mystran wrote:kryptonaut wrote:For generating bandlimited sounds with 'stretched' (or compressed) harmonics, you can experiment with the formula given on the first page of http://www.jamminpower.com/PDF/Sine%20Summation.pdf - these waves can't be put in a wavetable as they aren't periodic, but they can generate some interesting sounds.
I know this thread is a bit old by now, but you can put these into wavetables --- or rather, you can play any wavetable with stretched or compressed harmonics. It's actually fairly simple (and only slightly more expensive computationally when compared to regular wavetable playback):
Yes, pitch-shifting plus frequency-shifting is another interesting way to make sounds with stretched partials. I hadn't considered doing that with a pre-calculated complex wavetable, that's a nice technique.
My original post was more to draw attention to the sine-series-summation formulae (derived similar to the Dirichlet kernel) that allow you to easily calculate a perfectly bandlimited sum of partials, which can be harmonic or stretched/compressed, and can also be given an exponential decay so that higher frequencies are rolled off or emphasised. Combining two or more of these can give more interesting partial profiles (e.g. notches or peaks), with scope for modulation as well.
It's an interesting synthesis technique to explore, anyway.