It's more like it's a circle of both fifths and fourths, in both directions.

For example, C-G is a fifth if you go up, or a fourth if you go down. C-F is a fourth if you go up, or a fifth if you go down. So it can be a circle of fourths clockwise or counterclockwise.

Circles don't have up and down. :) Going clockwise is always a fifth, counterclockwise is always a fourth.

Circles don't, but intervals do. If you start at middle C (C4), you can go up to G4 to get a fifth or down to G3 to get a fourth. Ergo C-G can, in the abstract, be thought of as a fifth or a fourth.

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

> 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.