Functional Harmony

All the the diatonic chords of a key have a function and by function I mean its job in a chord progression. Broadly there are three functions: Tonic, Sub dominant and Dominant.

The Tonic chords are the I, VI and III chord, these are the chords in the scale that feel at home because they have zero tension. In the C major scale the tonic chords are C major, A minor and E minor. The Dominant chords are V and VII, these chords naturally resolve to the tonic so their function is to take us back home. In the C major scale the dominant chords are G major and B diminished. Finally the Subdominant chords are the II and IV,  they lead you to the dominant. For the c major scale the subdominant chords are D minor and F major.

Their are two main theories behind functional harmony. But both theories take inspiration from Jean-Phillippe Rameau's Traité d'harmonie of 1722. The German functional theory and The Viennesse theory of the degrees.

The German Functional theory

Created by Hugo Riemann in 1893, the theory is called the theory of functions. It originates from Germany and is still used in German speaking countries and in North and East-European countries. It involves three tonal functions: Tonic, dominant and subdominant which are written as T, D, and S. Each of which could take on a more or less modified function in any chord of the scale.

The theory outlines three abstract functions, the tonic, the dominant (its upper fifth) and the subdominant (its lower fifth). In addition he believes that the minor scale was the inversion of the major one. In 1903 D'Indy summarised the theory in three points: There is only one chord, a perfect chord; it alone is consonant because it alone generates a feeling of repose and balance, this chord has two different forms, major and minor, depending whether the chord is composed of a minor third over a major third, or a major third over a minor and last of all this chord is able to take on three different harmonic functions, tonic dominant or subdominant. Despite how confusing this theory is, his ideas had a significant impact.

The Viennesse theory of the degrees

Created by Simon Sechter, Heinrich Schenker and Arnold Schoenberg among others. This theory as opposed to the German theory this describes the relation of the chord to their tonic in the context of harmonic progressions mostly following the circle of fifths. This theory is still commonly practised in Western Europe and the United States. The idea is that each degree has its own function and refers to the tonal centre through the circle of fifths. It emphasises harmonic progressions above chord quality. 

There are seven different functions, these are Tonic, Supertonic, Mediant, Subdominant, Dominant, Submediant and Leading tone. Using the C Major scale and its diatonic chords like last time i'll explain these seven functions. The Tonic is I (C) and is home, the Supertonic is the ii (Dmin) and naturally resolves to a chord with a dominant function, the Mediant is the iii (Emin) it functions as a very weak Subdominant (its rarely used), the Subdominant  is the IV (F) and leads you towards the dominant, the dominant is the V (G) and naturally resolves to the Tonic the I (C), the submediant is the vi (Amin) its a weak Subdominant and most commonly leads from the Tonic to Subdominant and lastly the Leading tone is the vii° (Bdim) it has several functions, either used as a passing chord or as a incomplete dominant seventh chord.