No you can't do that unless you use calculated field to generate them. But they won't recognized as date fields by Tableau.
Marc is right that Tableau won't recognize the calculated fields as dates, but you can just name them what you want to emulate specific periods (3rd's, half's of a year, etc.)
That being said, using the original date pill in the formula, Tableau knows that it is a date field that you are working with, hence, you get the correct values for your measures (i.e.; Sales, Profit, etc.) for those newly created periods.
Not sure if that's exactly what you're looking to do, but here is how it was done:
Calc for 3rd's:
Calc for half's:
Hope this helps.
Thanks a ton Marc and Don.
I was looking for a direct way to do it, thanks for the help.