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Thread: Why are saw tooth waves harmonically rich?

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    Why are saw tooth waves harmonically rich?

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    oohps now reposting in sound design..

    Easy all, quick qu: why are saw tooth waves harmonically rich? Why should they be richer than say e.g a triangle wave?

    Any answers much appreciated!

    Carlos
    Last edited by DJ Carlotek; 03-19-2012 at 04:57 AM.

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    why are saw tooth waves harmonically rich?

    Hey quick qu: why are sawtooth waves harmonically rich? Why should they be richer than e.g a triangle wave?

    Any answers much appreciated!

    Carlos



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    Sawtooth waves have both odd and even harmonics... Each harmonic is equal to the inverse of it harmonic number...so if you have a 100Hz sawtooth wave, it will have harmonics at 200, 300, 400 all the way up to infinity. The amplitude of the 200Hz wave will be half that of the 100Hz and the amplitude of the 300Hz will be 1/3, the 400Hz 1/4 etc.

    Triangle waves only have odd harmonics so using the 100Hz example again it would have 300, 500, 700, 900 etc. The amplitude of a harmonic in a triangle wave is equal to the inverse square of its harmonic number, so if the fundamental 100Hz has an amplitude of say 1 the 300Hz will be 1/3 squared which is 0.111. As you can see the 500, 700 and 900Hz rates shrink in amplitude far quicker than the sawtooth wave.

    So you've got 2 different wave forms
    1. - Sawtooth - lots of harmonics (odd and even) which are relatively loud in relation to the fundamental
    2. - Triangle - Fewer harmonics (only odd) which reduce in amplitude much more quickly as we climb through them, meaning that we hear far more of the fundamental anyway.


    Hope I this helps
    Last edited by maskedsam; 03-19-2012 at 05:44 AM.

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    Quote Originally Posted by DJ Carlotek View Post
    oohps now reposting in sound design..

    Easy all, quick qu: why are saw tooth waves harmonically rich? Why should they be richer than say e.g a triangle wave?

    Any answers much appreciated!

    Carlos
    This is a very good question.

    First of all, the term "harmonically rich" isn't very accurate and really depends on the context. Fact is, all basic waveforms except the sine are harmonically "rich" in some way. The sine has no harmonics at all, it consists of one single frequency.

    But, the term was probably used in a special sense: The sawtooth waveform has a special property that other basic waveforms (triangle, square) don't have. They contain even harmonics, that is, even multiples of the fundamental frequency. This is directly related to it's asymmetry around the zero point. All other waveforms are symmetric around zero and thus only consist of odd harmonics.

    This difference in very important in synth patch design.

    I hope this helped!

    Take a deeper read here, or at least, try to understand the pictures: Fourier series - Wikipedia, the free encyclopedia
    Last edited by moses; 03-19-2012 at 08:09 AM.


    I run Tokyo Dawn Records. Check out my latest audio plug-ins over at the Tokyo Dawn Labs.

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