“Mary Had a Little Lamb”
This famous children's song is best known for its melody — the line of single notes that is commonly sung. Here it is in F major.
But combining (or harmonizing) the melody with some chords helps to fill out the texture. This is an example of a simple chord progression: a series of chords played in a particular order. In many types of music, chord progressions are used to create a sense of tension and release, by moving away from the tonic of the song and then back again.
What are these chords?
The chords we've added are F major and C major triads. But why did we choose these chords?
If you look at the melody, you can see that the notes that appear most often are notes that are in the accompanying chords. In the first bar, for example, the Fs and As are both part of the F major triad — these notes are chord tones. The Gs are non-chord tones, but they sound like they're simply "connecting" F and A. Non-chord tones that are between two adjacent chord tones are called passing tones.
This suggests one approach to choosing chords: look for chords that contain the notes of the melody.
But there's another principle at work here; these chords are built on the first and fifth notes of the scale (F and C). You can call these chords the 1 and 5 chords, respectively. Chord progressions that alternate between 1 and 5 create a strong sense of departure and arrival, tension and release. Compare the "stable" and "grounded" sound of the 1-chord passages with the "tense" and "unfinished" sound of the 5-chord passages.
Try to experiment with different chords, as well as with using different rhythms for the chords.