How do you label a sequential interval when the second note is lower in pitch than the first?

Question

Consider the interval D3 G3. This would form a perfect fourth.

In a sequential interval, say a quarter note D3 followed by quarter note G3, this still "sounds" like a perfect fourth so using that interval label seems fine.

However, suppose instead the sequential interval is D3 followed by G2, thus the second note is lower pitch rather than higher. Would it be more appropriate to label this interval as perfect fifth instead of a perfect fourth?

In other words, should an interval be labelled based on the lowest pitch, regardless of whether it comes before or after another note in time?

Answer 1

The interval label is always going to be based on the number of half-steps between the two pitches.

Since there are 5 half-steps between D3 and G3, that is a perfect fourth. Thus, the 7 half-steps between D3 and G2 make it a perfect fifth.

Answer 2

A fifth and a fourth are two sides of the same coin, like an implication and its contrapositive.

"If it is a real piano, it has strings inside" means the same thing as its contrapositive "If it does not have strings inside, it is not a real piano." It's the same but different.

Likewise D3->G3 amd D3->G2 are "the same" because they both have a D and G and can be used against the same chords, but "different" in that one goes up a fourth and the other goes down a fifth.