Hector Martin

This has nothing to do with dynamic range. Dithering is required in order to have *consistent* quantization noise (a flat white noise floor) and to be able to encode the content with zero distortion. Dithering per se is not a perceptual hack.

Our perception of audio is in the frequency domain, not the time domain. This means that even though, say, a 1kHz tone at -100dB is *below* the broadband noise floor of 96dB, it is *above* the noise floor in a narrow band around its frequency.

That means we can perceive it as above the noise floor. Since music isn't a flat broadband noise source but strongly tonal, this means that the effective dynamic range of 16-bit PCM is *higher* than 96dB, because we can encode the information content above the noise floor.

This is all *without* shaped dither. Shaped dither *further* increases dynamic range by taking advantage of the frequency-dependent response of the human ear, to lower the noise floor in the bands where it most matters.

This is all graphically easy to see on a spectrum analyzer, which is a good visual tool to look at audio the way our ears perceive it. That's why the noise spectrum of dithered silence at 44.1kHz/16 is not -96dB, but significantly lower (depending on FFT parameters).

@xiphmont has a footnote in the article I linked that notes how with an infinite window size, the dynamic range is effectively infinite; of course our ears don't have an effectively infinite window size. We can come up with a representative approximation for perceptual purposes.

Ultimately the real point is: the dynamic range of our ears is defined as the difference between the loudest (ear-damage level) sound and the quietest sound *we can perceive*. Since *we can perceive* a sound encoded at <-96dB in 16bit PCM, that is *not* the dynamic range.

Remember the absolute threshold of hearing is defined for a *pure tone*, not broadband noise! It would be way higher for broadband white noise.