We
are indebted to Goldman not only for identifying and but also for
explaining the most common of these mechanisms of intervention, namely
substitution. As implied by the name, substitution takes place when one function (or a
group of functions) replaces another (or several) in the systematic
progression through the cycle.
Figure 11
This
diagram of the circle of fifths shows the most frequent types of
substitution as well as where they occur. The function I
is by far the most susceptible object of a substitution by
way of the functions VI, IV, III, V of..., not only at the end of an
H.S.U., but also sometimes at the beginning. This explains the
formation of H.S.U.'s such as:
- III - II6 - V - I instead of I6 - II6 - V - I
- VI - V - I - instead of I - V - I
Figure
11 highlights the interchangeability of the functions IV and II within
an H.S.U., be it the tonal or the plagal type. Thus, we often find:
- I - VI - IV - V - I instead of I - VI - II - V - I : tonal H.S.U.
- I - II6 - I instead of I - IV - I : plagal H.S.U.
Plagal
U.S.H.'s also take advantage of the substitutes found in the
figure above and thus may appear with varied content:
- I - IV - I
- I - II - I
- I - N - I
- VI - IV - I
- VI - II - I
- VI - N - I
- V of IV - IV - I
- III - IV - I
- III - II - I
- etc.
Goldman
sought to define another source of substitution through recourse
to tonicization. This concept refers to a perspective that gives
priority to the tonal unity of the work, or at least a
fragment of a work, and, in order to do so, avoids the tendency
to modulate for each altered chord. Tonicization involves the
temporary emergence of a tonic
other than the principal tonic and implies, by extension, the
establishment of a secondary dominant. We find the same
distinctive characteristics in a secondary dominant-tonic couple as we do in the principal dominant-tonic couple:
Figure 12
As shown in the following examples, the
use of secondary dominants, which results in the substitution of one function
with the secondary dominant of the following function in the cycle, involves a mechanism of
intervention that affects the components of the chords but retains the
sequence of roots determined by descending fifths.
Figure 13
Figure 14
Figure 14 also reveals the tonal limit of a sequence of consecutive secondary
dominants as shown by the rupture in the chain of perfect fifths evident in
the root movement of the chords. This limit is linked to the
intrinsic nature of the major or minor mode in which the secondary
dominants exist.
Example 23 : F. Sor : Etude for guitar, op. 31, no 20 (mm 5-8)
In the context of a tonicization,
other
types of substitution may occur through this first mechanism of intervention in the fundamental
structure, but here we will limit ourselves to the main points in order to
succinctly show the principal tendencies of the mechanism of
substitution as defined by Goldman.
Striving to take into account if not all of the harmonic gestures in the
harmonic discourse from Bach to Wagner, then at least the greatest
possible number of constants, I was lead to identify and subsequently
elaborate two other mechanisms of intervention in the fundamental
structure, namely the mechanism of interpolation and the mechanism of
deviation.
