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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


Interpolation occurs when an extra function (or a group of other functions) is inserted between two neighboring functions in the cycle. Three distinct categories of events illustrate the most common types of interpolations that appear in the harmonic discourse. 

1) First, the use of secondary functions and, more specifically, of secondary dominants

Figure 15


Example 24 : F. Mendelssohn : String Quartet no 2, op. 13, IV, Presto (mm 224-232)
Mechanism of interpolation with the systematic insertion of a secondary dominant between all consecutive functions in the circle of fifths (with one exception)


It is possible, on occasion, that a secondary dominant appears after a secondary tonic rather than before it - following the example of the principal pair V - I being treated in retrograde, thus I - V.

Example 25 : F. Schubert : Winterreise, op. 89, no 11, Frühlingstraum (mm 1-4)


2) The use of harmonic sequences other than those which reproduce the fundamental structure (the descending circle of fifths) and which are assimilated into an interpolation due to imitation of the fundamental pair V - I.

Example 26 : F. Liszt : Transcendental Etude no 1 (mm 5-6)

3) The use of pleonastic elements where we find a juxtaposition of the same functions which, with respect to the first mechanism of intervention, could act as substitutes for one another.

Figure 16

This results in a sort of standstill, a loss of momentum, as demonstrated in the following H.S.U.'s:

- I - VI - IV - II - V - I

IV and II = pleonastic elements

- III - I - II - V - I

III and I = pleonastic elements