I'd have to re-visit some old textbooks, but I think that pitch is inversely proportional to scale length and to mass (and proportional to tension).

Mass will be proportional to the square of diameter.

The proportional difference between the shortest common scale lengths for an ordinary guitar and the longest (about 24 3/4 to 26 inches - but 25 1/8 is a lot commoner than 26") is a sniff over 5%, while the proportional difference of the square of the diameter is 20%.