Aha, I never got that far. Yes, it is a very striking progression, isn't it.
I'd call that second chord C#7/G# myself; the Faug sounds more like a C#/F to me ...; it's that G# that really stands out. Great change.
So, to me it's more of a I > III7 > I > III7 > vi > vi7 > IV > VII > IV > III progression ... but the orchestra is covering all kinds of extra flavors in there too.
The tune as a whole is very unusual, modulating and changing time signature every chance it gets. I find it very Beatlesque, like from the Sgt Peppers era. I'm afraid I have no great revelations theory wise. It's just a great example of a tune that doesn't stick to convention, that keeps moving to the least expected change.
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