Pick any number. Do these calculations. Your answer was 3, wasn't it?

http://raytomes.posterous.com/cycles-cycles-cycles-usuk-exchange-rate

step 1: get a noisy time series

the exchange rate between the US Dollar and UK Pound

step 2: filter out everything that doesn't come in 9 year cycles

UK/US exchange rate 1791-2007 less 9 yr. mov.avg

(emphasis added)

result: you got something with a 9 year cycle, didn't you?

an 8.25 year cycle

Just the same way wind instruments work. Make white noise, and pass it through a tube of a certain length, an it filters out all the frequencies that don't resonate, leaving just the frequency you want and some of its harmonics.