There are many tunings for the short scale and standard scale tenor banjo. The tunings most often used are:
GDAE which is the same tuning as a mandolin and fiddle - popular in traditional music
CGDA which is the same tuning as a mandola and viola - standard tenor
DGBE which is the same tuning as a guitar's top 4 strings - popular for playing chords. Also known as Chicago tuning
String
Tenor
Listen
Irish
Listen
Chicago
Listen
Bottom or Fourth (thickest)
C
G
D
Third
G
D
G
Second
D
A
B
Top or First (lightest)
A
E
E
For all tunings:
Tuning is often done starting with the A (in GDAE tuning) or D (in CGDA and GDBE tuning).
Each of the other strings can be tuned up or down to get them in pitch.
For GDAE tuning, get a reliable 'A' from other instruments and tune the second string to it.
For CGDA tuning, get a reliable 'D' from other instruments and tune the second string to it.
For DGBE tuning, get a reliable 'D' from other instruments and tune the fourth string to it.
Often necessary to tune to the fixed pitch instruments such as the reeds (accordian, melodeon or concertina) as they may be slightly north or south of concert pitch
Then, for GDAE and CGDA Tuning:
Hold the second string down on the 7th fret, and adjust the first string until it sounds the same.
Hold the third string down on the 7th fret, and adjust the third string until it sounds the same as the second.
Hold the fourth string down on the 7th fret, and adjust the fourth string until it sounds the same as the third.
Then, for DGBE Tuning:
Hold the fourth string down on the 5th fret, and adjust the third string until it sounds the same.
Hold the third string down on the 4th fret, and adjust the second string until it sounds the same.
Hold the second string down on the 5th fret, and adjust the first string until it sounds the same.
Alternatively, buy an electronic tuner and tune each string using the indicator on the tuner.
Tips:
Deaden the other strings if you tune with an electronic tuner since the ringing of the other strings sometimes confuses it.
Tune frequently (before you start to play each session).
When you tune, if you take the string too sharp, tune flat again and tune up to the note. (Tuning down has a tendency for it to slip flat a little further as you play especially with old-style guitar/mandolin tuners rather than geared planetary ones.)
Check the tightness of the tuner periodically and tighten the small screw if the tuner feels loose. The screw is on the end on the tuner for the guitar/mandolin type and on top of the tuning head itself for the planetary type.
Change the strings regularly, and change them in sets. Old strings will not sound quite as though they are in tune, even if an electronic tuner says they are!