What constitutes a circle of fifths progression?
Is a circle of fifths that goes backward (eg. D G C F Bb) still considered a circle of fifths progression?
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The circle of fifths progression is I - IV - VII - III - VI - II - V - I.
The circle of fifths progression is commonly a succession through the seven diatonic chords of a diatonic scale by fifths downwards, including one progression by diminished fifth, (in C: between F and B) and one diminished chord (in C major, Bdim), returning at the end to the tonic.
In major keys, it will be I - IV - vii° - iii - vi - ii - V - I. In C major, it will be: C - F - Bdim - Em - Am - Dm - G - C.
In minor keys, it will be i - iv - VII - III - VI - ii° - V - i. In A minor, it will be: Am - Dm - G - C - F - Bdim - E - Am.
Typically, a circle-of-fifths progression is a progression that moves by descending fifths. Thus, your progression is a standard circle-of-fifths progression!
The reason descending fifths are so common is due to the dominant-to-tonic relationship between two adjacent chords. In your example of D G C F, D is the dominant to G, G is then the dominant to C, C is then the dominant to F, and so on. One of the many reasons this dominant-to-tonic relationship is so convincing is that each chord contains the leading tone of the next chord. G contains the leading tone to C (B), C contains the leading tone to F (E), etc.
Ascending fifths are much harder to pull off convincingly because it lacks this dominant-to-tonic relationship, and consequently each chord lacks the leading tone of the next chord.
However, in the ascending-fifths progression, each chord has the leading tone of the chord before it! So if any fifth progression is "backwards," it is the ascending one.
Is a circle of fifths that goes backward (eg. D G C F Bb) still considered a circle of fifths progression?
The point is:
The circle of fifths IS going BACKWARD!
The symbolic representation of the circle like a clock is only accidentally, respectively to read it clockwisely has been your decision.
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