Jul 12, 2011 at 1:49am

I’ve been reading about using Fourier Series harmonics to create other wave types from sine wave harmonics. The context of all those readings infers that the process is additive synthesis. Yet, when I attempt to add harmonics together, I don’t get the desired result. My guess is I’m doing something wrong, so could someone explain to me why this example doesn’t look work? I have combined the first four harmonics at 1/h in amplitude which I thought would begin taking the shape of a sawtooth, but it doesn’t. Thanks!

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#57981
Jul 12, 2011 at 2:50am

You’ll need to phase-align the individual cycles to get the waveshape you’re looking for, though in fact the timbre will be nearly identical either way, as long as the phase differences are static. You’ll also need a lot more than 4 harmonics to start to approach a decent complex waveform (sawtooth or any other).

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#208055
Jul 12, 2011 at 3:02am

Thank you Steven, that’s exactly what I was looking for! Yeah, I know you need more than 4 oscillators, I just did that for the example. It was the phase alignment thing I wasn’t getting. I had tried 1. and 0. for phase alignment, but not 0.75. If I could ask one more question, why does 0.75 work for the phase, but not other valuse? Thanks, again!

#208056
Jul 12, 2011 at 3:21am

I wouldn’t do it this way if I was doing this today, but I have an example called PartialWorkshop that illustrates some of the concepts involved in synthesizing basic waveforms, with simple bandwidth-limiting.

#208057
Jul 12, 2011 at 3:29am

0.25 works too, but changes the direction of the resulting waveform. It basically has to do with what ‘position’ the waves are starting in, so how they mathematically add together to form the composite. Have a look at the following link, and check out in the graph where .25 and .75 are in terms of the waveform for a cosine wave (which is what [cycle~] produces). Hope this helps.

#208058
Jul 12, 2011 at 3:57am

Chris and Steven,

Thanks so much for you explanations. Yeah, I wouldn’t “do” it that way either, I’m just trying to wrap my brain around some concepts, and sometimes just building things in a basic way really helps me understand. Steven, in your last post, you mentioned a line, but it’s not there. I think I see what you mean by the .25 and .75 of a cosine wave, but would still like to see the link if you have a chance.

Again, thanks so much!

#208059
Jul 12, 2011 at 6:25am