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PART 1 - 1.1 - Genesis of the analytical model :: 1.2 - Description of the analytical model :: 1.3 - A practice of analysis in the tonal harmonic discourse from Bach to Wagner :: 1.4 - By way of a general conclusion

1.2 - Description of the analytical model || 1. The generative pair and a related issue: the Neapolitan sixth :: 2. The fundamental structure :: 3.The discrete grouping unit :: 4. The mechanism of substitution :: 5. The mechanism of interpolation :: 6.The mechanism of deviation :: 7. Some rules of the game concerning H.S.U. division :: 8. Application to two texts


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.