vaginapagina | Confused About HBC

The way I understand combined birth control pills is that you need to take at least 21 active pills and no more than 7 placebos to maintain protection. Is there any reason for the 21 days? Am I even remembering that correctly? Obviously missing pills in the middle of the active pills can be a problem, but the 21 continuous days seems sort of arbitrary and I can't find any explanation for it.

I'd like to adjust when my period comes and the easiest way would be to cut my active pills a few days short, then start a new pack after 7 placebos (so something like 19 active/7 blanks and then return to my normal 21/7 schedule for the next month). How much is this compromising my protection? Any tips on adjusting my cycle? I'm on Tri-Sprintec (a triphasic pill), if it matters.