Pagan / Earth spirituality question

I know the various names for the days in between the equinoxes and solstices, but are there names for the half-seasons that occur within? Is there, for example, a different name for the part of spring that begins March 21st (or thereabouts) and comes to an end in a couple days to distinguish it from the time period that begins on the First of May and culminates with the Summer Solstice? I assume that there are already names in place, and I won't have to continue the process bubbling in my brain right now to come up with names for them.

Thanks in advance, Blessed Be, Do what thou wilt, I love you.