FabR[Senior Patek Moderator]
26166
A beautiful dial (and back side as well :-) There seems to be no info on their website, so here's my guess on the 5 hours and 20 minutes:
Aug 06, 2019,07:10 AM
Since 5h and 20m is 1/(4.5)=2/9 of a day, choosing this cycle means that the moon will find itself on the opposite side of the dial at any given time on any two consecutive days (e.g., perhaps romantically, if you see the moon at 12 o'clock at 9pm tonight, tomorrow at 9pm you will find it sitting at 6pm, and so on).
Given that there are 24 x 60 x 2 minutes in two days, to create this effect using a cycle measured by a "round number" (5h and 20m looks pretty round), you need to divide 24 x 60 x 2 by an odd number. Its odd divisors are of course the same as the divisors of 45 (namely, 1, 3, 5, 9, 15, and 45 itself). Given this, they chose 9 among them, which is probably the same choice I would have made.
For instance, if they chose 15, there would have been 7.5 cycles a day, each of 3h and 12m, but I guess 5h and 20m is even more round ;-) The number 3, yielding 16-hour cycles, was of course a very good choice (but perhaps too long).
Again, this is just the first guess that comes to mind to a PhD mathematician on vacation in Italy (whose methods used here can be figured out even to a third grader...
), so please check with the Barcelona brand if this is indeed what they had in mind!
If they do, then I deserve one of their enamel watches...
Cheers.