Where Art Meets Science: Symphonies and Sonatas

It would be possible to describe everything scientifically, but it would make no sense; it would be without meaning, as if you described a Beethoven symphony as a variation of wave pressure. -Albert Einstein

I believe that from that Earth emerges a musical poetry… which evolves from the universal known as the harmonic series. -Leonard Bernstein, explaining the symphony in terms of wave pressure

In this chapter, we will see the Beethoven symphony both through the eyes of a romantic scientist and an analytical artist. First, through the eyes of the storyteller: a bit of a masterclass with maestro Ivan Fischer to whet the appetite.

We've talked plenty about music's ability to portray a specific character, mood, movement, and more. It's time to consider its ability to tell a long-range story without any reference to the physical world.

The interpretation chain is just:

Composer Imagines a Sound > Converted to Notation > Performers > Audience

and we have to ask how we can be taken for a journey—often a single, 20-minute-long drama—from just the vibration of the air.

The title Sonata tells us only we have a piece of music that is played, not a song that's being sung (in Italian, that would be a cantata). It's as close to “Untitled” as you get in music, although a sonata is nice enough to identify the instruments being played, as in a Sonata for Piano and Violin or Symphony. ^📖

The Sonata-Allegro

The next four chapters take on the typical four movements of a sonata: a fast (Allegro) opening movement, a slow movement, a lighter scherzo movement, and a fast finale. We'll discuss exceptions along the way.

So let's dive into the first one, the Sonata-Allegro.

When I was in high school, playing my first Schubert Sonata in a competition, I received what I thought was a compliment. “You have such a good understanding of structure,” the judge told my teacher Natalie and me, “that's the most important thing to teach after phrasing.”

After turning it over at home, I realized, I'm pretty sure I had never been taught phrasing—the art of making a melody's direction clear to the listener. Maybe that's why I didn't win that competition…

Natalie was less interested in phrasing, which only helped make sense of a few notes at a time. It was always subservient to the structure which made sense of the whole piece. The most important piece to her—and, still, to me—was the sense of the music's Grande Ligne: the Long Line.

The Analytical Artist: The Long Line

Unlike the variations we saw in the previous movement, a sonata does not “chunk” as cleanly into characters. A single movement can run for 25 minutes before there's a clear break. If there's no sense for where the whole thing is going, it can be easy to get lost. (Like a bad acid trip, Jeremy Denk once told me about the Alban Berg sonata.)

A piece can be made to feel shorter, though, by chunking it into bigger units.

If a performer (or a listener) keeps smelling all the roses, the journey will feel quite a bit longer than if they zoom out and see the whole forest (not to mix metaphors).

Zander explains in his TED talk, in a condensed example from Chopin:

This is a miniature of what we might call the long line—multiple individual notes coalescing into a single impulse. Copland writes,

A great symphony is a man-made Mississippi down which we irresistibly flow from the instant of our leave taking to a long foreseen destination… the creation of that continuity and flow—that long line—constitutes the be-all and end-all of every composer’s existence.

That responsibility then passes to the performer, too. Otherwise, you may just leave thinking that the composer is a bad composer, says Yo-Yo Ma.

Should any of that responsibility pass to the listener? Does the listener have to try to hear dozens of notes as a single statement?

Personally, I don't think the listener should have to know the piece's underlying structure any more than a reader needs to know the “hero's journey” archetype to follow along with a novel. Still, some listeners will find that having signposts along the way makes it easier to hear the music in sentences rather than words.

So, very briefly, here's what you might expect:

In the exposition, there is a strong, bold first theme that establishes the key:

That's followed by a lyrical and beautiful second theme in a related key:

Theorists used to call the first theme the “masculine” protagonist and the second theme the “feminine” supporting role, but these stereotypes have outlived their usefulness, and are broken more often than they're held.

The exposition is sometimes repeated so we remember what we heard, then the composer begins a free-wheeling development, going crazy with their themes, like a stream-of-consciousness variation without any constraints.

We end up with themes deconstructed, in far off keys we would never have predicted.

And then finally in the recapitulation (or recap) we hear the original themes again, but both of them have returned to the home key.

We expect the recap to be exactly the same as the exposition, but composers can capitalize on that expectation to add a surprise.

Often, at least, a coda is added to the end for a big finish:

If each of these five sections can be played to feel like it's in one breath, it will feel like the movement isn't 500 words, but 5 sentences. The 500 words might be pretty, but 5 sentences can tell a story.

It's much easier to figure out where those sentences begin and end in a piece that you've heard before. But how does this apply to the first listen? I explore a brand new piece in the Pocket Concert below.

The Romantic Scientist

The signposts give us a foothold on the music, but they only work as well as the composers decide to adhere to them.

At some point, sonata form got so complicated that it can take hours—or centuries—to really figure out what the structure is. There could be three themes on the first page of the sonata, but the next half hour is really just those three in disguise, and then the middle turns into a slow movement, but that might just be the development, and then a fugue starts that might be a scherzo, or the recapitulation, or the on-ramp back to the recapitulation, and the recapitulation is much shorter and doesn’t bring everything back, and there’s no pause anywhere, so the whole thing might be one movement or it might be four… or something like that. Scholars have been trying to tease apart the Liszt Sonata since the 1850s, and they still don’t agree on where the recapitulation starts.

But the most complex sonata still holds together to listeners because its heart is not its melodies, but its harmonies. And even though it sounds like following key changes would be way harder than following themes, it speaks to us more intuitively—because these harmonies are actually built into the world's natural laws of physics.

Physics??

Sound is, of course, vibration. Imagine that 100 vibrations per second (100 Hz) give us a pitch that sounds like a “C.” (It's actually closer to 130, but we'll stick with the round number for arithmetic's sake.)

When you activate a string on, say, a piano or a violin, it sends a bunch of waves back and forth down the string.^💬 The waves that are exactly the right speed to bounce back and forth along the string (100 Hz) will keep the string resonating and keep going until it's out of energy, stacking up like someone pushing a swing at just the right time.

But there are also other frequencies that will resonate too. At double the speed, 200 Hz, the sound wave will still hit the beginning and the end of the string at the right point in the wave. And at triple the speed, 300 Hz. And at 400 Hz, and 500 Hz, and 600 Hz (albeit much weaker). Which of these we hear and how loud they are depend on the instrument. ^💬

OK, so what does this have to do with key relationships and sonata form? Well, check out what notes those overtones sound as. 200 Hz is another C, but the next strongest overtone at 300 Hz is a G, an interval of a fifth above C.^📖

A quick demo: on a piano, that G will actually resonate through the C string.

This first “new” note is called the dominant, because it is the most powerful note in the scale, forever married to the original note. Whenever you play a C, you will also be playing a G—quieter, but omnipresent.

Thus the key of G will sound like it belongs in the key of C. They are so intertwined that there is even a counterpoint “rule” that two voices should never move together in the interval of a fifth, or else the two voices will lose their independence.

On the other hand, a key like an F# does not belong in the key of C. To get there, you'd have to go to G's own dominant (D), then D's (A), then E, then B, and only then to F#—in fact it's about as far as you can get.^📖 It does not resonate nicely with a C. And so an F# will sound very distant from C.

This is the real foundation of the sonata—and really, most of Western music. If we play a bunch of melodies in C, the listener has that in the ear as the main key, the tonic. From there we can easily get to a nearby key, like G for a second theme that's still in our comfort zone.

But once we start adventuring past that, we are not just “far away” because the composer said so, we are far away by the physical basis of the western key system. So the final return, when we play both themes in the tonic once again, feels meant to be.

Heavenly Length

We'll take a harmonic adventure in Schubert's B-Flat Sonata, with its first movement that clocks in over twenty minutes. Robert Schumann coined a term for this when writing about a Schubert symphony: “heavenly length.”

Trying to do a thematic analysis of this piece while listening live would quickly turn into a frustrating experience. There seem to be more than the usual two themes. None seem “masculine” or “feminine.” Harmonically, he takes us to foreign keys long before he's supposed to.

But if we surrender ourselves to just feeling the arc of home > away > home, we'll get the journey.

The most remarkable thing about the opening theme, to me, is how ordinary it sounds. The melody does not particularly reach or yearn. It is beautiful, simply, without trying to be. Then a low trill rumbles under it like distant thunder, and the music pauses. That sound could be an omen, an interruption from another world. But I also hear it as something that seems to belong there, against all odds, part of the landscape from the beginning.

These are already personal interpretations, of course. “Ordinary” and “thunder” are my ways of pointing toward what I hear. It's possible you hear the opening as anything but ordinary. Andras Schiff hears the sea; Alex Ross notes many hear communication from the beyond. But no matter how you choose to interpret it—or whether you give it a programmatic association at all—it sets a grounding for what “home” is, and how it feels.

Throughout the exposition, Schubert “breaks the rules” over and over again taking us places that shouldn't exist in B-Flat Major, from diversions in G-Flat Major to F-sharp minor.^💬 It honestly doesn't really matter if you know you're still in the narrative's setup or if you think you're already in the action in the middle. It doesn't matter if you call the F-sharp minor theme a new theme, or just a diversion. It feels as if Schubert is testing the limits of what “home” is.

Fortunately, I don't have to hold the entire sonata in my head while it happens. A melody catches my ear; later, its return catches my memory. I may notice a change of mood without knowing what caused it. Even when my attention wanders, a new sound can bring me back. Listening needn't be an uninterrupted feat of concentration.

So when we do get to the middle of our odyssey, it can sometimes feel like we're not even sure how we got there. But we know that we're far from the comforts of home as we let Schubert spin us away, deeper and deeper.

When the performance carries me along, the changes feel natural even as they surprise me. Only later do I realize how far we've traveled.

Again, there are many potential stories we could give this section. The storm draws near, a spiritual struggle with a higher power, a couple reaching a split, an origin story from long ago.

No matter what programmatic choice you might make, the Schubert guides us emotionally towards our arrival back home from our odyssey. There's a sense of rightness, a familiarity—and yet a sense that something has changed, that time has passed, and the music might be the same, but the world is not. What does it mean that even here, we have our ominous low rumbling?

And sometimes, of course, none of this happens. I once left a concert before Schubert's Great Symphony because I could tell, given my mental state, that I would almost certainly fall asleep and wake up to some brand of regret. Stravinsky probably would have stayed… he wrote:

So what if I doze off occasionally when listening to Schubert, as long as I always find myself in Paradise when I wake up?

When Form Breaks Down Completely

Beethoven started to break down the sonata form practically as soon as he started writing sonatas. He wrote 32 piano sonatas, consistently writing in the form throughout his life. At each step, he radically changed the form, from adding a then-non-traditional fourth movement in Op. 2 to his last work, Op. 111, which uses only two movements and puts the emphasis on the 18-minute long theme-and-variations second movement.

In between, he did everything imaginable to mess with the form. By the time he hit Op. 27 around the age of 30, the form barely resembled the “sonata” that we started the chapter with. He called the two Op. 27 sonatas “Quasi una fantasia,” like a fantasy. Today, Op. 27 No. 2 is known as the Moonlight Sonata (named after his death).

The thing is, most of these innovations no longer startle us when we hear them in the concert hall like they did the audiences of his time. When you get to the concert hall to see the Moonlight sonata, you've either heard it before or you haven't. If you've heard it before, you're not going to be surprised that it starts slow and dreamy rather than fast like a typical sonata. If you've never heard it before, you honestly probably haven't internalized sonata form so thoroughly that you're surprised when it starts slow. Maybe you've gone to a pre-concert lecture where you're told how surprised you should be… but in my experience this doesn't exactly make people gasp in shock when it starts.^💬

I think the disintegration of the traditional sonata form tells us two things. First, it gives us permission to experience the narrative unfolding of a sonata without rigor.

But second, it shows us that all the non-sonata music really isn't that far off from being a sonata in the first place. We can look for the long line, the narrative development, and the arrival home—the hallmarks of a sonata—in just about anything.

Fantasy

Before Beethoven, the fantasy was largely an “anything goes” improvisational genre. But after Beethoven blurred the line between Sonata and Fantasy with the sonata quasi una fantasia (Moonlight), a torrent of other composers followed suit. The new fantasy inherited the general arc of the sonata, but with a focus on the free development of their themes.

Schubert, Schumann, Mendelssohn, Chopin, Scriabin—all of them wrote multiple masterpieces as solo piano sonatas. I think each one only wrote one masterpiece simply called Fantasy.^💬 But it's that fantasy that shows each at their most heart-on-sleeve moments, with their most Instagrammable climaxes.

I don't believe it's a coincidence. Perhaps they chose the most flexible form possible when they wanted to shout from the rooftops. Or maybe the relaxed constraints also brought out in them a more extroverted musical language.

Here's Mendelssohn's F-sharp minor Fantasie, with its mix of improvisatory freedom and sonata structure.

Right from the outset we hear both fantasy and sonata together. But it's the climactic development that feels more sturm und drang—storm and stress—than the opening would foretell, as if Mendelssohn's shackles came off and he let it all out.^💬

In its denouement, the fantasy essentially fulfills the standard structure of a sonata, but it never feels structured, like it was made up on the spot. And in this piece, it disappears the same way.

Fantasies, like sonatas, can continue seamlessly (attacca) into their next movement, or return us to a brief moment of silence.

If you've ever been unsure whether to clap at the end of the first movement, there's a collapsible aside for you below.

In the next chapter, we'll move on to the typical second movement—the slow movement.