  A white noise signal can access any possible configuration of values, though
statistically over many samples tends to a uniform spectral distribution, and
is highly unlikely to produce intelligible sound. But how unlikely? The
probability that white noise generates a music-like signal over different
durations is analyzed, based on some necessary features observed in real music
audio signals such as mostly proximate movement and zero crossing rate. Given
the mathematical results, the rarity of music as a signal is considered
overall. The applicability of this study is not just to show that music has a
precious rarity value, but that examination of the size of music relative to
the overall size of audio signal space provides information to inform new
generations of algorithmic music system (which are now often founded on audio
signal generation directly, and may relate to white noise via such machine
learning processes as diffusion). Estimated upper bounds on the rarity of music
to the size of various physical and musical spaces are compared, to better
understand the magnitude of the results (pun intended). Underlying the research
are the questions `how much music is still out there?' and `how much music
could a machine learning process actually reach?'.
