Analysis by Key: Another Look at Modulation

CARL SCHACHTER
implicit in every moment of the piece'.3
Obviously the tonic triad as matrix is a chord elaborately prolonged or
composed out (auskomponiert); this applies to the main tonic of a piece (for
Schenker the only true tonic) as well as for most temporary 'tonics' produced by
modulation. Every tonic conceived as a matrix is a prolonged chord, but not
every prolonged chord is a tonic. The D minor and G major triads of Ex. 3 are
not. Although D and G govern their prolonged harmonies, they have no special
relation to the non-harmonic notes of the melodic lines, nor does either form the
point of origin or expected goal of a self-contained tonal progression. D and G
are centres of a sort, for they are harmonic roots or fundamentals, but they are
centres in a much more limited sense than tonic notes, for they exercise no
control over scalar functions, over the syntactic properties of subordinate
chords, over form or design. Their governance is looser and far less elaborately
hierarchical. In Schenker's terminology, the pitches of Ex. 3 are subject to the
control of a C major diatony. Thus although f2 in b. 2 and bl in b. 3 are consonant
with the roots of their chords, they project a dissonant character with respect to
the C major triad; and they eventually resolve into the third and root of that
chord.
Ex. 3
.LL_L z
a lf#! ,, ..
C D G C
(C: I II V I )
A Change of Centre within a Prolonged Tnad
The tonal centre of a passage may change during the prolongation of a single
harmony - a realignment, as it were, in the magnetic fields of the notes that form
the musical atoms of the passage. Example 4 contains foreground and
middleground reductions of the Presto section from the E minor Prelude of
WTC I. Tovey characterizes this passage as 'first asserting the key of A minor
(bars 23-26) . . .; and thence proceeding for twelve steps . . ., till E minor is reestablished
in bar 32. After this it quickly proceeds to a dominant pedal . . .'4
Now it seems self-evident to me that the E minor triad of b.32, though
containing the same pitches as the Prelude's tonic chord, does not function in a
deep sense as a tonic - as a significant beginning or goal of motion. Instead it is
a detail of motion, clearly on the way to the A minor sixth at the head of the next
bar, which continues the prolongation of IV begun in b.23. The governing
harmony of bs 23-33 is A minor (IV); within the prolonged IV, the E minor of
b.32 fulfils a contrapuntal function: it provides consonant support for the
292 MUSIC ANALYSIS 6: 3, 1987