Tuning the air chamber by changing the area of the sound hole(s) is pretty basic stuff. I did that 20 years ago and the results were interesting and told me my sound holes were too big on my F sound hole mandolins so I reduced them. On Gibson type oval hole mandolins it certainly is advisable to get the main air mode in between notes, otherwise if it is tuned to G or G#, you can get a big boomy note on the G or the G# on the G strings. I have also used a fingerboard overhang to lower the air mode tuning so it sits in between notes on my Custom model mandolin which has a smaller body so the air mode is a bit higher. Some mandolins will have an air mode that is tuned below the low G strings (e.g. Lyon and Healy, most flattops) so it doesn't really matter what the frequency is. The Lyon and Healy's are lower because of the big fingerboard overhang which reduces the effective area of the sound hole. My A5 mandolin fairly consistently tunes D# nowadays so I don't worry about it and usually don't bother to measure it. However, note that most of the sound comes from the main top mode, not the air mode, so stressing out about the main air mode may be a waste of time. All this stuff is very well covered in the first Gore Gilet book, although you might need to bone up on your maths chops to fully understand it all. They talk about how the frequencies of vibration can affect tone and intonation, and how to adjust the frequencies in an assembled guitar. It is a lot more difficult in a mandolin because there is no easy access to the interior of a mandolin, so you are mostly stuck with what you have got once it is assembled.
I came to the conclusion that the only thing I could consistently observe from my database of measurements was the relationship of the modal frequencies of the top and back plates did affect the sound I was getting in my mandolins. Years later and lots more measurements, which recently have included modes of vibration of assembled instruments, I am beginning to understand why. Basically, just about everything affects the frequencies of the modes of vibration of an assembled mandolin (even the tailpiece and tuners), so there is a lot of noise from instrument to instrument because wood is so inconsistent. So any correlation between the frequencies of the modes of vibration and free plates gets lost in the noise. However, the relationship between the top and back will always remain the same. The noise is what makes music instruments so difficult to work out what makes them tick. The relationships are so numerous that no existing supercomputer can model them effectively - i.e. the degrees of freedom in the model gets too big for current technology (this is also covered in the Gore Gilet books).
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