A0 resonance is a strong function of the length of the classically shaped f-hole. When lengthening the f-hole, two measurable effects occur:
1. The resonant frequency increases, and
2. The power efficiency of the radiated sound near the resonant frequency increases.
For the first effect, I agree with Don Noon that the A0 frequency in relation to the other main modes is probably more important than the actual value of A0. Remember that a fundamental mode actually vibrates at the frequency of the note being played, not at its resonant frequency. The further the note frequency is from the resonant frequency, the less that mode contributes to the power of the note.
So if the resonant frequencies of nearby modes are too far apart, then notes played between the mode resonate frequencies will sound weak. But if the resonant frequencies of two modes are close together, then notes played near those frequencies might sound too booming.
For the second effect, the perceived power increase would be mostly for notes played in first position, G through A strings. By the time one gets to the E string, the note frequencies are far enough removed from the A0 resonance frequency to have less of an effect on the power of the notes than other modes.
Violins made during the Amati period tend to have f-holes in the 65mm to 75mm length range. Stradivari violins tend to have f-holes tightly clustered in the 70mm to 75mm length. Guarneri violins have a wider range of f-hole lengths but, on average, push the lengths to well over 75mm. The A0 frequencies steadily increased over those times, as well as the perceived power of the instruments for lower notes.
For the mathematically minded, two equations are available to get an idea on what to vary to experiment with different values of A0.
First, compute a sound hole factor as follows:
F = S x L / V
S is a sound hole shape factor which you can ignore for just thinking about small changes to a classic f-hole shape.
L is the circumferential length of the f-hole.
V is the air volume of the interior of the violin.
The A0 resonant frequency is related to the square root of F:
f ~ sqrt(F)
The power of notes played near A0 is related to F squared:
P ~ F x F
For anyone thinking about radically changing the f-hole shape to dramatically increase the power, there are limits based on air flow velocities and the thickness of the top plate at the f-hole in relation to the f-hole length.
F-holes became narrow and long because the air flow through the middle of the opening detracted from projected power. If the f-hole is made too narrow, then air flow along the edges will shift into the turbulent range and power efficiency will suddenly drop off.
If the f-hole is made too long, then certain physical effects that can be ignored for a typical violin will become important and alter the behavior.