Prolongations and Embellishments (week 4)

This week we continued working with concepts from the last two weeks, putting them together to look at the details of musical phrases. Remember, different analysts are looking for different things. There is more than one right answer.

Prolongation begins with the idea that T, P, and D are more stable or structural chords than any others. (This is why we relate other chords back to these three.) However, if we only wrote music with these three basic chords, it would get repetitive fairly quickly. If a function (such as T) is embellished in such a way that it is implied to last longer than the chord itself, we say it has been prolonged. There are 3 main ways of doing this: changing the bass pitch (inversion – covered last week), adding extra notes in upper voices (see below), and using other chords to extend the function’s influence (also below).

If the melody (or other upper voices in a texture) sounds pitches that are not any of the 3 or 4 associated with the current harmony we say these pitches are non-chord tones (NCTs). NCTs usually resolve by step to a pitch that is part of the harmony/chord (either the current harmony or the following one). There are specific names for approximately 12 types of NCTs, but we aren’t concerned with the names at the moment. Often we simply circle NCTs and then ignore them while we are doing a harmonic analysis.

Sometimes, NCTs contribute hugely to voice-leading in a way that is analytically interesting. Then it may be useful to track which NCTs are where. This can be done with arabic numerals, as we see here with an excerpt from Bach Well Tempered Clavier book 1 prelude in C major (mm. 24-27): 24-27

Starting in the second measure of the excerpt, we can follow the voice-leading of the 2 uppermost voices with the arabic superscripts.

When several NCTs appear simultaneously, they can form their own chord. Depending on the tempo and/or the level of detail you are interested in analyzing, it may be interesting to note each verticality as its own label. What follows will illustrate both the concept of levels and then prolongation. (Click to see larger version)

K331 Theme

Depending on the performance, most listeners either perceive the dotted quarter (beat) level or the whole measure level as the primary unit of harmonic motion. If you, like me, focus only on about 1 chord per bar, the top analysis may be sufficient detail for you. However, the second analysis is more detailed, and shows inversions, added tones, and the cadential motion that I originally glossed over. Both analyses are correct, one merely has more details than the other.
There are at least 2 additional levels in just these four measures.
If you wanted to slow the tempo down and write a new variation at the new slow tempo, the sixteenth note chords in the first 2 measure might become relevant. These we normally ignore as NCTs, but when isolated do make up chords as well ( D5 and T, respectively).
The biggest level is the prolongation. Notice that the downbeat of m. 1 and m. 4 are the same. All the chords in between are said to have prolonged the tonic for 3 entire bars. We know that the prolongation is over because we have moved to a new functional area (P) so that the cadence can begin.

There are many types of common Tonic prolongations. The most basic are (T-D5-T3) and (T- D3-Tr) which then acquire more variations and additions to increase interest and variety.

p56minor slashDP6Similar types can be found prolonging Predominant or Dominant. A famous Dominant prolongation is the Dominant pedal (like the the above Bach example), where the bass stays on scale degree 5 while many things flow above it.

Assignment 4

10 thoughts on “Prolongations and Embellishments (week 4)

  1. In this post and I think in a previous, there are examples of the predominant with a line above it, but I don’t recall an explanation of what that line means.

    It’s an interesting method of analysis. I like that it simplifies functionality to just T, D and P, and along with the concept of relative and variant relationships. Also, I’m in favor of thinking about dominant function without the root; the vii0 doesn’t make much sense on it’s in the same way that it’s generally implied that a dominant contains a 7th.

    I’m not sure what to think about the use of numbers with this system in regards to inversions and higher extensions on chords. It doesn’t seem quite as intuitive as in roman numeral analysis.

    I’m looking forward to reading more of your posts soon.

    • Oops! I should put that somewhere. When I’m handwriting labels, I use the line to mean lower case on letters where it might be ambiguous: p, m, c, that sort of thing.

      What do you find intuitive about RNs? Most students I’ve chatted with/taught seem to think that RNs aren’t intuitive at all, so I’d like to know your point of view!

      • Ok, that makes sense about the line now.

        In answer to you’re question: I tend to think of the the numbers being as much about analysis as they are for performance indications. With roman numerals I find it easier to put a name on a chord, or can even visualize transposition much easier from RN than having to think about T,D,P and the variations.

        And that’s probably why I said I’m not sure about the numbers in this system, because I’m trying to think about them for something other than for analysis. What is clear though, with what you’re doing here, is how well it can explain things in ways that maybe RN’s can’t. I just need to get more familiar with it, which I’m planning to do.

        A question for you: Do you think it’s possible to understand this system without having experience using roman numerals?

      • Absolutely! I would definitely like to keep this system independent from RNs. When I was teaching this pilot class, one of my students was not a music major and had not had core theory before, but still said that he enjoyed the class and found the system helpful.

        I have also had several other less formal interactions with freshmen theory students and found that they only understand RNs functionally: thus the RN becomes the extra label they have to learn, while it is the function that makes sense.

        What is your background, if I may ask? What do you use RNs for most often?

      • I suppose my background is in jazz, or that’s where theory started for me, so I learned to build chords long before understanding their function. I think it’s common in jazz to think about the chord symbols using letter names and/or roman numerals pretty much at the same time; notating extensions beyond the triad for both is usually the same, and really like figured bass even for the RNs. Inversions are pretty much ignored unless it’s really important to the bass movement. It’s all reduced to iii-vi-ii-V7, and not much tonic-dominant analysis, although it is there.

        It’s hard for me to not think about RNs even when considering the ideas that you’re sharing here. Maybe they validate each other for me.

        It’s good to hear that you’re getting through to students.

        In the end, do you think that it’s all just different ways of saying the same thing, or do you think they each have a different purpose?

      • I think that RN and Functional Analysis should be separate, and have different purposes. One of my particular issues with the way RNs are currently taught (where I’ve been, anyway) is that RNs are trying to act as functional labels without being designed to do so. So, some might perceive what I’m doing as “the same” as RNs, but I hope it’s clearer and better designed to describe Functional relationships. I was a cellist first, and so I think of music harmonically; relating chords to a scale (RNs) instead of to the functional cadence doesn’t makes sense to me.

  2. Hello. This section has been delightful to read. I feel that this theory describes the framework for a lot of the things I do automatically when I improvise on piano. But I got stuck when trying to apply the theory to a certain idea, so I would like to ask for help.

    Please correct me if I get any of this wrong. I’m making some assumptions since I haven’t had a complete formal music theory education.

    Pv and Tr are the same chord. You differentiate between them through their function—Pv only shows up right before a D, whereas Tr is for tonic prolongation.

    An example:
    ||: CM Am CM Am | CM Am G G7 :||
    The notation below is incorrect.
    ||: T Pv T Pv | T Pv D D7 :||
    The notation below is correct.
    ||: T Tr T Tr | T Pv D D7 :||

    My question is this: If you have the chord sequence I’ve written below, how would you notate it without using P between each T?
    ||: CM FM CM FM | CM FM G G7 :||

    What follows is my best guess for the solution to this question.
    The notation below is incorrect because it has T following a P.
    ||: T P T P | T P D D7 :||
    The first two F chords need to be some kind of tonic prolongation.
    Would it be this notation, which strong-arms the A minor into an F major?
    ||: T Tr* T Tr* | T P D D7 :||
    * this would be a 6 above and a 6 below the letter, to denote a 6 in the bass and a 6 instead of 5 in the upper voicing.

    Thanks for your time.

    • Thanks for your question! Your first distinction between Tr and Pv is right. With the progression of CM FM CM, it is perfectly acceptable to say T P T. This is because there can be nested levels of T P D T functional pulls within a given phrase. Roughly speaking, there is one level of structural T P D T per prototypical phrase, but each of those functions can be prolonged with relative and inversions, or even the other stronger functions, if they have been weakened metrically, melodically, or harmonically.

      a CM chord could be prolonged by a CM FM GM CM before moving to the structural P D T, so long as it was clear thru metric, melodic, or bass indications that the initial GM CM was not a cadence. Just as a T can be prolonged with a D (CM G/D C/E), it can also be prolonged with a P.

      I hope that helps, and let me know if I can clarify anything further!

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