Let's say I'm listening to an AM radio station in the United States at 680 kHz. From my understanding that means there's a carrier wave at 680 kHz and the bandwidth for the station goes from 675 kHz to 685 kHz.
When I move the tuner of my SDR in 1 kHz increments, the AM audio doesn't sound any different until the carrier wave is out of the 10 kHz slice of the spectrum I'm listening to. Once the carrier wave leaves, the audio becomes very garbled, but not high-pitched.
I'm surprised by this, a bit; my naive understanding of tuning slightly off-carrier like this is that, from the radio's perspective, everything changed pitch - the carrier that was at the exact frequency we were tuned to is now at 1 kHz, the spectrum below 676 kHz is gone, and everything is shifted by 1 kHz. Indeed, when I set my SDR to listen directly to the modulated audio, this is what I hear - a 1 kHz tone and everything is pitched up.
I did try to study how AM tuners and demodulators (in general, not specifically for the SDR I'm using) worked, learning about envelope detectors and how they use a simple capacitor and resistor to follow the modulated signal upward and decay relatively slowly. The tuner itself uses low- and high-pass filters (I guess) to clip away anything out of the 10 kHz bandwidth. I also read about carrier recovery, but the Wikipedia article didn't say anything about its use in AM radio.
Here's a video I took of 680 WHBE that demonstrates what I'm talking about.
(sidenote: being off-tune in FM works like I'd expected; the demodulated audio clips as the carrier wave moves in and out of the bandwidth. It's just AM that's not making sense to me.)