On the face of it, there's a lot about our measurements of time that aren't obvious: we do almost all of our counting these days in base-10, and yet we have twenty-four hours in a day split into two blocks of twelve, twelve months in a year, different numbers of days per month, seven days in a week, sixty minutes in an hour and sixty seconds in a minute, and so on.
Much of this is legacy stuff - we use these numbers because our ancestors used those numbers, and making a change would be so difficult as to be impossible. And it's also worth noting that efforts to construct a decimal clock have generally met with failure, because while a day can be divided any way you want, making it fit our natural patterns of wakefulness and sleep is exceptionally difficult.
But, of course, it's not just legacy stuff. Sure, we use those measures because our ancestors used them, but by and large those ancestors didn't just arbitrarily pick them either. The day, obviously, comes from the rotation of the Earth. The year, equally obviously, comes from the orbit of the Earth around the Sun. (These were actually observed by the rising of the Sun and the passage of the seasons, but that's the underlying reason.) The week comes about because the Moon has four phases and a cycle of just under 28 days. And then we get to sub-divisions, which are largely due to number systems used by the Egyptians and/or Sumerians. (Base-12 is thought to come from the number of finger-joints in the hand, excluding the thumb, while base-60 may well be to do with circles.)
(Obviously, there's more to it than that. This is a post on an RPG blog; it's not a comprehensive study of measurements of time!)
What this means for RPGs is that there's potentially some significant mileage for world-building in considering changing some or all of these assumptions. For example, it's very likely that creatures of the Underdark wouldn't have a concept of a 'day' or 'year' at all - they'd measure time very differently. Moving further afield, if the first major species on the planet instead had only four fingers on each hand then it's possible there would instead be eighteen 'hours' in the day, each ninety of our minutes in length. A world with two moons, or no moon at all, would likely have a very different measure of the week.
Of course, it's also worth considering the question of just how far to go here - although the natives of the world would naturally come to all these different assumptions, the game is played by people native to this world, and changing too much means you're effectively playing a game in a foreign language, to the detriment of immersion in the game. A seven-day week is nice and obvious, even if the names of the individual days are different (and the FR's 'tenday' is also suitably easy to understand); a week of six days would probably confuse. So tread carefully.
(Ultimately, my advice would be to change one or two things in big, obvious ways, and then leave the rest as-is. That way, things are recognisably different when they need to be and yet clear and obvious where they don't need to be different.)
Oh, one more thing: Apparently, humans really struggle to adjust to a different day length (for example, when on the International Space Station). So when moving the PCs to a different planet or a different plane, that's certainly something to consider...
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