That is only half of it. The first demo shows that a tone at < 96dB is still above the noise floor even with flat quantization noise. Shaped dither just improves things further. SNR is already > 96 on a band basis, which the article I linked later goes further into.
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.
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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.
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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).
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