Amplitude scaling invariance
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Amplitude scaling invariance is a symmetry of music. It corresponds to our ability to recognise the same item of music played more loudly or more quietly. It is not specific to music (or speech), because the brain must necessarily be able to recognise the equivalence of sounds that vary in perceived loudness because their source happens to be correspondingly closer or farther away.
Although seemingly trivial, it may be non-trivial for the brain to implement. In particular louder sounds actually activate a larger set of sensory cells in the Organ of Corti, so it is non-trivial for the brain to recognise the equivalence of softer and louder versions of the same sound.
One aspect of music perception which is not invariant under amplitude scaling is that our level of enjoyment of music that we like is increased when that music is played more loudly. A common consequence of this preference is deafness caused by listening to over-loud music. Other emotional impact can also be effected by volume, haunting music for example may be perceived differently at a louder volume.
