Circle-Fifths

We have seen how the Lament Bass progression is essentially a progression from the tonic to the dominant whereby it is not essentially to spell out the specific harmonic functions of the intervening chords except to use an arrow to denote the directionality of the overall progression. Sometimes, a series of chords moving by the circle of fifths is embedded within a large progression, in which case, this circle-of-fifths fragment can be heard as effecting a transition like those connecting chords in a lament-bass progression.

In Ex. 1.2, the first tonic chord initiates a series of circle-of-fifths sequence towards the perfect cadence:

V i iv VII III VI ii^o V I

D T --------------------- > D T

While it is true that ii^o can be indicated as PD, or the entire iv-VII-III-VI-ii^o can be heard as a PD expansion using the circle-of-fifths progression, this detail does not matter: the pertinent understanding is that the first T is moving towards the structural cadence of the phrase. Notice that the entire iv-VII-III-VI-ii^o-V-I is actually based on the circle of fifths, but seen in the present context, the closing V-I is taken as the structural cadence.

Ex. 1.1 provides a well-known example from Vivaldi.

Sometimes, a sequence can extend so much that it returns to its harmonic point of departure so that the entire passage is taken as an expansion of that original harmonic function, in which case we use a horizontal line with no arrow head to signify the expansion of the functional region in question.

Ex. 13.8 The Chacconne progression can be simplied as a tonic expansion based on the circle-of-fifths, leading then to the dominant to form an imperfect cadence:

i - iv - VII - III - VI - vii^o6 - i - V

T -------------------------------------------------- D

Note that vii^o6 is substituting for V.

Of course, it is possible to interpret the progression as such too:

i - iv - VII - III - VI - vii^o6 - i - V

T PD ----------------- (D) - T D