Functional theory
Harmonic analysis after Hugo Riemann.
What it means
Functional theory describes chords according to their task within the key. It assumes that every sonority of a tonal piece can be related to one of three principal functions: tonic (I) as the point of rest, dominant (V) as what leads toward it, subdominant (IV) as what leads away from it and prepares the dominant. All other sonorities appear as substitutes, variations, or extensions of these three. The system was worked out by Hugo Riemann in the late nineteenth century.
In the notation
Labelling is done with letters below the staff: T, S, D, capital letters meaning major and lowercase letters minor sonorities. Additions name the variations — p for the relative, g for the mediant, appended numerals for added notes as in D7. Brackets or arrows mark secondary dominants, which relate to a degree other than the tonic. In addition the degree can be given in Roman numerals in brackets.
Musical use
The advantage of the system lies in the fact that it names relationships instead of mere positions: it says not only on which degree a chord stands but what it serves for and where it aims. In this way cadences, modulations, and deceptive cadences can be described independently of the key. Its limits show where the tonal tie slackens — in modal music, in strongly chromatic music of the late nineteenth century, in large parts of the twentieth century.
It is to be distinguished from the theory of degrees, which names every chord by its degree in the scale and says less about its role, and from figured-bass figuring, which merely gives the intervals above the bass. All three describe the same music from different angles; within one analysis one should stay with one system.
Performance practice
When working up a piece, write the functions below the bass line and look first for the cadences; from there the rest orders itself. Watch what precedes a resolution — that is usually the most revealing place. And use the analysis for memorizing: whoever knows the harmonic connections retains a piece far more reliably than through the fingers alone.