Theymos provided the following information in another recent thread:
This is period #1135. Period #1136 will start in about 11 hours, when the unix time 1374560000 % 1210000 == 0.
It seems that Activity is incremented when unix time is divisible by 1210000.
By my calculations, the next increment should be at unix time 1375770000, which is on Tuesday 6th August 2013 06:20:00 UTC.
Edit: Looks like my Activity just incremented, so my calculation seems to be out by a day or so?