BRUSSELS—The military band of the North Atlantic Treaty Organization is a few tubas short of a full brass section.

It’s also missing some French horns, and a clarinet. In fact, there are only 12 military musicians, all from the U.S., who spend a lot of time trying to sound like 20.

“A lot of the anthems we perform, how should I say it, are pretty bare-bones,” said U.S. Army First Sgt. Tom MacTaggart, the outgoing band leader. “They are simplified. They are not the full versions. If you go to a country and there is a 40-piece band you get all the bells and whistles.”

To compensate, the NATO band will occasionally try to borrow musicians from other countries, or reorchestrate the score, or use guitar effects to mimic other instruments. That only goes so far.

“With 12 members, you are not going to march down the street in a parade,” said Sgt. MacTaggart. “So we don’t do too much of that.”