Harmonic functions are the way chords are grouped according to the notes of the scale (key) that compose them and in turn, the way they function diatonically at a cadence according to the hierarchy they receive.
Traditionally halftones in the major scale are called diatonic chromaticism.
The power of attraction and resolution to the ascending and descending chromaticism reaffirm and clearly set the key in question.
Depending on how many of these chromatic notes are in the diatonic harmony, chords can be classified into Root (Tonic), Sub Dominant or Dominant.
Tonic Group: is conformed by the degrees I, VI and III, although the III degree can be taken as a chord closest to the Sub Dominant group because of the B note (chromatic diatonic). In the same the sonority is relaxing, culmination of cadence, and usually does not need another chord.
Sub Dominant Group: is conformed by the degrees II and IV. In the same there is only one chromatic diatonic note and the feel of these chords is semi unstable. That is, may or may not need another chord to continue the cadence.
Dominant Group: is conformed by degrees V and VII. In it the two chromatic diatonic notes are in every chord. The sonority is unstable and usually lead to another chord in order to resolve or not the cadence.
These three groups helps organize each chord functions and in turn to derive the way it can be used to generate different cadences in a composition or in a analisis. Note also the number of notes in common that have the chords of each of the groups.
Below I discuss some examples of cadences, of the many that may exist, based on this concept.
Dm7 (sub dominant) | G7 (dominant) | Cmaj7 (tonic) ||. Also called perfect cadence or in the language of jazz: 2 5 1.
Cmaj7 | Dm7 | Em7 | Fmaj7 | G7 || also called stepwise movement.
Is worth clarifying that in a diatonic reharmonizing any chord can be replaced by another of the same group.
Dm7 (Fmaj7) | G7 (Bm7b5) | Cmaj7 (Am7/ Em7) ||
I hope you enjoyed this brief harmonic post. See you next time.