[aurelian15]

As you expected, you probably shouldn't read to much into these calculations. ;-)

The Shannon-Nyquist sampling theorem guarantees that we (as in the DAC in your computer) can perfectly reconstruct the analogue signal for any discretised signal that is bandlimited to frequencies below Nyquist, i.e., 24 kHz for a 48 kHz sample rate. No matter how crooked the sample points may look to you. And 440 Hz is way below the 24 kHz limit.

Sure, this doesn't take quantisation into account, but 16 bit is sufficient to encode the difference in amplitude at the individual sample points between 440 and 440.8175 Hz with plenty of headroom (about 210 digital steps at 109 samples). Indeed, the smallest frequency difference that would have a zero difference after 109 samples due to quantisation is about 0.001 Hz (modulo mistakes in my hasty calculations). And this doesn't take dithering into account. Dithering essentially gives you an infinite dynamic range (depending on your definition of dynamic range) at the exchange of a higher noise floor. Of course your signal is likely also longer than 109 samples.

See this excellent video [1] by Xiph.Org's Chris Montgomery for a whirlwind overview of digital signal processing.

[1] https://www.xiph.org/video/vid2.shtml