The basic chord progression in many Christmas, religious and folk songs is called a I-IV-V progression, because it uses major chords built on the first, fourth and fifth tones of any major scale. This chord progression is displayed below:

Playing the above chord progression can be a little awkward for the left hand (since it has to jump around a lot), so here is the same chord progression with inverted chords (this example uses G7 instead of G, as the V chord is most often a V7 chord):

Any chord can be inverted (meaning that the notes can be played in a different order) for a slightly different sound and to add variety to music. Typically a song will end with the root of the chord in the bass. For example, a song in the key of C will end with a C chord in the root position of C-E-G. But that same C chord can be played with its notes in a different order (E-G-C or G-C-E) throughout a piece.
Songs in a minor key can use chords similar to the I-IV-V7 progression, but minor chords are notated with lower-case roman numerals. Here is a i-iv-v7 minor progression:

The basic chord progression in jazz music is the ii-V7-I progression:

It's important to write and play chords within the usable range of the piano. Sometimes low notes can sound a bit "muddy," as in the following example:

This problem can be solved by playing the chords an octave higher (the right hand can be moved an octave higher as well to avoid conflicts with the left hand):

Another way to solve the problem of "muddy" lower tones is to remove the third, which determines if a chord is major or minor and tends to be the "muddiest" of the three tones in a major or minor chord:

Another useful chord technique is called chord substitution. Two examples of C chord substitution appear below. The first involves using an Em chord instead of C, since Em and C share two notes. The second involves using an Am chord instead of C (since again, Am and C share two notes). This technique can add variety and interest to your chord progressions:

In certain contexts major 7th and minor 7th chords can be substituted for major chords to give songs a more contemporary sound:

Here are the chord progressions used in a few popular songs:
Viva la Vida (Coldplay): IV-V-I-iv
Back to December (Taylor Swift): I-iv-IV-V
I Just Wanna Run (Downtown Fiction): i-III-v-iv
Hallelujah (Leonard Cohen): I-IV-V-vi-IV-V-iii-vi
You Found Me (The Fray): iii-V-IV-V-I
When improvising, I often use the following I-IV-V-vi-V-IV-I progression to provide the harmonic structure:

Try experimenting with your own chord progressions and see what unique harmonies you can come up with!
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