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Day doesn’t start at 12, it ends at 11:59 before turning back over to 00:00
Personally I’d argue for base 36 time!
36 hours, each consisting of 36 minutes, each consisting of 36 seconds.
Lets you treat time as a 0-Z number with two decimal points, the day ends at Z.ZZ at night, plus base 36 is SUPER conveniently divisible, which jives really well with how most folks actually consider how much time they need to do whatever or what time it is.
