[sdiy] Silly vector synth question

[Tristan]

Interestingly, the circle approach should give a perfect linear mix
for 3 oscillators spaced 120 degrees apart around the circle.

On reflection, for 4 or more oscillators it has the weakness that
component 2 will be an equal mix of all sources, even when the vector
position has differing distances from each source. For a true 4 source
x,y vector approach, as you move from the circle to the centre, the
source at 180 degrees around the circle should initially be weaker
than the two at 90 degrees. With large numbers of sources on the
circle, moving the vector control toward the circle would emphasize
that wave position but only against an equal mix of all other waves.

However, with 3 sources on the circle, spaced 120 degrees apart,
and a 4th independent source as component 2, you could have 3
mix zones each offering different mixes of 3 of the 4 sources.
But this would only ever have a mix of 3 sources at once.

/Tristan

Monday, February 7, 2011, 6:38:49 PM, you wrote:

TW> I think the clever part of Sequential's original vector mixer is
TW> that it manages to get most of the "useful" settings of a four
TW> oscillator mixer whilst reducing the complexity significantly.
TW> There are many settings of a four-input mixer that you can't do
TW> with a joystick, but there are other limitations that you can
TW> impose (you probably want a reasonably consistent signal level,
TW> for example). The Sequential vector mixer gives you most of those
TW> useful settings (you still can't get a equitable three-osc patch
TW> though) with only one waggly knob.
TW> If you're thinking of redesigns, you need to capture this same
TW> quality of simplicity and utility.

TW> T.

TW> On 7 Feb 2011, at 05:22, Tristan wrote:

>> 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
>>>