Monday, June 24, 2013

Harmony as Structure

I titled yesterday's post "Chord Progressions", which is the familiar term. But it would have been more correct to call it "Chord Successions". The distinction is one made by Arnold Schoenberg in his very useful book on harmony, Structural Functions of Harmony. He says,
A triad standing alone is entirely indefinite in its harmonic meaning; it may be the tonic of one tonality or one degree of several others. the addition of one or more other triads can restrict its meaning to a lesser number of tonalities. A certain order promotes such a succession of chords to the function of a progression. A succession is timeless; a progression aims for a definite goal. Whether such a goal may be reached depends on the continuation. It might promote this aim; it might counteract it. A progression has the function of establishing or contradicting a tonality. The combination of harmonies of which a progression consists depends on its purpose--whether it is establishment, modulation, transition, contrast, or reaffirmation. A succession of chords may be functionless, neither expressing an unmistakable tonality nor requiring a definite continuation. Such successions are frequently used in descriptive music. [then follows an example from the Prelude to Lohengrin by Wagner]
The harmony of popular music often consists only of a mere interchange of tonic and dominant, in higher forms concluded by a cadence. Though a mere interchange is primitive, it still has the function of expressing a tonality.
I have quoted this at such length because it expresses well some fundamental principles of harmony. We live in what I have called "post-tonal" times. In both popular and contemporary music, even if the composers are using ordinary triads, they are still avoiding the expression of real tonality in favor of vaguer, more ambiguous successions of chords such as we heard in the two songs by Bob Dylan. A recent collection of pieces by Nico Muhly, to give a contemporary example, consists of pieces based on drones: by their very nature, allowing no real definition of tonality.

Schoenberg's slightly Germanic English needs some elaboration. He is saying that tonality, real tonality, is a network of functional relationships. A single chord, on its own, a triad to be exact, implies no tonality:

That looks like C major, right? But what if it were followed by these chords:

Now we see that we are actually in E minor and that C major triad is actually a VI chord. The whole progression would be analyzed as VI III6/4 V i (uppercase Roman numerals stand for major chords, lower case for minor). Want another example? That C chord could be the beginning of a progression in F major:

We would analyze that as V vi ii N6 V7 I. The N6 stands for "Neapolitan sixth" chord, which is a major chord built on the lowered supertonic in first inversion--a very popular and exotic way to set up the dominant. Want to hear that? I think I can put up an audio file:


The point of all this is that from the Baroque through to the late Romantic period, harmony was understood as something functional. That is to say, it was a structure of relationships in which each chord had a different function. The tonic is the destination. Often it is also the beginning, but more and more composers liked to start with an ambiguous harmony and let the tonic be revealed later. But during the whole of this period, you had to end with the tonic and to define it, you had to have a cadence which consists of the dominant, often with a seventh, followed by the tonic. There are an awful lot of other chords, some of them quite exotic, that are used to prepare, to set up, the dominant and make it more dramatic--to 'seal the deal' as it were. The Neapolitan sixth is one of these kinds of chords. But the dominant can be preceded by ordinary chords like the ii chord or the IV chord or other exotic chords known as the "augmented sixth" chords. Any of these harmonies can be extended, prolonged in various ways. The ones that are most commonly prolonged are the tonic and the dominant.

As Schoenberg points out, the composer may decide to fool us by setting up one tonality and then switching to another. Or he may keep us in the dark for a long time before finally revealing the tonality. This is what Mozart is up to in the introduction to the first movement of his "Dissonant" quartet (K. 465) that I put up yesterday. Here is the score:

Click to enlarge

Mozart is making brilliant use of the kind of ambiguity Schoenberg was talking about. That opening C pedal is contradicted by the notes in the other instruments: A flat, E flat and A natural! By the time the A natural arrives, the viola has moved to G, then F#. By measure five, the cello is on B flat and the other instruments have G flat, D flat and G natural. The whole Adagio is a kind of contradiction of C major. But it ends up by arriving at a nice dominant seventh in C major. This page was so disturbing to one Italian publisher that he wrote asking for the misprints to be corrected! Despite all the chromatic ambiguity, this page has a very simple and obvious harmonic function: it is an elaborate prolongation and setting up of the dominant which in turn sets up the tonic. The allegro which follows is in C major.

Schoenberg points out later in the book that every chord can be understood in terms of its relationship to the tonic: direct, indirect or remote. This relationship is defined by those Roman numerals that we theorists are fond of. If I write bVI, that tells us exactly what the relationship of that chord is to the tonic and also tells us what chord is the tonic.

Let's end with another performance of that quartet by Mozart. Here is the Litton Quartet with the introduction and first movement:

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