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Well, if we agree about Phi-harmonic systems, then the recurrence of Phi everywhere is just an emergent property. There may or may not be a particularly good reason for it at progressively larger scales, but because it's Phi based on the lower levels, it's the default starting point.
As for why we'd use Phi based music rather than, say, e. Presumably, our ears are Phi based, so Phi based chords might set up nodes and standing waves at all the right places in our Phi based ears. e based music would also set up nodes and standing waves, they just wouldn't be in the right places, as far as out Phi based ears are concerned. It's a bit of a chicken and egg problem, honestly. And I don't actually know if Phi shows up in the structure of our ears.
As for "Why Phi?" It could have some empirical advantage over e or 2^0.5 (haven't a clue how to go about evaluating that) or it could just be Phi was the first out of the gate, and the others, if/when they finally showed up, never really caught on or couldn't compete in the Phi-based environment.
On to visual appeal... if we ignore the question of why Phi shows up in various biological ratios, and merely note that it does... Than a beautiful human, for example, one that was perfectly formed, would have Phi this and Phi that. So on some deep instinctual level Phi just looks right, because it means someone developed pretty healthily, has good genes, etc. And, being the smart apes we are, apply the same asthetic to our manufactured items.
It could also be simple ergonomics. If the ratio of your thigh to your shin is Phi, then the ratio of a comfortable chair's seat depth to its height will also be Phi.
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Simple Machines in Higher Dimensions
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