Test yourself to find out if you can work out which chords fit best with the melody? 

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Here are 6 examples of how a simple lead sheet (melody plus chord symbols) can be developed in a variety of different ways. (Only the first half of each verse is played). The arrangements become gradually more complex as we go through.  

Amazing Grace 1

The first performance is a basic playing of the lead sheet, using held triads (3-note chords). 
Example 1

Amazing Grace 2

This arrangement uses the same notes as the first one, but the left hand repeats a chord at the start of every bar, rather than holding until a new chord comes along. 
Example 2

Amazing Grace 3

The third example uses the same triad notes, but plays them separately rather than together.  The G major chord has been brought up an octave, to create a gentler-sounding arrangement. 
Example 3

Amazing Grace 4

This one takes the lower note of every triad (e.g., the G of the G chord) and plays that note in octaves, creating a more rhythmic accompaniment. 
Example 4

Amazing Grace 5

The accompaniment here has constant movement in the left hand.  The notes are picked from the bottom of every triad (played in both low and high octave), and in between these octave notes is the top note of the triad.  So, in the first bar, the left-hand notes are low G, D, high G. 
Example 5

Amazing Grace 6

The right hand is playing notes from the triads now too, as well as the melody.  The left hand is using similar notes to example 5, but in a swing rhythm.
Example 6