At what time of day is it normally allowed for a Roman Catholic Priest to celebrate the Mass?

I cannot select a Best Answer as I do not yet have a response to my original question as to why a Priest in 1920/30's Mexico might have been given a dispensation by his Bishop to celebrate Mass before dawn and after mid-day.

In other words - what then would have caused the obligation to normally celebrate between Dawn and Midday.

As a Quaker with an interest in comparative religions and practices and their origins, I am also curious as to why a Bishop needs to give authority about such things to a Priest, who I might have imagine that once qualified and inducted might be capable of determining what was right for his congregation - in all matters as long as it does not demand anything of any other congregation.

thanks for the contributions thus far.