The "Sweet Georgia Brown" example is a four-step ladder, not a circle. There are longer ladders in untempered Renaissance music.

josepp's table (28 Mar 12 - 05:54 PM) doesn't actually use the circle of fifths at all. Everything in it would still hold in a system that didn't close round on itself. He even uses double flats, which are a concept derived from untempered music.

The circle of fifths does two things, neither of which anybody here has given any use for in the sort of music Mudcat is about.

One is undoubtedly musical: it closes, so you can modulate round the circle to where you started and use enharmonics to extend the range of chords and progressions available (as in pieces like Schoenberg's First Chamber Symphony and Coltrane's "Giant Steps").

The other is geometric: josepp is very insistent that a fifth measures an angle of exactly 30 degrees. I'm not holding my breath to wait for an example where that does anything at all for anybody.