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La Follia chord peogression is usually written as:

i - V7 - i - VII - III - VII - i - V7 (first eight bars)

i -V7 - VII - III - VII - i,V7 - i (second eight bars)

I can understand how this progression works for the most part but I don't really understand the motion VII - i from the point of view of classical functional harmony. Is there any explanation for its use from this point of view? (I'm not looking for an analysis from the point of view of popular music or jazz, I'm aware of some ways to rationalize the progression from those standpoints).

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In a relative major key, VII - i would become V - vi which can be viewed as a deceive cadence.

Because of this, you can think of certain sections of this progression dipping into the relative major where VII - III can be looked at as V/III - III and the deceptive resolution as a non functioning secondary dominant V/III - i which is expecting to have the V - I resolution.

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I have seen the basic "La Folia" described as a "double tonic" progression. The patterns i-V-i alternate with III-VII-III or i-V-i in the minor key followed by V-I-V in the relative major. Contemporary theorists mostly thought of this progression as a bass line with some stuff above it. The bass line is 1-V-1-7-3-7 with the melody 1-7-1-2-3-2-7 in the soprano.

Sometimes the Romanesca, Passamezzo Antico, and Passamezzo Moderno were treated the same way but with a different melody. At the time of La Folia's early incarnations, functional harmony had not been codified.

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