Sunday, October 9, 2011

Harmony Revisited, Part 3

I've published quite a few posts on harmony. The reason is that harmony is, I think, the big problem for composers at this moment. Why? The period from the 12th century up until a little after 1900 saw a long and fairly consistent development of harmony. It started with the most basic fundamentals, simply learning how to combine two voices and what intervals were consonant and what dissonant. There was a long see-saw between the differing demands or possibilities of harmony (the vertical) and counterpoint (the horizontal) but there was, until some time in the 19th century, a continual development in the sense of the composer learning to handle more and more possibilities. Then, in the late 19th century the system simply became overloaded and ultimately broke down entirely as Schoenberg called for the "emancipation of the dissonance" which meant the end of harmony as true harmony depends on a relationship between consonance and dissonance. Well, so does counterpoint, actually. This situation did not last very long. For one thing, audiences fairly decisively rejected atonal music and for another, in the late 60s and early 70s a number of composers, the so-called 'minimalists', revived harmony. This was not, and still is not, entirely successful, though. Today, I'm going to try and show you the reason why.

First, here is an excerpt from a score by Steve Reich, the slow movement of Electric Counterpoint written in 1987:

Click to enlarge

And here is a performance of this movement. The excerpt above appears about 1'05 into the performance.

All through this piece, Steve Reich is doing fascinating things with rhythm as he always does.  As one would expect from the title, the counterpoint is also rich. What we see on the page excerpted is one motif beginning with a falling fourth and with a rising third decoration in sixteenth notes. This is heard in different voices starting at different places in the meter and on two different pitches. It begins on either E or B.

But I want to just look at the harmony. If we look at any one beat, say for example, the first beat in the excerpt, we find the following notes from bottom to top (considering the whole beat): B, E, F#, B, E. The second beat is B, E, F#, B, E. Third beat: D#, F#, G#, C#, D#. Fourth beat: G#, D#, B. This can't really be analyzed in traditional ways at all. But the effect is a shimmering and pulsing harmony of E major blended with B major with the C# as a kind of 'non-harmonic' tone. This fits with the counterpoint as the C# looks like a decoration there too. The only thing I want to point out is that this harmony is static and remains so for long periods. Later on, the bass puts an A underneath this, but the upper voices remain pretty much the same. In the absence of cadences or other structural load points, we accept this constellation of notes as 'tonic' harmony. So, tonic blended with dominant all the time.

Now, let's compare this with a piece from the days when harmony was at its best.

This is the sarabande from the First Partita for solo violin. This is my own transcription for solo guitar and I have modified the bass line slightly and added one bass note, but that will have nothing to do with the point I will be making. If you notice in the score above, I have inserted boxes here and there. These boxes are the only places in the score where Bach has tonic harmony. All the rest is devoted to non-tonic harmony. For example, in the first few bars he moves from i to iv to V of III to VI before having a weak cadence in measure 5. The first half ends with a half cadence. There are 32 measures in the whole movement for a total of 96 beats. Of these 96 beats, tonic harmony occupies a mere 12 or 12.5%. Seven-eighths of the piece is taken up with other harmonies that are related to the tonic either directly or indirectly. For example, as telegraphed in measure 1, in the second half there is a significant modulation to the subdominant minor, E minor, with a full cadence in that key in mm 16-17. Bach does not need to belabor the tonic because he is working within a harmonic system where he doesn't have to. It is like a delicately calibrated solar system with all the planets orbiting the tonic sun. Steve Reich on the other hand, has to really sit on the tonic because the system of relationships between tonic and other chords has been wiped out. I think that further examination will show that most composers writing tonal music now seem to cling to the tonic with little of the harmonic freedom that composers enjoyed in the days of "common practice" harmony, from about 1600 to 1900.

Here is a performance of the Bach Sarabande:

So the question is, if your 'harmony' consists in sitting on the tonic all the time, is that really harmony?

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