[sdiy] Chorus question

[Scott Nordlund]

I was actually just thinking about this the other day before getting confused and giving up. If you're doing a DSP delay with a fixed sample rate and interpolated delay read, it's pretty straightforward. The pitch change is proportional to the derivative of the modulating signal, so a triangle wave modulator results in square wave pitch change. There's some additional complexity here if you want to ensure that the detuning is symmetric, i.e. the amount of detuning in cents is the same for the rising and falling portions of the modulator. The solution is to vary the shape of the modulator depending on modulation depth.

But anyway, you'd think that since a triangle wave is frequently used as a modulation signal in BBD delays that it would be the same. It's similar but not identical, and I think this is part of why BBDs are sometimes preferred for chorus effects. 

So here's the problem: a modulated DSP delay is like a tape delay with a movable playback head. A modulated BBD delay is like a tape delay with variable tape speed. I was trying to formulate some way to make these equivalent without using an interpolated delay write (which would be the more or less straightforward way to do it). It's easy to demonstrate the difference if you have, for example, a VCO-clocked digital delay. You can turn the delay time knob and notice that the pitch change persists after you stop turning for the length of the delay. For a DSP delay, the pitch change would stop instantaneously.

I tried to sort of restate the problem, but didn't work through it all the way. Basically, you can think of the variable rate case as traversing a fixed distance d at a variable speed v(t). Distance traveled D(t) is the integral of v(t) with respect to time. I think the goal is to solve for the time interval T(t) that it takes to traverse
 the distance (i.e. D(t) = d), and use this to make the two cases equivalent. 

I think you could emulate the BBD behavior in DSP by putting the modulator through some sort of self-modulated delay. But I'm hesitant to really give this the attention it warrants, as it's distracting me from other stuff...


> From: tom at electricdruid.net
> Date: Tue, 22 Apr 2014 17:17:58 +0100
> To: tom at electricdruid.net
> CC: Synth-diy at dropmix.xs4all.nl
> Subject: Re: [sdiy] Chorus question
> 
> Ok, here's a link to what I've got so far:
> 
> http://www.electricdruid.net/ChorusStudy.html
> 
> You can see the way a simple sine modulation gets bend out of shape by the changing delay.
> 
> T.
>