vibrational modes, which are Overtones - which often nearly coincide with harmonics of the zerth overtone (the fundamental). It is sloppy terminology that's used and sloppy terminology, in other cases, seems to be important to PF. How bad (what error) would it need to be before the difference in actual frequency value would be enough to acknowledge the difference in name?
  21. Feb 28, 2013 #20


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    Which seems, to me, to be a good reason for giving them the correct name. :smile:
    It could avoid a lot of confusion at times.
    The word Harmonic is also often used wrongly when describing many other of the products when a signal passes through a non-linearity. People must just lurve it so much - it is a nicer sounding word than Overtone, Intermodulation or Cross modulation, which sound a bit deprecating.
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