EMB-190 Captain reported a musty odor in the cockpit during busy approach. No odor elimination procedures were completed or reports submitted.

Narrative

Descending through the mid twenties (approx FL250) I noticed a musty smell. I had noticed it very faintly on the previous leg for a brief time once we hit some humid air in ZZZ1 down around 8;000 ft.; but thought it was nothing because it was so faint and transient and didn't exactly match the 'dirty socks' smells I've smelled before; and it was gone fairly quickly. It didn't seem like dirty socks; more of just a faint musty smell coming from the air vent. We got on the ground in ZZZ2 and I didn't think anything of it. We took back off for ZZZ3 and on descent into ZZZ3 it was more noticeable this leg; still not all that bad; but noticeable. I asked the First Officer if he smelled it; and he said he did. By the time we finished talking about it; we were somewhat busy with the arrival; and it didn't seem too bad and we were close to landing; so I decided we would continue normally and deal with it on the ground. We didn't have time to perform the odor isolation procedure. Everything was normal with the landing. We got our Gate assignment and proceeded in to the Gate. Upon parking; I asked the flight attendants if they smelled anything. Neither they; nor a commuting pilot in the back; smelled anything. I got up and smelled some air from some of the Cabin gaspers and it smelled normal. I went back and smelled the Cockpit gaspers and they still had the musty smell; so there was definitely a difference in the air smell coming from pack 1 and pack 2.