The banjo mandolin is a crossover instrument. It has the drum body of the banjo and the small size and paired strings of the mandolin. The bridge is a wooden piece that rests between the strings and the drum. The position of the bridge sets the sounding length of the strings. When the bridge is in the correct position, all the strings will be in tune at every note. While it is impossible to get every note exactly in tune because of the instrument's design limitations, a good-sounding compromise is possible.
Tighten the strings to moderate tension
Slide the bridge beneath the strings. Move it to the approximate location of where the bridge was before. Line it up with previous markings on the drum of the instrument.
Slip each string into the correct slot in the bridge. Each pair of strings has a corresponding pair of slots.
Tune the instrument. This is only a rough tuning to enable placing the bridge correctly.
Touch the first string lightly, directly over fret 12, and pluck the string. Do not press down on the string. The objective is to make the string stop vibrating directly over fret 12. This cuts the frequency of the string in half. It should make a ringing sound. This is called "playing the harmonic."
Depress the first string fully at fret 12. Pluck the string. This is called "fretting the note."
Listen to the difference in pitch between the fretted note and the harmonic note.
Move the bridge until both notes are the same. Move the bridge toward the neck if the fretted note is lower. Move the bridge away from the neck if the fretted note is higher.
Repeat the bridge-setting procedure for the second string. Pivot the bridge under the first string to avoid changing the position of the bridge under that string.
Repeat the bridge-setting procedure for the remaining strings. It is impossible to have all the strings perfectly intoned, even with precise adjustments of the bridge, so find a workable compromise for all the strings.