It's all contract dependant; if your contract says 6 months then regardless of your pay period, it's 6 months notice as that's what you've agreed to. So check that.
If you don't have a contract or it's not mentioned in that document, it'll be the same as your pay period.
It is usual for full time permanent staff to have their notice periods determined by calendar month, rather than 'working weeks' weeks. So I agree with your boss. Unless you have a contract of employment which says differently.