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Learning to change keys on the banjo, guitar, ukulele and other string instruments is a matter of counting the music alphabet up or back on the neck. The FINGER PATTERNS for the chords of a particular song stay the same.  Just move the FINGER PATTERNS back and forth on the neck to change keys. If you are in the key of F, move everything you are doing up two frets and the sound will come out as the key of G.  You don't play any differently but the sound changes. This applies to playing accompaniment chords or chord melody.
The names of the chords will change depending on the key, but your chord FINGER PATTERNS will remain the same and not change. The music alphabet for chords and keys is C_D_EF_G_A_BC etc.  There are two frets between all notes except E to F and B to C, which are one fret apart.  It works best to play movable chord formations where all 4 strings are pressed for each chord.  Chords at the nut can be moved up, but you will need to bar your index finger across the strings to press any strings that were being played open on the nut.
Learn the song well in one key and you should have no problem moving the FINGER PATTERNS back and forth on the neck to change keys.  As you change keys focus on the FINGER PATTERNS, not the chord names. You can figure the chord names out later as you play more.

Look at this Eddie Peabody plectrum banjo Lesson #8 on YouTube.  Eddie plays the song "Waiting For The Sunrise" in the keys of C and F, and the chord FINGER PATTERNS stay the same.  As Eddie says on the video "The fingerings are exactly the same, all we do is move them up a fret or two". 
Click here for the Eddie Peabody lesson on Youtube
Notice that Eddie has chosen the keys of C and F in the lesson.  With the C tuning on the plectrum banjo, the 4th string is a C note which can be left open for both C and F chords.  This applies to the tenor banjo as well.  Because of this, many of Eddies' chord FINGER PATTERNS show holding down only 3 strings as movable chords.
For many simple chords the 4th string can be used as a "wild card" and used either open or fretted.  If any chord sounds good to your ear with the open 4th string, then it's probably OK and can add fullness to the sound of the chord.  Use your ear to decide. "Use the music notation to learn a song and use your ears to play the song."
Chords can be played in various ways either at the nut or as movable chord inversions along the banjo neck.  Following is an explanation of three ways of playing chords on any banjo or other stringed instrument:
1.  Playing chords at the nut is called playing "In The Box", your finger positions stay near the nut and do not move up and down the neck.  The "In The Box" idea can be moved to anywhere on the banjo neck, with an imaginary nut at any of the frets.  When you move away from the real nut, any open strings of the chord form must be pressed accordingly at the imaginary nut location. 
2.  "Chord Inversions" (alternate finger forms for the same chord) can be played and moved up and down the neck, the chord will keep the same name at all locations.  The finger form changes for each postion on the neck, but the chord name remains the same.
3.  If you play the "Same Finger Form" at another location on the neck, the chord name will change, but the pattern of your fingers will stay the same.   
Click here for a chart that shows 3 ways to play chords on the neck of the Plectrum Banjo. (pdf file)
(This chart also works for the 5-String banjo with C-Tuning)
Click here for a Video "Three Ways to Play Chords on the Plectrum Banjo"
Click here for a chart that shows 3 ways to play chords on the neck of the Tenor Banjo. (pdf file)
Happy strumming,
Jim Bottorff

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