Here is what I mean, nothing needs to be vague. My model predicts that the preferred pitch should track something like this with date and latitude: https://s11.postimg.org/mkw753lpf/image.jpg

The only free parameters are:

  F0 = the pitch of A4 on the when there are 12 hours of day/night
  k  = a scaling factor that determines how much to change the pitch based on duration of the variable second

Here I used F0 = 432 and k = 1, but those values will probably need to be determined by experiment.