What causes a musty smell with no visible mold?

The usual Adams County answers are a damp crawl, a wet coil pan, cardboard on a basement floor, a dry plumbing trap, or humidity high enough to make dust smell like a cellar. Sometimes there is growth in a cavity you have not opened. The order of operations is still: look and meter, then test if the look was not enough.

If the smell only happens when the heat or air kicks on, start at the air handler. If it is strongest at the crawl hatch, start there. Do not tear plaster as the first experiment.