I have three cats and four litter boxes. I use scoopable litter, and I scoop the boxes at least once a day, sometimes more than once a day. As far as changing the litter, I don't have that on a schedule but when it remains discolored after scooping it, then it's time to replace the litter.
I live in a town that was built on coal ash from a paper mill that was here before the town, so my soil levels are very shallow. Apart from hauling compost, I compost pretty much everything compostable, including cat litter. I have three compost piles in the back of my property, and I compost everything compostable there. Since I'm using it to build up the soil levels on my lawn, I am not concerned about using cat litter, as I might be if I were using it for gardening, and I also don't mind having some clay mixed in with it. Generally, I use a mixture of premium scoopable clay litter, a fully compostable litter made from walnut shells by a company called Blue Buffalo, and sometimes other litters made from wheat or corn.
To answer your question though, litter boxes should be changed every day. It's been a while since I've had only one cat but when I did, I still scooped the litter every day. The house smells better and I've had cats who would refuse to use a litter box that wasn't clean. I went on vacation once and paid someone to feed the cats and change the litter. To make it easy on her, I bought some extra boxes and pre-filled them, telling he she could simply leave the used ones in on our back porch until we returned, and I'd take care of it. For some reason, although I presume the cats were fed, since they weren't starving, she never touched the litter boxes, and it was a mess, made worse by the fact that at least one of my cats decide enough was enough at some point, and used the floor.
