Understanding chord prolongations?

Question

Harmonically oriented neo-Schenkerian analysis and generative theories have in common the concept that a single chord can be "prolonged" over a given span of music, even if not every (or even any) note in the chord is playing at every moment during that span. When is it valid to say "chord *x* is prolonged throughout passage *y*?" As an answer, I could imagine either a general definition/theory, or a list of common prolongational patterns; either would be welcomed.

Answer 1

A chord/harmony can be prolonged/expanded through a number of devices:

-An arpeggiating bass-line can outline the chord, simply altering the "inversion" the chord appears in while the harmony above remain unchanged.

-The bass can remain constant- called a "Pedal"- under changing harmony above. This usually occurs under the V or "dominant" function to contribute to the suspense at the end of a phrase, but can be used to prolong other harmonies as well. This device is also very common in the chord progressions of Jazz tunes. (the entire 'A' section of "On Green Dolphin Street" is a pedal that expands/prolongs the tonic.)

-A chord progression may prolong a harmony by means of other contrapuntal devices, usually having to do with a desired bass motion such as I->V4/3-> I6, with the bass moving up by step- or I->V6->1, with the bass used as a lower neighbor tone. You can usually tell aurally that these are prolongations because they will occur within a musical phrase (usually near the beginning) rather than make up an entire musical phrase (in which case you would usually consider a V->I progression a "cadence").