Dither—my explanation of how it keeps details below quantization level, Was: "Dither" (TOS #6) Options

[KMD]

To help with the understanding of dither, I am posting an explanation, of how signal details smaller than the quantization level are retained, after quantization, when Dither Noise is added to the source material.
A small signal detail with height less than the quantization level, and centred half way between two quantization steps, is too small to cross a quantization step. It is lost when the waveform is quantized. With a Dither Noise waveform added, the height of the two waveforms summed is occasionally greater than the quantization level. At these occasional points the waveform crosses a quantization step. So now when this waveform is quantized, although the result is noisy, the shape of the original signal detail is retained.
Discussion invited.

[NullC]

I highly recommend the first few sections of this thesis for a careful technical explanation of how dither works and why it's important. It starts with the sampling theorem, shows how quantization breaks it, then shows how dither (of the right kind) fixes the breakage. It's well worth the read, even though the latter parts are dealing with image processing rather than audio.