I have the following patch, built partially from this tutorial...

The idea is that there are two identical audio signals generated by the two oscillators, with a filter applied to only one of them (which one is filtered depends on the value of the horizontal radio control). As intended, when I set the filter frequency to a reasonable number and play a note, varying the value of the radio control has no effect.

However, I when I slightly detune the Cents of the two audio signals so that they are no longer identical, the result I expected was that varying the value of the radio control would yield a very slight variation in the sound, but what actually happens is auditorily similar to Amplitude Modulation (a strong Amplitude Modulation, even for tiny, fractional-Cent detuning). The sound is also bothersome to my ears if I play it too long, whereas Amplitude Modulation is not.

Is there an intuitive explanation for why I get this extreme effect, instead of a very subtle change?

Hi,
The add of two quite-similar sinus results in beats, it's mathematically exact:

@Metronome To elaborate on @FFW, you produced a beat frequency. A beat frequency is the difference between the two frequencies, if your frequencies are 110 and 111hz then your beat frequency is 1hz and it will have an effect similar to amplitude modulation with a 1hz LFO because every 1 second the two sinewaves are 180 degrees out of phase, they mostly cancel each other out and then as the phase move away from 180 degrees sound returns. Beat frequencies are one of the things which determine consonance and dissonance in harmony, if the beat frequency of two notes is harmonically related it will sound more consonant, if they are not they will sound more dissonant. Do the simple math to figure the beat frequency of different intervals and compare that frequency to the harmonic series (Fourier series if you prefer) of the root note (the lowest in frequency of the two notes) you will find a very simple and useful relationship and the foundations of harmony and western music theory and well as other traditions, but those others were not quite as deliberate and did not make this the core of their music.

Interesting, I was aware of the beats phenomenon. However, it had not occurred to me at the time I posted because in my experience, it normally requires much more pronounced detuning to become audible.
Generally, choursing occurs first and beats later as detuning is increased, but the filter seems to be having a very sharp magnifying effect on the beats.