[sdiy] Silly vector synth question

[Tristan]

I like this idea!

But if component 1 was represented as a circle rather than a square then you could have an 
arbitary number of different sources, uniformly or non uniformly distributed, around the circle. 
Moving the stick around the edge of the circle would give a crossfade between each successive pair 
of sources. This would be like wavetable/wave sequencing.

Component 2 would be the sum of each of the sources divided by total number of sources. So 
moving the stick closer to the centre of the circle would crossfade from the wave mix at that angle 
on the circle to the sum of all sources, as for vector synthesis. You could also add quirks by adding 
additional sources to component 2 that are not present on the circle or removing sources present 
on the circle. Changes in the number of sources in component 2 would require adjusting the divisor 
accordingly. 

So for one source on the circle the vector movement would have no effect. For two sources 
distributed at 180 degrees on the circle you would get a linear crossfade. But for 3 or more sources 
you would have many interesting vector synthesis possibilities.

/Tristan

On Mon, Feb 7th, 2011 at 3:26 PM, Richard Wentk <richard at wentk.com> wrote:

> I'd guess it works like this:
> 
> Component 1 is a simple four axis volume control, with zero in the middle.
> Pushing the stick N scales the N output from 0 to 1, but with no S.
> Pushing it S scales from 0 to 1, but with no N. E+W work similarly.
> 
> Component 1 gives you the correct mix around the edges, but creates a zone
> of silence towards the middle. 
> 
> Component 2 is a static 0.25*(N+S+E+W) mix of all four components that
> fills in the zone of silence. 
> 
> The relative mix of 1+2 is scaled by the *radius* from the centre
> position. So when the radius is 0, you get component 2 only, with the
> correct centre mix. When radius is 1, you get the edge mix from component
> 1. 
> 
> For all other radius values, you get a correct proportional mix of all
> four components.
> 
> Doing the rect to pol conversion is slightly more work, but you only need
> to do it for each control change. 
> 
> I'm not sure linear scaling covers this. At - say - NE, you should get
> 50:50:0:0. If you use linear scaling, you get some element of W+S mixed
> in, because the x & y distances from W+S aren't 100%.
> 
> R
>