Why would urine have a musty smell?

Not sure, but...: Not sure about urine smelling musty. Urine can smell stronger (more ammonia / urea odor) if one isn't drinking enough water. It can smell like ketones during fasting or certain medical problems. Some foods give urine odd aromas, such as after eating asparagus. A primary care doctor can evaluate if one keeps having such aroma symptoms, to rule out a urine infection, and look for other causes.

Metabolic/PKU.: A musty odor of the urine would likely mean a metabolic disorder, possibly pku (phenylketonuria). Although this is usually diagnosed in infancy or early childhood, it can be mild as long as foods high in phenylalanine (phe) can be avoided, like meat, milk, eggs, nuts, cheese, and fish. If not , it may be pronounced, with the musty urine smell. Other causes are liver failure and infection.

Many causes: Much nonsense is written about urine odor. If you have phenylketonuria or serious liver disease, you would know it. I am going to assume that you have nothing else to suggest a bladder infection. A variety of components of your diet can produce a smell in your urine (not just asparagus); these are poorly understood. If you are otherwise healthy, don't worry.