Kodak used to operate on this 13 month calendar. When I asked someone who used to work there, she was shocked that I knew about it and said that it was the best thing about working there. The original plan that this calendar is based on called for a liminal day between years for New Year's Day with 2 days for leap years
I work for a company which used to have 13 financial periods. It was great. Then they switched to 12 and we now have a couple of 5 week periods thrown in to balance the year out. I don't know why they decided that but it's not as good now.
I'm surprised they successfully attempted that and that it resulted to be taken positively. It seems as every out-of-the-norm scheduling idea is so frowned upon that even in small companies you can steer them to anything but the same ole.
I've used iso-weeks for this purpose. I don't really care for dates if I don't absolutely have to. It's nice to refer to "week 44 five years ago" in my journals. Truth be told, no one else around me uses the weeks and the only mention to it I've heard was not positive.
I'm responsible for our databases and work with our BI guy a lot. Changing from 13 to 12 periods was a right pain. We had snapshots, budgets and loads of forecasting data, all of which needed to be updated to reflect the new calendar. It wasn't as easy as dumping a new calendar in, well it perhaps could have been if we were given ample time to plan it.
In regards to week, period, year, quarter, etc that's all easy for the user to switch to their preferred view in the BI system. The ERP system will use the financial calendar but reporting is done against whatever the user sees fit.
13 period financial calendars don't break down into quarters that easily. One reporting quarter will always have an extra period.
5-4-4 creates even quarters except it requires either one extra day every year or one extra week every five to six years. It's most beneficial for companies that either experience high seasonality or high consistency, such as retail and manufacturing.
Most other companies just use calendar month since it's simple, easy to determine, and allows for rather consistent year-over-year comparison.
There is a choice between having an extra day in the holiday season and counting up the extra days plus leap days, and inserting an extra week every several years
Adding the extra day annoys people who value weeks continuing as they have since ancient times
Using a leap week rule makes the calendar track the seasons a little worse. Solstices and equinoxes will move by about a week over several years