Babalonian: Assuming a 1:1 elapsed time ratio between AH time and real time, the different time cycles (frequency) between AH and real time results in:

(amplitudes different so that cycles are more readable)
AH time would operate at a 1.92 AH day (12.5 hour) cycles for every 1 real day (24 hour) cycle. This difference in frequency results in an incremental 1 hour change in the arena for every 24 real hours of real time.
For instance (assuming 6:00-18:30 AH day cycle) let's say a player gets on a 8 AM real time every day and that the first day (Day 0) in AH is also 8 AM, we would get:
Day 0 Clock: 8 AM, AH_Clock: 8 AM
Day 1 Clock: 8 AM, AH_Clock: 7 AM
Day 2 Clock: 8 AM, AH_Clock: 6 AM (6:30 PM)
Day 3 Clock: 8 AM, AH_Clock: 5:30 PM
...and so on.