In "The Man Who Mistook His Wife For A Hat," there's a chapter where Oliver Sacks makes a similar argument about music stemming from the case of two autistic twins who couldn't do arithmetic but played a game with each other where they named increasingly large primes. Basically says that music/harmony is a kind of innate appreciation of the numerical relationship between sounds, much like naming primes is an appreciation of the _lack_ of a numerical relationship between numbers. The experience of a resonance between two different things (frequencies, numbers, and in this blog's case words) can exist extremely strongly outside of the ability to operate on those things in the first place. Interesting read.
I've read that music and dancing memory is mainly handled in the cerebellum, which is separate from many other types of memory. This is also theorized to mostly explain why playing familiar music can help "stabilize" people with dementia who otherwise feel lost (funny enough also something Sacks has talked about[0]), because the cerebellum is typically less affected than the neocortex by whatever process is causing the brain to break down.