Recommended range for BPF's rq

Is there a recommended range for the rq values of the band pass filters? I have seen in the video tutorials of Eli, that the range should be “more than 0 and less than 1”. Is there a why for this?

rq can be any nonnegative value, although you’ll get some precision issues if you set it above 20 or so, or significantly less than 1e-6.

A “magic number” for rq is 2.sqrt ~= 1.414, because in low- and highpass filters, this gives the maximum slope without introducing resonance. That is:

  • rq > sqrt(2) (or Q < sqrt(1/2)), rolloff is slower.
  • rq = sqrt(2) (or Q = sqrt(1/2)), rolloff is optimal without resonance.
  • rq < sqrt(2) (or Q > sqrt(1/2)), rolloff is sharper, with resonance.
// requires sc3-plugins and wslib

var n = 512;
var rqs = [2, 2.sqrt, 1, 0.5];

rqs.collect { |rq|
	BLowPass.magResponse(n, 44100, 1000, rq)
.lace(n * rqs.size)
.plot(numChannels: rqs.size);

For bandpass, higher rq just translates to a looser filter. (Though, in practice, if rq is too high, it could increase the risk of blowing up at low or high center frequencies.)


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