[sdiy] SVFs with different gains in the integrators

[Guy McCusker]

In Chris McDowell's recent thread I made an off-hand remark about
setting up an SVF with different gains in the integrators. I don't
know how well-known this is but I'm wondering what list members know
about the history and use of this idea in synthesizers.

The theory, if I have it right, is that with different integrator
gains, the natural frequency is given by the geometric mean of the
unity gain frequencies, and the Q is enhanced by something like the
square root of the ratio of the gains. So you can vary Q without
varying the bandpass feedback.

The only use of this that I know about in synthesizers is the Serge
Variable Slope filter (VCFS). The claimed varying slope is really
varying the Q, so that the slope near the natural frequency changes;
the asymptotic slope is still 12dB/Oct. Are there any other examples?
Does anyone know any more of the history of this idea?

Incidentally, thinking about this always makes me smile at the
marketing smarts of Serge in the 1970s. He marketed three filters:
variable Q filter, variable slope filter, and variable bandwidth
filter. Since Q and bandwidth are the same thing (one is the
reciprocal of the other), and since the variable slope filter is
actually varying the Q, all three of these are in fact variable
bandwidth filters... but he managed to distinguish them by calling it
three different things. Smart!

Guy.