In other words, given "2 Tues", (e.g. today, 2 July 2013), for how long must I wait until it is Tuesday on a 2nd of the month again?
How does this interval change for each week? Is it constant or does it fluctuate? If it fluctuates, is there a minimum bound on this duration of "day/day-of-week certainty"?
P.S. I actually have a real reason to use the answer for. You see, in my current zsh shell command prompt on my terminal on my computers, I print out the day of the week (so I can reasonably tell how recently I did something), and also the day of the month (because something more than 7 days old would be ambiguous without at least this info). The goal was to produce a format that is easy to parse and helpful for quick relative calculations (e.g. "Tues" is more helpful than "7/1/2013", if for no other reason than the fact that I'm more apt to know the day of the week than the day of the month). I can't think of a practical reason not to also stick the month in there (as it'd take up only two or three extra characters), so clearly the practical importance is low, but it did get me thinking about whether adding the month really would reduce the uncertainty period by a factor of exactly 12 or not.
Edit: You know, I'm not sure how e.g. 28 days in February (and how that is divisible by 7) slipped past me. Feeling stupid right about now.