sawtooths and other continuous waveforms

[AJYoung]

That's a whole deep topic on DSP and oscillator design. Some synths generate it mathematically in real-time. Others are sampled, others still have table-based lookup, etc. Gets even more complex once you start factoring in FM or RM operations between oscillators.

It's going to differ for almost every synth.

Since you brought up Sylenth, I'm fairly sure that it's oscillators are based on wavetable-lookup. Not exactly "sampled" per se, but several different versions of the waveform pulled from memory depending on the pitch of the oscillator.

Run Sylenth through a frequency analyzer with just the basic Saw wave, and go up and down the keyboard. You'll notice that at one or two places, the number of high harmonics changes. That's the switch-point between different values on the lookup-table.

This is not to be confused with "Wavetable Synthesis", such as synths like Serum, Rapid, etc. Those have yet their own different way of generating a waveform.

[m@RV]

and there is the issue of how digital synths ha...

[Initium_Thoth]

The benefit of using table-lookup(slightly diff...