[sdiy] Analog computers

[Czech Martin]

I think, most components that an analog computer would need,
are readily available in a decent modular synth.
Perhaps piece-wise-linear-functions are missing.
The only thing that is usually missing is the single integrator,
perhaps with controlable time constant.

I think this is some kind of problem, because the integrator input
(be it the - pin of the op amp) is a high impedance node.
So maybe problems arrise when patching cables to that.
If you include the integrator resistor, i.e. patch
behind that resistor, things may get better, but then you need
a variable resistor, 1000:1 or so. 

This thought leeds ma to an important thing: 
analog computers for mathematical
or engineeering work have usually fixed parameters
for the integrator. That is naturally so if you think
for solving a differential equation. 

But this is quite not natural for music work.
The integrator constant will 
usually lead to the notion of frequency, obviously fixed frequency
can be boring and variable frequency can cause all the problems
we discuss here over and over.
Basically all VCA and triangle VCO circuits aim in the same direction.
Another problem is integrator frequency error:
at higher frequencies the additional poles of the integrator become
visible and may fudge the system response.

But since there are working VCA and VCO circuits out there,
I can see no reason why this shouldn't be overcome.

btw.: initial condition setting is important, you should not
omit such a circuit for the integrator. It makes quite a difference
which intial phase of a waveform is present or not and if you
are able to control it.

If you look at synthesis from the analog computer approach,
you program the differential equation of e.g. a simplified
"struck string" model. That means: amplitude, pitch and harmonic
information is computed at once, you do not need VCA, VCO and VCF.
(Of course you can use those modules , too).
In order to get the right response, time scaling as well as initial
conditions are absolutetly essential.

m.c.