Re: Mold, Mineral Deposits, or What?
Something has run down from up above and splattered across the joists.It may have occured during the construction. What kind of underlayman material was used. Is it subfloor, floor, carpet pad, carpet? It looks almost like a plaster material. Perhaps a bucket of plasterboard mud being filled with water to rinse them out, then spilling onto the floor. Or plaster on the floor was cleaned up with water, running down into and through the floor. Be curious what is seen up top, under carpet.
Either way, the musty smell indicates a mold problem. This smell only occurs during certain stages of mold growth. So, just because you don't have the musty smell, doesn't mean there is no mold. But, if you have the musty smell, it is a pretty good indicator there is some degree of mold problem. Is there carpet? If so, I would have the carpet and pad torn out. Perhaps consider throw rugs instead.
Much of the mold problem is a result of wall to wall carpeting coming in during the 1970s. When they are shampooed, it is difficult to get the pad dry, especially if a lot of water is used. If water spills, usually mold will grow, to one degree or another. Especially if it is a whole bucket of water. Unless the carpet is pulled up immediately and dried out. If building materials are not dried out within 24-48 hours, mold WILL grow.