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Musical residual noise is created when a noisy signal passes through a noise reduction algorithm. For instance, please see the paper: Esch, T; Vary, P: "Efficient Musical Noise Suppression for Speech Enhancement Systems", IEEE Intl Conf Acoustics, Speech and Signal Proc, (ICASSP): 4409-4412, 2009.

Noise reduction techniques that are relying on spectral weighting rules often generate annoying musical noise artifacts in the processed signal.

What exactly does it sound like? Are there any sample clips available (for example, a wav file before passing through a noise reduction algorithm routine and a wav file after noise reduction with musical noise) for comparison?

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    $\begingroup$ Not a proper answer but low bit-rate mp3 artefacts sound very similar. There are plenty of examples of these around. $\endgroup$ – tobassist Oct 1 '13 at 12:15
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Here's one example: http://www.izotope.com/tech/aes_suppr/

Googling "Musical Noise" certainly turns up a lot of noise music, so I'd suggest looking for academic papers that have web links to sound examples.

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There are some examples in this blog post.

http://iosr.surrey.ac.uk/blog/2013-12-16.php

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