Harmonic Functions

Given a specific key we get seven different base chords, taking the C major scale as an example C D E F G A B C, we get these chords:

Cmaj7, Dm7, Em7, Fmaj7, G7, Am7, Bm7b5

We can of course built other types of chord and still remain on the same key and scale, but the base chords on the C major key are these. Each chord as a specific function inside the key that lends itself to indicate the key you are in. Some of these chords have a feel like the song as ended or a feel like the musical phrase as resolved, others feel like unresolved or like they are "catapulting" us somewhere, these last ones are chords with tension.

There are three main harmonic functions in a key. The tonic function, sub-dominant function and the dominant function.

Having the tritone as an indicator, the dominant function describes chords that have the most tension in a key, these chords "ask" to solve this tension to the tonic function chords. If a chord includes the tritone then it has a dominant function, in the case of C major scale the tritone is from F to B (an augmented fourth), so because G7 includes it (G B D F), it then has dominant function, as does the Bm7b5 chord (B D F A).

Going forward to the sub-dominant function, these chords mediate between the tonic and the dominant function chords, to set the path for the dominant. The sub-dominant chords do not include the tritone, they might have the fourth degree of the scale but never in conjunction with the seventh of the key, they have a little bit of tension but not as much as the dominant chords: Dm7 is a sub-dominant chord, Fmaj7 is another.

Finally the chords with a tonic function are chords that do not include the tritone of the key, they might have the seventh of the scale but don't include the fourth, on these chords the fourth would add lots of tension and these chords are meant to have a stable sound, the Cmaj7 chord is a tonic chord, you might use it to begin your song or to finish it, the Em7 and Am7 are also tonic function chords. Notice that if you add an F to Cmaj7 it will clash with the E on the chord by a half-step. On the Em7an F would be a b9 (or b2) and would clash with the root note of the chord and on the Am7 the F becomes a b6 clearly adding tension to an otherwise stable chord by making an half-step with the fifth of the chord.

So in summary: The tonic function: I, iii and vi, the sub-dominant function: ii and IV, the dominant function: V and vii.