Day Eleven: Harmonic Reduction

Beethoven's Sixth. The larger structures of tonal music have at its core a much simpler and more basic harmonic skeleton.

This post is part of 14 Days of Harmony, a free course for musicians who want to deepen their understanding of harmony, and learn how to develop their connection with sound as a result. You can view the entire course here.

Hearing the big within the small. 

The purpose of this lesson is to start putting to use everything that we've learned and apply it to bigger sections of pieces. I think you'll start to see that there are very basic patterns of interconnectedness within any tonal piece of music. 

Just to recap the story so far, we first saw how elemental tones can come together in us to form the smallest level of music: the interval. Then, we built chords and diatonic chord progressions from those 12 tones based on how they all related to one another. We then learned about the expression of a stable tonality with the cadence. Recently, we connected cadences of many different keys through modulation. 

With the exercises, we learned how to build and smoothly connect chords, and discovered that the music of J. S. Bach expresses everything that is harmonically possible in the system of harmony that we still use today: the system of tonality. 

By way of the principle of tonality and the relations of the tones, you can come to understand that the larger structures of music have at its core a much simpler and more basic harmonic skeleton. And the reverse is true too; a simple harmony can form the basis of an entire movement. 

Complex harmonic structures can be "reduced" and still retain the essence of what we experience.

To get a sense of what I mean, let's start with a familiar modulation. Here I've labeled all of the tones based on their interval relation to the chord root: tones with style.

Figure 1 - Can you hear what the arrows in the diagram depicts?

Figure 1. Here's our classic modulation from C major to F major via D minor. The three moments of the modulation are the initial cadence in C major, the neutral field that goes to D minor, and the final cadence in F major. This time I use the unconventional method of labeling the ii65 chord a IV6 chord to mean a IV chord with an added sixth above the bass, not a first inversion IV chord. The benefit here brings attention to the more important fifth in the chord in the context of F major. Labeling as ii puts more importance on G-D, and labeling as IV puts the importance on Bb-F. 

We hear the C major, D minor, and F major as the points of stability in the modulation. It is going by way of D minor from C major that we can live F major as the new tonic, and not hear F as the subdominant of C. Those chords are stabilized with their upper fifths, and the two "tonics" also have their subdominant chords to help define and support their stability. 

Figure 2. A harmonic "summary". You can think of each chord in this measure as a representation of the "backstory" behind the main structural moments in the modulation. This is an example of a harmonic reduction. And, each chord and its backstory in the reduced modulation could itself be expanded upon to form the original modulation or a variation of modulation. The more familiar and in tune you are with the smallest elements of music, the more you can imagine the full universe of musical possibility.

Any element of harmony can be extended in time by other parameters in music: melody, rhythm, timbre. 

Let's look at an example of a mini modulation that appears in one of Beethoven's symphonies, between the first two themes of the Pastorale.