Bill Finnegan claimed that the hard-clipping 1N34A germanium diodes are the signature component of the Centaur's sound. However, testing by ear, as well as waveform analysis have since showed that, if anything, the effect of these diodes is marginal.
There's quite a bit of gain on tap, and that, combined with the hard-clipping diodes means the Centaur can hit distortion territory if required. At the maximum settings on the gain control, it's an almost square-wave distortion, caused by clipping inside the op-amp. Most players, however, value its touch-sensitivity and run it at much lower-gain settings.
Key to the circuit are two filter networks that amount to a clean blend. The first is controlled by the dual-gang gain control. As gain is increased, a filtered clean signal that runs in parallel is reduced in amplitude, and vice-versa. This is another reason why players running it at lower gain settings find it to be the 'cleanest' boost or drive that they've played.
The second network is more simple, adding a bit of 'thickness' back into the tone. This applies a low-pass filter to the clean tone, which is then blended back into the distortion sound. Each of these waveforms - the two filtered and the distorted - are radically different to one another. It's their sum that makes the Centaur so interesting.
All of this detail serves to point out that most of the magic happens in these filter networks and the gain stage itself. Though the original tone control is interesting - an active high pass shelf above 400Hz - modifying the EQ stage doesn't affect the essential character of the circuit as much as you might expect.