Downton Abby, the British period drama television show, has a time dilation of approximately 3.1.
|Highclere Castle, location of period drama Downton Abby.
The first two seasons cover the period of time from April, 1912 to sometime in 1918 (assumed to be July 1918), an elapsed time of 6.25 years. But these two seasons encompass two years of our current time, hence time passed on the show 3.12 times faster than it passed in our reality.
This will have some odd effects if the show continues indefinitely. For example, by doing the math, we can see that in 2041, Downton Abby will cover the period of time from 2009 through 2012, overlapping the broadcast start of the series. We can call this the meta-phase of the show, wherein for the next fourteen years, the show will be primarily concerned with the making of the show in previous years.
The real hiccup occurs in 2056, when the show will cover the period from 2056 through 2059. Then it will transform from a period piece to a futuristic speculative fiction series.