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The phrase "24-7" is a common term for "all the time", referring to the 24 hours in a day, 7 days in a week. Early in one of the games I'm playing in one of the other players made an in-character comment of: "38-6". At the time we thought it was hilarious and allowed it to become cannon for our world. We now have a 38 hour day where characters only long rest once per day. We also have a 6 day week, though I don't think this poses as many issues.

I was recently running a session where one of the side effects of this came up. The players spent all night on a heist mission, finishing at dawn (~9am). They then took a long rest and got up in time to attend a presentation by the lord at mid-day (19pm). I ruled they could do this since there was 10 hours between dawn and noon in this world. However I am wary of exploits going forward.

What are the consequences of having more than 24 hours in a day?

Other than the obvious resting issues that I encountered, I also remembered there are some spells/abilities that are once/24 hours rather than once/day. I'm interested to know if there are any problems with continuing to allow this in our game.

We have a large party of level 4-5 characters and play a mostly story driven game with rotating DMs. None of the players are power gamers that are likely to deliberately exploit issues but we may abuse it by accident.

(Assuming you are not necessarily jamming more encounters into the day just because it is longer:)

Certain spells have a duration in hours that are expected to last anywhere from a good chunk of the adventuring day to 'an entire dungeon crawl'- spells like aid, higher level versions of hex and hunter's mark, mage armor, and most of the other results that turn up if you search for "hour" in spell durations & effect text.

My first thought upon hearing a 38 hour day is that if longer days mean your encounters have more time between them, there's a higher likelihood that these spells will fall off and cause casters dependent on them to have to spend more slots per day to maintain them. Mage armor lasts half the time you're not resting in a 24 hour sleep cycle world, but in a 38 hour sleep cycle world that goes down to ~27% of the time you're not resting.

To put it more broadly, 38 hour days indirectly nerfs any encounter-assisting spells or abilities that have a 'long' duration- I'd say anything 1 hour or up- assuming it has a limit on how many times it can be used per long rest/day.

The other effect I can think of is that there's more room for short rests in the day, assuming they remain at 1 hour. This won't necessarily help health recovery- you're still throttled by available hit dice- but if the party can fit in more short rests, that means their per-short-rest abilities are available for more encounters each day.

If most resource-draining encounters take place within an 8-16 hour timespan, as with 24 hour days, these concerns are more or less minimized. If you're now spreading things out over your 30 hours of wakefulness, however, you might run into odd things that need accounting for such as the above.

A history of the Hour

We all know there are 24 hours in a day because that's how the Sumerians divided up the day. And we know that a hour is 60 minutes of 60 seconds (again Sumerians).

And some of us know that one second is "the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom" (at a temperature of 0 K) - this we do not get from the Sumerians because they didn't know about "radiation", "hyperfine levels", "caeseam-133" and "0 K".

What they did know is that when the sun comes up, that's the start of hour 1 and when the sun goes down, that's the end of hour 12 and the start of hour 13 and when the sun comes up again, that's the end of hour 24. Now we (and the Sumerians) know that daytime in summer is longer than daytime in winter and so, logically, a summer daytime hour is longer than a winter one and vice-versa for nighttime hours.

This makes perfect sense for a society that measures its hours by the sun and operates at the speed of a person on foot (or horseback). It doesn't work so well for a society that measures its hours by atomic clocks and uses them to coordinate a global society.

So we changed what the arbitrary, human-made hour was defined as.

This change started when we began fiddling around with clocks. Because clocks run on springs and cogs and caeseam-133 and not on dawn and dusk we redefined the hour. Later, when trains came along and it became necessary for people a long way apart to agree on a common 'time' we invented time zones. NASA's Mars missions divide the Martian day (a 'Sol' = 24 hours, 39 minutes, and 35.244 seconds) into 24 Martian hours and their scientists and engineers adopt the rhythms of a planet 225 million km away (on average). Later still, Einstein worked out that how long an hour was was all relative anyway because hours and metres are actually interchangeable.

The point is: an hour is a human-made invention - it is as real as 'Santa Claus', or 'justice', or 'love'. That is, its real to us but not to the universe.

Consequence of changing it

None.

Seriously, none.

For a start, you haven't even told us if your fantasy world's day is half as long or twice as long as Earth's. Or, for that matter, if it even has a day/night cycle. Or, if it does have days and nights if they are any way cyclic- my campaign world is the severed hand of a long-dead god orbited by what most people believe is the god's glowing eye (they're wrong - the reality is much, much worse) and the thumb and fingers play merry havoc with things like "dawn" and "dusk": some days have 1 of each and some can have up to 5.

Outside of combat, timekeeping is not very important. Sure some spells and effects last 1 minute, 10 minutes, or 1 hour or 8 hours or 24 hours but if you just substitute 1 encounter, 1 while, 1 longer while, about 1/3 of a day and 1 day nothing's going to break that you can't fix with a ruling.

The types of issues that you suggest might be issues are simply not issues unless you choose to make them such.

You get 1 long rest rest per day - there is nothing to suggest that this downtime corresponds with day or night. Humans are awake for roughly 2/3 of the day and while this generally coincides with daytime hours this is hardly universal (e.g. shift workers, teenagers, babies and their parents). If you miss a night's sleep you sleep might sleep away the morning but no one would sleep through till dusk.

From a mechanical standpoint, you only get long rests when you need them - do you track long rests during 3 months of downtime? Of course not, you assume the PCs go through a normal sleep-wake cycle for each of those days. The mechanical impact of a long rest is to reset damage and spellcasting - this is only worth worrying about if there has been damage and spellcasting. mechanically you should be taking long rests after 4-6 encounters - too few and combat becomes too easy, too many and it becomes too hard - allow your PCs to rest when the pace dictates and don't sweat how long it all takes.

None at all, assuming the hours are 22 minutes shorter.

Instead of changing the length of the day, change the length of an hour. An hour is a unit of arbitrary length after all - the only reason that it is the length that it is was because someone in the past liked dividing the day into 24ths. Maybe this world likes 38ths?

This means that all the spells that last for X hours will instead last for X*19/12 hours, as will short and long rests, but the actual time in minutes will remain the same.

Oddly enough, a 38 hour day requires hours that are about 38 minutes long. This seems like something that you could have fun world building with.

This could lead to unbalance among the classes

This answer assumes that the party will still have a similar number of encounters per 24 hour period.

As CTWind's answer pointed out, longer days will effectively nerf any spell that has a duration of 1 hour or more and doesn't replenish on a short rest. This also nerfs almost all of the caster classes, as nearly all of them only replenish spell slots on a long rest.

Magic based classes will be weaker

A wizard, for example, is a powerful class because they are incredibly versatile and can cast so many spells between rests. But, they can't get those spell slots back without a long rest, meaning your wizards will have to be very reserved about which spells they cast and when. Classes with fewer spell slots, like the sorcerer or cleric, will get hit even harder, because they have far fewer spell slots to begin with.

Mixed classes will also suffer

"Mixed" classes that do both combat and magic, will still be impacted, but less so than the pure casters. The ranger, for example, often relies on a mix of magic and combat to be effective, though it relies far less on magic than the pure caster classes do.

Non-magic classes will probably be fine

Non-magical classes like the fighter and rogue I think will be impacted the least - especially the rogue, which often relies heavily on being able to sneak and use bonus actions, neither of which has any constraints on how often they can be used.

The non-magic classes will be stronger compared to the other classes

This will (generally) result in the non-magical classes becoming stronger relative to other classes, with that discrepancy growing the more reliant on magic the other class is.

Exceptions

There are a few exceptions though.

Low-level barbarians will probably suffer more than, say, a fighter or a rogue, since they only have a limited amount of rage between long rests. By stretching out the time between those long rests, the barbarian becomes much more vulnerable, at least until higher levels.

Paladins will also be impacted, though I'm not sure to what extent. I've never played one, but I know that Paladins are a "nova" class, meaning that they can do a genuinely stupid amount of damage all at once, but then they can't do that again until they get a long rest in. Extending the day also prolongs the downtime between paladin damage bursts, which could significantly reduce their damage output. That said, Paladins are also just really good at soaking damage and dying very very slowly, so that might not be as big an issue as I think.

Then there's the warlock. Unlike other magic-based classes, the warlock restores its spell slots after a short rest. This means that while the wizard, sorcerer, druid, and so on are carefully conserving their resources, the warlock is free to cast its spells with no regard to the longer daytime hours! As long as it can get in an hour of downtime here and there, those spells can keep on flowing! This is effectively a buff to the class, rather than the nerf that other caster classes get from this!

If you're going to do this, treat it as a playtest

I don't know to what extent this will actually impact your game. You might try this out and find that with your pace, the game isn't really impacted at all. On the other hand, your pace might lead to some really unusual balance issues as described above. I haven't done anything like this, so I don't actually know how noticeable the impact will be. So, if you decide to play this way, I suggest treating it like a playtest, and be ready to tweak the game to try to keep things balanced. Just make sure your players are alright with that beforehand!

On the other hand...

If players and DM are both fine with it, exploiting a broken mechanic can actually be a lot of fun!