3. THE DISCRETE GROUPING UNIT
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)
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.
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
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...
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).
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
- I - VI - II - V - I : Tonal H.S.U.
- I - II - V - VI : Tonal H.S.U.
- I - IV - I : Plagal H.S.U.
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.