So it sounds like your wife's company is "re-setting" the pay period (by pushing the 28-day period back by one week, with that one week forming an extra, mini-pay period).
If your company doesn't do that, I think you'll find that you would get 13 pay periods in almost every year, but very...
Over here in the US my company has a bi-weekly payroll - we get paid every other Friday. (I think that is fairly typical over here).
Doing the maths, that means that in most years we get 26 paychecks. However, 26 x 14 = 364, so every few years we effectively will get a 27th pay period.
I...