According to a report posted on the FAZ, it does matter a lot when you book your ticket.
The ticket is cheapest if you book it 3 weeks before you travel, earlier or later than that usually gets you the ticket at a higher price.
If you plan to travel for anything less than 7days, then you’d pay less if your trip starts on a Monday while you pay the most if your trip starts on a Friday. On the other hand if you plan to travel for longer than 7 days then you pay least if you travel on Tuesday and pay the highest again if you start your trip on Friday.