September 10, 1997

Secondary functions on multile layers. Another way of expanding the tonal system is illustrated by the use of secondary functions many layers deep. Walter Piston makes the point in his Harmony book that one could look at such music in two ways:

As an example, we used Hugo Wolf's song Mignon. Here is an analysis of bars 4-7:

Point of view a:
                        4                  5                    6           7
	A flat Maj  V/V |                  |                    |           |
	e flat min   V  |  I               |              V/IV  |  IV    I  |
	d flat min      |  II       V      | ( I          V/V ) |           |
     	a flat min      |          V/IV    |  IV           V    |   I       |
Point of view b: 
                        |                  |                    |           |
	g min       V/VI|  VI   V/IV/IV/VI | IV/IV/VI   V/IV/VI | IV/VI  VI |
Both views are correct and each of them shows a different aspect of the piece: the first one how it modulates (and how unstable to tonality is), while the second one stresses the (tonal) unity of the piece.

Mignon has the G minor key signature but there is only one G minor triad (in first inversion) in the entire piece (bar 14, fourth beat). Nevertheless, all chords, starting with the N6 opening the piece and ending with the V closing it, can be labeled in G minor according to our second point of view.

A few other less unusual procedures seem to point towards the fact that this composer is testing the limits of the tonal system here. Among them,

For the discussion on modes started during the same session, see September 11

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