[gnaritas]

> Circles don't, but intervals do.

Great, but we're discussion the circle of fifths and fourths, not the intervals. You've moving the goal post. A fifth and a fourth are the same interval, but in the context of a key they are not, thus the circle is only fourths in one direction. You can't decide if an interval is a fifth or a fourth without knowing the key.

> I think what you are trying to say is that going clockwise gives you successive dominants, while going counterclockwise gives you successive subdominants.

I'm not trying to say it, I said it.

Pick any note on the circle, it's fifth (dominant) is directly clockwise and it's fourth (sub-dominant) is directly counterclockwise. Counterclockwise is always the fourth of the note you're moving from.