A banjo is a drum with a neck bolted to it. That is not a joke about the sound — it is the reason two adjustments most players never touch will move your tone further than any purchase.
Head tension
The head is a drum head under tension, and that tension sets the instrument's voice. Slack reads warm and thuddy and dies fast; tight reads bright and loud and rings on. Neither is correct — clawhammer often wants it slacker, bluegrass tighter — but a head that has never been touched since the factory is usually looser than anything anyone would choose.
Adjust in small, even steps: a quarter turn per bracket hook, all the way round, then listen. Going round unevenly warps the rim and is the one way to do real damage here.
The bridge
The bridge is not glued down. It is held by string tension alone, which means it can be in the wrong place, and on a surprising number of instruments it is. Its position sets intonation: too close to the neck and everything fretted plays sharp, too far and it plays flat.
Find the right spot by ear rather than by ruler. Play the twelfth-fret harmonic on a string, then fret the same note; if the fretted note is sharp, move the bridge away from the neck by a hair, and if flat, toward it. Repeat on an outer string too and split the difference. Ten minutes, no tools, and it fixes a banjo that has felt subtly out of tune for years.
Bridge height and action
Height changes how hard the strings press on the head, which changes both volume and feel. Taller drives the head harder and raises the action; shorter is easier to play and quieter. Change one variable at a time and give yourself a day between changes — ears adapt fast and you will otherwise chase your own adjustments in circles.
Then check the tuning
Every adjustment here moves pitch. Retune after each one, and check the fifth string in particular: it is short, it is under the least length of tension, and it drifts first. The fretboard explorer is a quick way to confirm a fretted note lands where it should once the bridge has moved.