Harmonic Expansions 4.7

HARMONIC EXPANSIONS

CHAPTER 4: INSERTING PRE-DOMINANTS AND THE CIRCLE PROGRESSION
4.7 Limits on the sequence of chords in circle progressions

Why do circle progressions tend to begin on vi and end on I? If chords tend to follow the circle of fifths counterclockwise what is to prevent the progression from going around the circle forever and never stopping at all? Well, stopping at I can be explained by the fact that I is the most stable chord in any key, and that the V - I progression at the end of a piece is an expectation which is basic to western music--as represented by the fundamental harmonic progression. In fact once the last V is reached, it is hard to imagine a piece ending with anything other than I. This is not to say that I never goes down a fifth to IV; we have seen that I - IV6/4 - I can expand the initial tonic--and in the next chapter we will see that IV5/3 can can be used in the same way--but once V - I is encountered on a deep level with I as the final tonic, it is hard to imagine either V moving to anything other than I or that I will be followed by some other chord.

Well, OK, there is the notable exception of "amen" harmonized by IV - I being tacked on to hymns which essentially have already been completed. But even though the "amen" is "tacked on," for the sake of argument, why does IV not anticipate a chord a fifth down during a final "amen?" That is, after hearing "amen" sung after a final tonic so that the sequence of chords is, say in the key of C: G - C (end of piece), F - C (harmonizing "amen")--why during the F chord are we not anticipating a B-flat or B root, both of which are a fifth below F? There are two answers, one for each chord:

B-flat (a perfect fifth down from F) is not in the original key, and there is no chance that a listener would anticipate a chord that is not diatonic when a piece is coming to a close
if we are to stay in the original key, root movement between F and B (IV to vii°) is down by a diminished fifth, not a perfect fifth. Our music, in terms of both keys and root movement is based only on perfect fifths.

So much for ending on I.

Now, what prevents the circle progression from extending backwards in the other direction beyond vi? Sticking only to diatonic triads and root movement by descending perfect fifth, why are full vii° - iii - vi - ii - V - I progressions so rare? The reason for this has to do with the fact that the strength of movement from one chord to the next is not the same for each adjacent pair of chords. By "strength of movement" I mean the amount that the listener anticipates the next chord. Or to put it an other way, how much one chord makes someone anticipate the next. Specifically:

Movement from V - I is extremely strong when I is the final tonic, as noted above.
Movement from ii to V is strong, but not quite as strong.
Movement from vi to ii is weaker still. For instance when hearing vi it would not be terribly surprising if it were followed by V, and did not go to ii at all.

So there is a pattern. As we approach I in the circle progression, the strength of movement from one chord to the next gets stronger. This increase in strength of harmonic motion is symbolized in the cartoon above and by the image to the left by arrows which become bolder as they get closer to tonic.

By the time we get to root movement from iii to vi, the strength of movement is so weak that iii serves little purpose in giving the phrase any sense of direction at all. This may well be the reason that iii is used so rarely in Baroque and Classical music (though its use increased during the Romantic era). Some Music Theory professors in fact expressly prohibit the use of iii in exercises where students are to choose chords to harmonize a phrase.
So where does that leave vii°? Though it cannot go to iii (iii has been banned and has been sent to progression prison in the cartoon at the top of the page!), vii° does have a tendency to proceed to I, this by virtue of the leading tone which tends to resolve to scale degree one.

And so that's it for this chapter. I hope you have enjoyed your journey around the circle of fifths, however short it has been!

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