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Old 10th October 2020
As others note, in equally tempered systems, the relationships between intervals remain the same, the same piece of music is generally quite recognizable when transposed note for note into a new key.

BUT... pitch context is not nothing... Take a given composition and transpose it up or down a whole octave -- and it's easy to hear at least some aspects of the change in 'vibe'...

That said, I don't think there's anything particularly 'cosmic' about that or about any specific key (or reference pitch, for that matter). The thinking of those who believe the difference between A440 and A432 systems (for example) is something more than an 8 Hz difference in pitch (which is NOT nothing, for sure) pretty much goes right past me.