Welcome :: Glossary :: About / Contact us :: Thanks / Credits :: Website plan

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 now equipped with the tools that enable us to proceed with the division of the tonal discourse into H.S.U.'s, but first it is necessary to learn a few rules of the game: 

1) In case of ambiguity regarding the point of division (for example, does the H.S.U. end with V or with the I following V?), we must consult the other organizational parameters of the musical discourse (formal context, phrasing, abrupt changes of dynamics, texture, or figuration, etc.)

2) The last term of an H.S.U. may coincide with the first term of the following H.S.U. - for example, in a case where both H.S.U.'s are part of the same musical event (phrase or phrase member) or following an evaded cadence (such as a principal dominant followed by a secondary dominant)

3) We may find a repetition of 2 consecutive terms within an H.S.U.

for example: III - VI - III - VI - II - V - I (we note that III - VI is repeated)

4) When determining the H.S.U.'s, always continue until I (or a substitute of I) unless dissuaded by an indication from another parameter (for example, a clear half-cadence)

5) All H.S.U.'s contain V (in the role of a principal dominant), except in the case of plagal H.S.U.'s such as I - IV - I or VI - IV - I

6) An H.S.U. may contain only one function; this would necessarily be the function V (principal dominant) and the H.S.U. would usually be followed or preceded by another H.S.U. which confirms the function V as the principal dominant in a more explicit manner

7) In the case of a non-modulating harmonic sequence other than one which reproduces the fundamental structure (a descending circle of fifths), it is possible for the H.S.U. to contain the function V (as principal dominant) more than once because, exceptionally, and only in this case, the H.S.U. encompasses the model of the sequence, the reproductions of the model, and the closing formula. However, in the case of a sequence that articulates the fundamental structure (which will later be classified as a type 1 sequence), it goes without saying that there will be as many H.S.U.'s as there are cycles of the the circle of fifths.

Having concluded the presentation of this model of analysis for the tonal harmonic discourse, explained in detail the theory of constants, and specified the rules of the game, we are finally ready to tackle the procedure for division into H.S.U.'s. To begin, we will apply it to the first prelude of the Well-Tempered Clavier, volume I, by Johann Sebastien Bach, a prelude which opens an eminently significant corpus and bears the constants which have been the object of this research. For the time being, we will adopt a modulating perspective (tonal plan: C major - G major - C major) in order to keep the context of the entire corpus in mind (the other 23 preludes all modulate). Then we will apply this technique of division to a waltz by Schumann (no 4 from op. 24), another modulating context (tonal plan: A minor - F major - A minor). Each of these two pieces will first be heard in its entirety, then fragmented into H.S.U.'s in such a way so as to clearly demonstrate the intrinsically tonal nature of these units.