Stufe

(Ger.: ‘degree’).

In Schenkerian analysis (see Analysis, §II, 4), a harmony of structural significance; the Degree or scale-step on which that harmony is based. The term appeared in Schenker’s Harmonielehre (1906), where it was used for basic harmonic occurrences as opposed to chords of secondary significance. In the ritornello of the aria ‘Buss und Reu’ from Bach’s St Matthew Passion (ex.1, after Schenker, 1906, fig.153), a complete C major triad appears at the point marked with an asterisk. In Schenker’s terms, the listener is prevented from hearing this triad as a ‘fifth Stufe’ (V) by the harmonic rhythm of the preceding passage, where there is consistently one change of Stufe per bar (I–IV–VII–III–VI). It would be superfluous, moreover, to accept a fifth Stufe at this point since one arrives in the very next bar; all three notes in the triad can in any case be explained in linear terms. The triad is therefore merely a passing configuration of the three parts and does not have the importance of a Stufe.

In the subsequent development of Schenker’s theories Stufe, like all other musical phenomena, was understood in terms of structural levels (see Layer). In his analyses from the mid-1920s on he described the basic harmonic structure of a piece as a progression of Stufen entirely within a single tonality (Tonalität). At later levels in the analysis these would be expanded into harmonic regions, or keys, in their own right (Stufen der Tonalität als Tonarten); for an illustration, see Analysis, figs. 19–20.

This view of tonality and modulation need not be applied only to large stretches of music: in a song or self-contained theme the harmonies can also be interpreted differently at different structural levels. Schenker illustrated this in his analysis of the ‘Emperor Hymn’ from Haydn’s String Quartet op.76 no.3 in Der freie Satz (1935, fig.39/3; see ex.2):

The Stufen at levels a), b) and c) can be distinguished very precisely. In a) they govern the entire song: in b) they serve the entire intitial ascent from g' to d''; in c) they serve only a part of that ascent, from a' to d''. Thus the D major resulting from this last elaboration is only an illusory key (Scheintonart).

The term Stufe has been rendered in English – not wholly adequately – as ‘scale-step’, ‘harmonic degree’ or simply ‘degree’.

WILLIAM DRABKIN