Function (music)

[9] Even if the concept of harmonic function was not so named before 1893, it could be shown to exist, explicitly or implicitly, in many theories of harmony before that date.

[10] The idea of function has been extended further and is sometimes used to translate Antique concepts, such as dynamis in Ancient Greece, or qualitas in medieval Latin.

This symmetric construction may have been one of the reasons why the fourth degree of the scale, and the chord built on it, were named "subdominant", i.e. the "dominant under [the tonic]".

It also is one of the origins of the dualist theories which described not only the scale in just intonation as a symmetric construction, but also the minor tonality as an inversion of the major one.

As summarized by Vincent d'Indy (1903),[18] who shared the conception of Riemann: The Viennese theory on the other hand, the "Theory of the degrees" (Stufentheorie), represented by Simon Sechter, Heinrich Schenker and Arnold Schoenberg among others, considers that each degree has its own function and refers to the tonal center through the cycle of fifths; it stresses harmonic progressions above chord quality.

Moreover, unlike Funktionstheorie, where the primary harmonic model is the I–IV–V–I progression, Stufentheorie leans heavily on the cycle of descending fifths I–IV–VII–III–VI–II–V–I".The table below compares the English and German terminologies for the major scale.

Some may at first be put off by the overt theorizing apparent in German harmony, wishing perhaps that a choice be made once and for all between Riemann's Funktionstheorie and the older Stufentheorie, or possibly believing that so-called linear theories have settled all earlier disputes.

In particular, whereas an English-speaking student may falsely believe that he or she is learning harmony "as it really is," the German student encounters what are obviously theoretical constructs and must deal with them accordingly.Reviewing usage of harmonic theory in American publications, William Caplin writes:[21] Most North American textbooks identify individual harmonies in terms of the scale degrees of their roots. ...

The second type groups harmonies which feature the raised-fourth scale degree (♯) functioning as the leading tone of the dominant: VII7/V, V6V, or the three varieties of augmented sixth chords.