Arpeggios are simply a series of notes from a chord played separately (often in order). All the theory behind this has therefore been covered already, in the Basic Theory lesson. Arpeggios can be used in many situations - from playing the entire rhythm part of a song using them, to providing a break from the rest of a strummed piece.
For instance a C Major
chord follows this formula:
1, 3, 5
These notes are taken from the C major scale, which consists of the notes:
1 2
3 4 5 6 7
C, D, E, F, G, A, B
Therefore the notes that make up the chord of C major are:
1 3 5
C, E, G
So, in the C major arpeggio the notes will be played (when ascending the
arpeggio) in this order (although they are repeated).
Arpeggios are often used as a replacement for chords. If you see a chord, you
can replace it with the equivalent arpeggio. For instance the C major arpeggio
can be played over the C major chord. They both follow the same formula.
Arpeggios can be played both ascending and descending.
Here is one of the major arpeggio shapes (there are many different shapes to
play the major arpeggio, these are covered in the arpeggio
shapes lesson). Make sure you pick each note individually (this is not a
chord):

As ever, the red circle represents the root. To prove the point above, lets look
at the notes contained in this shape. When played ascending from the root, with
the root on the 15th:
C, E, G, C, E, G
Please note that the notes don't have to be repeated exactly 2 or
exactly 3 times (C, E, G, | C, E, G, | C, E, G). For instance one shape may go
C, E, G, C, E, leaving off the last G. As long as the notes are played in
correct order at least 1 full time, it is still an arpeggio.
The above shape can be moved all over the neck in the same manner as barre
chords.
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