[sdiy] Additive digital synthesis techniques

Brian Willoughby brianw at audiobanshee.com
Sun Feb 14 01:29:02 CET 2021

On Feb 13, 2021, at 14:11, Mike Bryant wrote:
> Hi Brian
> Yes I've been looking at the waveforms Tom linked to earlier.  I think I've worked out how to do it with additive synthesis but need to try it.  The thing is I suspect is that the imperfections of such a system, be in analogue or digital, are actually part of the sound people like and so replicating the pure tones shown by Electrodruid are only half the task.  If so I'll have to borrow a hard sync synth to analyse the waveforms more.

Any periodic waveform can be replicated with additive synthesis, but you need to know amplitude and phase of all the partials. If the relative pitches of the partials occur at non-integral multiples, then you can simply stretch out the buffer long enough to find the point where the partials' periods align again. I have implemented this in situations where it's viable, and I do actually prefer the results because the calculations can be done in advance, along with the buffer allocation and related variables. You can synthesize the individual partials at the output sample rate without SRC, and you can mix in the buffer without much processing at all.

As soon as the ratio of pitches between two sync'd oscillators changes, things get incredibly difficult at the same time that they get more timbrally interesting. Every period has a different shape when the relative pitch changes for the sync'd oscillators.

I think it's fair to say that hard sync is right up there in terms of synthesis techniques - as important as the more well-known ones. I say that because of the ability to create complex harmonics. It's less predictable than subtractive, but nothing is as baffling as FM.

Subtractive synthesis (start with rich harmonics, then low-pass, etc)
Additive synthesis (start with sine wave, if you have enough resources)
Frequency Modulation ... phase modulation is practically the same thing
(amplitude modulation) <- I think this one is relatively limited
Hard sync (of analog oscillators)
Phase-accumulator digital sample pitch shifting (lots of imperfections that some folks like)

Brian Willoughby

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