FabFilter

This only happens if you have "Gain-Q interaction" enabled. :) It's the little gear-like button between the Gain and Q knobs:
www.fabfilter.com/help/pro-q/using/bandcontrols

Cheers,

I've definitely not enabled the Gain-Q interaction: it isn't purple, which it presumably would be, were it activated.

I've included screenshots of a curve which demonstrates the differences between the expected valued produced by REW and the ones obtained in FF.

i.imgur.com/4alJKps.png
i.imgur.com/zks9nBc.png
i.imgur.com/a5HFcWO.png

That REW thing seems to be taking a little shortcut there by plotting the bit from 1k to 10k on a much smaller part of the y axis as the other octaves. So the q seems smaller but probably isn’t.

Here is the region between 1000 Hz and 20 000 Hz, zoomed in significantly:

i.imgur.com/SRaDhyI.png

It still doesn't quite explain the discrepancy between the curve in REW and that in Pro Q - but perhaps this does. From the REW website, www.roomeqwizard.com/help/help_en-GB/html/equaliser.html :

"The Generic Equaliser supports a full range of filters and filter settings (peaking = parametric, low pass, high pass, low shelf, high shelf and notch) based on the Robert Bristow-Johnson 'Cookbook' equations."

The said equations, in part, can be found here: www.w3.org/2011/audio/audio-eq-cookbook.html

Looks like REW is cramping near Nyquist, see here, which mentions specifically the Bristow-Johnson equations causing this:

vladgsound.wordpress.com/2015/01/12/a-classification-of-digital-equalizers-draft

Pro-Q3 is fully decramped in Natural Phase and almost so in Zero Latency, hence the discrepancy.

Cheers,

Just to clarify what I mean by "fully" and "almost" decramped: neither mode will result in a narrower bell than the equivalent analog one, but Natural Phase matches the shape exactly, while Zero Latency has a small deviation as it approaches 20kHz. See the plots in the Processing Mode section of the Pro-Q3 manual.

Cheers,

What a fascinating topic! I'm very glad I enquired, rather than just trying to figure it out on my own.

REW offer several types of eq emulation, as seen here: www.roomeqwizard.com/help/help_en-GB/html/equaliser.html. Which is the closest to Pro Q? I'd ask what Pro Q's equations are, that I might select the eq emulator myself - but I assume these are proprietary.

I was informed by the lead dev of REW in this (www.avnirvana.com/threads/new-eq-selection-request.4785/post-38766) post, that the Q factor scalar, seemingly derived from the cookbook mentioned above, is "sin(omega)/omega where omega (radians) = 2*Pi*Fc/Fs, Fc = filter centre frequency, Fs = equaliser sample rate.". Through trial and error, I discovered, that the inverse of this, namely omega/sin(omega), multiplied by the root 2 times the q value given by REW gives a very close approximation of the q value used by ProQ, iff Fs in REW >= 88 200 and Fs in the equation = 48 000. Clearly, this is not the correct equation: large gain values at large Fc values produce the wrong curve. Note that changing Fs in the equation to both a larger number, say, FsREW = FsProQ, and a smaller number, say 44 100, worsens results.

Can anyone give the correct equation? I'm assuming that the problem does not lie in the value of Fs - but it might. I've tried several values, all to no avail.

I would expect that scaling factor to work only to an extent as cramping is going to happen no matter what with a non-decramped EQ such as REW, so there's only so much you can compensate. Basically you're not going to find an equation that allows you to match a decramped EQ to REW exactly. I would also expect Fs to affect the results since the higher it is, the further away a given filter will be from Nyquist (=Fs/2) and the less cramping will occur.

As for the sqrt(2) factor you found, that's correct, for simplicity Pro-Q's Q is scaled by that factor (with respect to most other EQ's) so that for example a Butterworth high or low pass has a Q of 1 rather than 0.707, and the same applies to bell filters, I guess for consistency's sake.