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


From this premise, I deduced the substance of a definition for what I call the unit for division of the harmonic discourse. This unit, called a Harmonic Structural Unit (H.S.U.), is defined as a group of successive harmonic functions whose meaning is intrinsically linked to a systematic progression through a descending circle of fifths. This group may begin from any function in the cycle and concludes with the function V, the function I (or a substitute of I), or, occasionally, the function IV following I. For example, we could have tonal H.S.U.'s such as :

- I - IV - VII - III - VI - II - V - I
- IV - VII - III - VI - II - V - I
- VI - II - V - I
- VI - II - V - VI (substitute for I in a deceptive cadence)
- VI - II - V - V of IV (substitute for I in an evaded cadence)
- III - VI - II - V
- II - V
- VI - II - V - I - IV (more rarely)
- etc.

From this definition, we see that a tonal H.S.U. always contains one but only one V function as the indispensable element for establishing a tonal polarization, or, in other words a key. In fact, tonal orientation is established from the moment that the function V is identified as such. The H.S.U., therefore, corresponds to a distinct portion of the harmonic discourse, which itself forms a component of the tonal discourse. This idea, however, rests on one condition wherein lies another a priori of this theory that is shared by eminent theorists such as Charles Rosen and Goldman (to name but two): that we consider the harmonic parameter as fundamentally if not exclusively responsible for tonal orientation. The H.S.U. offers one response to our search for tools with which to identify and track auditory as well as visual markers, thus bringing us back to our original quest.

Before going further it is important to distinguish the harmonic structural unit (the H.S.U.) from the musical structural unit, such as, for example, a phrase which pertains to the musical meaning in and of itself (and which could contain more than one H.S.U.), while an H.S.U. refers exclusively to tonal significance (in the context of the H.S.U., we are focused on tonal affiliation).

It is also important to distinguish the H.S.U. from what we have called formulas of harmonic vocabulary. While these, too, correspond to clearly defined fragments of the harmonic discourse, a harmonic formula distinguishes itself from an H.S.U. as a distinct unit that recurs frequently throughout the repertoire and that may include more than one H.S.U. as in the following formula:

V - VI -     IV - V - I
1st HSU     2nd HSU

In other words: an H.S.U. corresponds to one tour around the circle of fifths. A formula is simply a stereotypical short succession of chords, which returns very, very, very, very often in the tonal repertoire (and which can itself be divided into H.S.U.'s). But we'll come back to this...


Besides the tonal H.S.U., given the frequent insertion of the plagal gesture in the tonal harmonic discourse, we will also consider a plagal H.S.U. which is characterized by a movement in the opposite direction in the cycle, thus leading from IV to I. This is the only H.S.U. which excludes the presence of V (note the broken arrow which returns to I in the figure below).

Figure 10

Tonal? Plagal?...

A tonal gesture is a gesture which features a dominant - tonic relationship (V - I) while a plagal gesture is one that features a subdominant - tonic relationship (IV - I).

Finally, and in accordance with the tradition for beginnning a work as emphasized by Goldman, the function I can always occur at the beginning of any H.S.U., as in the following examples:

- I - VI - II - V - I : Tonal H.S.U.
- I - II - V - VI : Tonal H.S.U.
- I - IV - I : Plagal H.S.U.

The H.S.U.'s above, as well as every example given thus far, illustrate the direct relationship between the structure of a descending circle of fifths and a progression through the harmonic discourse. However, tonal practice makes use of many other harmonic gestures which seem to contradict this systematic organization and which require additional theoretical information in order to account for the modes of intervention in the fundamental structure.