Sonata as Teaching Machine

Compare a sonata to a teacher. The teacher gets the pupils' attention, either dramatically or by the quiet trick of speaking softly. Next, the teacher presents the elements carefully, not introducing too many new ideas or developing them too far, for until the basics are learned the pupils cannot build on them. So, at first, the teacher repeats a lot. Sonatas, too, explain first one idea, then another, and then recapitulate it all.

(Music has many forms and there are many ways to teach. I do not say that composers consciously intend to teach at all, yet they are masters at inventing forms for exposition, including those that swarm with more ideas and work our minds much harder.)

Thus 'expositions' show the basic stuff–the atoms of impending chemistries and how some simple compounds can be made from those atoms. Then, in 'developments', those now-familiar compounds, made from bits and threads of beat and tone, can clash or merge, contrast or join together. We find things that do not fit into familiar frameworks hard to understand–such things seem meaningless. I prefer to turn that around: a thing has meaning only after we have learned some ways to represent and process what it means, or to understand its parts and how they are put together.

What is the difference between merely knowing (or remembering, or memorizing) and understanding? We all agree that to understand something, we must know what it means, and that is about as far as we ever get. I think I know why that happens. A thing or idea seems meaningful only when we have several different ways to represent it–different perspectives and different associations. Then we can turn it around in our minds, so to speak: however it seems at the moment, we can see it another way and we never come to a full stop. In other words, we can 'think' about it. If there were only one way to represent this thing or idea, we would not call this representation thinking.

So something has a "meaning" only when it has a few; if we understood something just one way, we would not understand it at all. That is why the seekers of the "real" meanings never find them. This holds true especially for words like 'understand'. That is why sonatas start simply, as do the best of talks and texts. The basics are repeated several times before anything larger or more complex is presented(l. No one remembers word for word all that is said in a lecture or all notes that are played in a piece. Yet if we have understood the lecture or piece once, we now "own" new networks of knowledge about each theme and how it changes and relates to others. No one could remember all of Beethoven's Fifth Symphony from a single hearing, but neither could one ever again hear those first four notes as just four notes! Once a tiny scrap of sound, these four notes have become a known thing–a locus in the web of all the other things we know and whose meanings and significances depend on one another.

Learning to recognize is not the same as memorizing. A mind might build an agent that can sense a certain stimulus, yet build no agent that can reproduce it. How could such a mind learn that the first half-subject of Beethoven's Fifth–call it A–prefigures the second half–call it B? It is simple: an agent A that recognizes A sends a message to another agent B, built to recognize B. That message serves to "lower B's threshold" so that after A hears A, B will react to smaller hints of B than it would otherwise. As a result, that mind "expects" to hear B after A; that is, it will discern B, given fewer or more subtle cues, and might "complain" if it cannot. Yet that mind cannot reproduce either theme in any generative sense. The point is that inter-agent messages need not be in surface music languages, but can be in codes that influence certain other agents to behave in different ways.

(Andor Kovach pointed out to me that composers do not dare use this simple, four-note motive any more. So memorable was Beethoven's treatment that now an accidental hint of it can wreck another piece by unintentionally distracting the Listener.)

If sonatas are lessons, what are the subjects of those lessons? The answer is in the question! One thing the Fifth Symphony taught us is how to hear those first four notes. The surface form is just: descending major third, first tone repeated thrice. At first, that pattern can be heard two different ways:

But once we have heard the symphony, the latter is unthinkable–a strange constraint to plant in all our heads! Let us see how it is taught.

The Fifth declares at once its subject, then its near-identical twin. First comes the theme. Presented in a stark orchestral unison, its minor mode location in tonality is not yet made explicit, nor is its metric frame yet clear: the subject stands alone in time. Next comes its twin. The score itself leaves room to view this transposed counterpart as a complement or as a new beginning. Until now, fermatas have hidden the basic metric frame, a pair of twinned four-measure halves. So far we have only learned to hear those halves as separate wholes.

The next four-measure metric half-frame shows three versions of the subject, one on each ascending pitch of the tonic triad. (Now we arc sure the key is minor.) This shows us how the subject can be made to overlap itself, the three short notes packed perfectly inside the long tone's time-space. The second half-frame does the same, with copies of the complement ascending the dominant seventh chord. This fits the halves together in that single, most familiar, frame of harmony. In rhythm, too, the halves are so precisely congruent that there is no room to wonder how to match them–and attach them–into one eight-measure unit.

The next eight-measure frame explains some more melodic points: how to smooth the figure's firmness with passing tones and how to counterpoise the subject's own inversion inside the long note. (I think that this evokes a sort of sinusoidal motion-frame idea that is later used to represent the second subject.) It also illustrates compression of harmonic time; seen earlier, this would obscure the larger rhythmic unit, but now we know enough to place each metric frame precisely on the afterimage of the one before. Then,

Now it is the second subject-twin's turn to stand alone in time. The conductor must select a symmetry: he or she can choose to answer prior cadence, to start anew, or to close the brackets opened at the very start. Can the conductor do all at once and maintain the metric frame? We hear a long, long unison F (Sub dominant?) for, underneath that silent surface sound, we hear our minds rehearsing what was heard.

The next frame reveals the theme again, descending now by thirds. We see that it was the dominant ninth, not sub dominant at all. The music fooled us that time, but never will again. Then, tour de force: the subject climbs, sounding on every scale degree. This new perspective shows us how to see the four-note theme as an appogiatura. Then, as it descends on each tonic chord-note, we are made to see it as a fragment of arpeggio. That last descent completes a set of all four possibilities, harmonic and directional. (Is this deliberate didactic thoroughness, or merely the accidental outcome of the other symmetries?) Finally, the theme's melodic range is squeezed to nothing, yet it survives and even gains strength as single tone. It has always seemed to me a mystery of art, the impact of those moments in quartets when texture turns to single line and fortepiano shames sforzando in perceived intensity. But such acts, which on the surface only cause the structure or intensity to disappear, must make the largest difference underneath. Shortly, I will propose a scheme in which a sudden, searching change awakes a lot of mental Difference-Finders. This very change wakes yet more difference-finders, and this awakening wakes still more. That is how sudden silence makes the whole mind come alive.

We are "told" all this in just one minute of the lesson and I have touched but one dimension of its rhetoric. Besides explaining, teachers beg and threaten, calm and scare; use gesture, timbre, quaver, and sometimes even silence. This is vital in music, too. Indeed, in the Fifth, it is the start of the subject! Such "lessons" must teach us as much about triads and triplets as mathematicians have learned about angles and sides! Think how much we can learn about minor second intervals from Beethoven's Grosse Fuge in E-flat, Opus 133.