Is there any kind of consistent relationship, say mathematical, amongst the various time intervals for which you can calculate a stock's volatility?
Volatility increases with the square root of time. E.g. to annualize a daily volatility you multiply it by the square root of 252 (the approx. number of trading days in a year).
For all intents that is correct (depending on whether you do or do not accept Benoit M's work). http://en.wikipedia.org/wiki/Volatility
Sure it's not perfect as there are some flawed assumptions behind this, but it is an easy and accurate enough way of scaling volatility.