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

As I often discover is my right in music theory, I tend to disagree with the notion of a right answer to this question. As a trained listener, I can pick out reiterations of previous themes in a piece by ear -- I can then solidify them through studying the notation, or strengthen them through faith by reiterating them in composition. The choice is mine. The validity of "chord x" being prolonged through "passage y" can be argued/determined by any brain with a voice. If you're currently in education and searching for a "correct" answer to this question, any prof should be approaching grading this question by noting the presence of an explanation, not some mythical applicability of that explanation. Why? No explanation is better than any other. They are all just lenses through which different conclusions can be reached. I hope this helped - more questions can seem like the opposite of an answer, but I often find that they lead to a deeper understanding of the practice itself.

Answer 2

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").