Harmonic expansion

As pointed out earlier, more than one harmonic phrase unit (whether complete or incomplete) can be strung together to support a melodic phrase.

Ex. 3.1b - the opening 4-bar phrase is supported by I-V-I-V, which can be construed as a T-D followed by another T-D, which forms the imperfect cadence

the next 4-bar phrase is supported by I-V-I-V-I; the closing V-I is the structural perfect cadence.

For both phrases, the initial I-V-I may be heard as a tonic expansion.

In contrast, the two phrases in the second section are both harmonized with a T-PD-D-T, which at the phrase level, may be regarded as two tonic expansions.

In short, both T-D-T and T-PD-D-T can be used to expand the tonic region

Apart from the above scenarios, there is other ways to expansion each functional element within a harmonic phrase unit.

* changing chord positions

e.g. I-I⁶ as expansion of T

* moving to another chord of the same function

e.g. vi-IV-ii as expansion of PD (within, say, I-vi-IV-ii-V)

* cadential 6/4

e.g. V 6/4 - 5/3 expansion of D (Note that this is the commonplace Ic-V; functionally, the Ic here is not a tonic function chord

but part of an elaboration of V)

* passing 6/4 or its substitute

e.g. I-V6/4 - I⁶ as expansion of T

* neighbouring 6/4

e.g. I 5/3 - 6/4 - 5/3 as expansion of T

V 5/3 - 6/4 - 5/3 as expansion of D

* bass neighbouring motion

e.g. I-V⁶-I (T-D-T on one level, expansion of T on another)

* 5-6 motion

e.g. I^5-6 = I-vi⁶ (may be regarded as T-PD or simply as an expansion of T)

IV^5-6 = IV-ii⁶ (expansion of PD)

* harmonizing neighbour- or passing tones

In these cases, the primary melodic line (which is typically one of the outer voices, i.e. top melody or bass line) is a neighbouring or passing motion but the accompanying voices are not, they may be leaping. Sometimes, the analysis may initially seem counter-intuitive to you, but once you understand the theoretical perspective taken here, you’d realize that it is a very powerful way to explain passing harmonies. Here, ‘passing’ is not taken in the narrower sense that you are familiar with but in a more general sense of passing between structural chords; it is in this sense that neighbouring harmonies are considered ‘passing’!

Harmonic Expansion and Voice Leading

Now, you may notice that the above expansions or elaborations all stem from some kind of melodic movement--largely stepwise (in the form of passing or neighbouring motion) in the upper voices or sometimes arpeggic leaps, especially in the bass. This aspect of tonal harmony is what we refer to as "voice leading". Here is the important fundamental understanding of tonal harmony: