Ligeti/Beethoven, the Nonesuch Records debut from acclaimed pianist Jeremy Denk, is out today. The album, which features Ligeti's Piano Études, Books One and Two, and Beethoven's Sonata No. 32 in C Minor, Op. 111, includes an essay written by Denk, a respected writer, both on his blog, Think Denk, and in such publications as The New Yorker and the New York Times Sunday Book Review. Here is that essay:

Just listen to pianists drilling away in a conservatory somewhere, armies of them doing their lonely work. Or pull out your dusty copy of Czerny's School of Velocity, which your teacher made you practice when you were ten, trampling your innocent love for music. There's nothing more perverse than piano études. Roaming scales, thirds, sixths, octaves, every possible finger contortion visited in every possible key—it's the stuff of nightmares. The exercises I grew up with had a pattern of four harmonies. They modulated up one half-step, then simply read "etc." You could imagine zoning out, lulled by the drudgery, modulating up and up until you fell off the keyboard altogether.

Ligeti's Études, written in the last decades of his life, are a crowning achievement of his career and of the piano literature; though still new, they are already classics. But one stroke of their genius is underappreciated: the way Ligeti celebrates the genre's perversity, repurposes it into wild, unheard-of art. Drawing inspiration from the étude's most unpromising attributes—obsession, monotony, ad infinitum repetition, mathematical dryness—he fearlessly redeems them.

This perversity is on full display in the third Étude, Touches bloquées [Blocked keys]. Any current or recovering pianist will have a flash of recognition when they see the score: classic strength-building studies where you are instructed to hold down a finger or two, silently, and then play twisted patterns with your other fingers. In Ligeti's version, you must hold down a block of notes, but then you must play a chromatic scale across them: a scale full of holes, of silent, frustrated notes. By requiring you to play notes that won't actually sound, Ligeti directs you toward the opposite of what your piano teacher always wanted: Instead of even, pearly scales, you get stuttering, scattered gestures, in irrational rhythms. This satire on technique (requiring considerable technique) continues in the middle section, where Ligeti writes a series of octave passages, with "wrong notes" built in. After many years of training to play accurate octaves, suddenly you must practice mistakes; the composer is monkeying with your deepest piano instincts.

Ligeti used a delicious, unforgettable image to describe this Étude: circus clowns "who pretend to be unable to execute some feat they can really perform wonderfully."


The flagship Étude, Désordre [Disorder], is an incredible essay in the ad infinitum. Here Ligeti is not satirizing the elements of exercises, but putting them on steroids, extending them in new and terrifying directions.

One of the recurring goals of piano exercises is independence—the independence of one hand from another, and the ability of each finger to do its work separately. In this first Étude, Ligeti chooses a simple way to put your left and right hands at odds: the right hand plays only the white keys, the left only black keys. Ligeti takes brilliant advantage of the arbitrary: The mere fact of there being more white keys (seven) than black keys (five) ends up creating a specific sound, a unique harmonic language. Ligeti exploits (here and elsewhere) the étude's obsession with independence of hands as a pretext to explore different sound worlds—almost like weather fronts—colliding with each other.

But the second, more profound independence-demand is that the pianist must learn to keep different senses of meter going at once: a virtuosity of discombobulation. This is visually obvious in Désordre's opening bars:

Ligeti's Étude 1: Désordre

The measures begin aligned, but then the hands slowly begin to drift apart. This process is quite "rational" at first, one barline slipping farther away from the other, incrementally, like a widening crack between two senses of time. But eventually the pattern goes haywire, and the effect is a joyous rhythmic riot, a continuous reinvention of the beat.

Ligeti claimed his Études "behave like growing organisms." You can think of the opening idea as a piece of DNA. It replicates, but there are accidents, mutations; they generate cells and beings (rhythms and harmonies) of all description. It's chaos, yes, but it's life-affirming too. Or you can think of it in mathematical terms. In Richard Steinitz's book György Ligeti: Music of the Imagination, there is a wonderful account of Ligeti's fascination with fractals and chaos theory, in which a small instability leads to unexpected consequences. Désordre is a classic Ligeti-style fractal, a small misalignment provoking an unthinkable canonic collapse.

We get a respite with Cordes à vide [Open strings], an essay in colors, evoking the worlds of Chopin, Liszt, and Debussy. Ligeti focuses on a single interval, the fifth, which happens to be the distance between the strings of a violin. The opening of this Étude evokes a violinist letting his bow pass casually over his instrument—a normative accident as foundation for a wild wandering. Movement by fifth has a special place in musical syntax: It is often the way you define a home key. Chains of promiscuous fifths create a sense of rootlessness, and Ligeti flaunts this freedom, leading us through a labyrinth of harmonies.

After Cordes à vide, and the incompetent falterings of Touches bloquées, the fourth and fifth Études wander into the world of jazz. Number five, Arc-en-ciel [Rainbow], is marked "Andante con eleganza, with swing." Paying homage to Bill Evans, Ligeti examines the properties of seventh chords. Seventh chords are essentially stacks of thirds, in which any note can pivot to become the foundation, and slight alterations can completely change the chord's direction and meaning. This elusiveness and multivalence is very useful in jazz improvisation; here Ligeti uses it to create a dream-like suspension, and to evoke, with melting and blurring chords, the prismatic rainbow.

In Fanfares (the fourth Étude), Ligeti satirizes a canonical gesture of Western music: the horn call. Back in the pre-valved days, the horn was largely limited to a few essential pitches, and so the horn call was necessarily an outline of a major chord. Beethoven, in the opening of his "Farewell" Sonata, famously rewrote the horn call, changing the last chord so that it switches to a different key, deceptively. Ligeti wickedly runs with this. No matter what "key" a Ligeti horn call begins in, it will certainly not end there; he makes deception the rule. The fanfares modulate zanily against an unchanging ostinato (a running scale with uneven rhythms); then they deteriorate, or evolve, into quick leaping riffs, like scat solos in jazz.

The last Étude of Book One, Automne à Varsovie [Autumn in Warsaw, the name of a festival], stands somewhat apart. The principal idea, its obsession, is descending chromatic lines, an iconic gesture of the past: The descending chromatic has been used for centuries as a symbol of sadness. Emulating a fugue, Ligeti allows you to hear the beautiful lament alone first (set against a quiet, quick background of pulsating fast notes). Gradually other chromatic lines enter, but, as we've almost come to expect now, at mind-bendingly irregular rates: some every five beats, some every three, four, seven, nine—the kitchen sink of ratios—but always lamenting. They make beautiful harmonies as they interact, but the urge of the piece is toward an ever-denser thicket of lines, an accumulation, crowding beauty out. The Étude has a desperate conclusion: The pianist rushes off the bottom edge of the keyboard, chromatically, as loud as possible. The idea of the piece has fused into a white-hot singularity, something infinitely forceful, after which there can only be silence.

Book Two begins much more calmly than Book One, in a reinvented Debussy world, with the "imitation gamelan" of Galamb borong [not really translatable, a nonsense phrase]. The two hands are split symmetrically, playing two different whole-tone scales in ecstatically fast pulsations, grouping and regrouping. This is immediately countered by the bright, Bartókian syncopations of Fém [Metal]. Fém's premise is "simple." The right hand plays a bouncing asymmetric rhythmic pattern, lasting nine beats, while the left hand plays a more straightforward pattern, lasting eight beats. Both hands stick to their patterns, repeating them for pages. The multiplication tables tell us that the two hands will come into phase only every 72 beats (9 x 8), and in the meantime the two unchanging elements create continually changing permutations, nine "verses" of syncopation. Ligeti requests "swing" again, and ad lib accentuation: In other words, the player has to flexibly interpret these permutations, has to be amused and delighted by them, in ways that the composer will not precisely specify.

Then comes the most fiendish Étude of all, Vertige [Vertigo]. Ligeti begins with a descending chromatic scale, then runs another one over the first, then another, and another, at shifting time-intervals, leading to every possible combination of fingerings and chords.

Ligeti's Étude 9: Vertige
At this beginning he writes prestissimo, that is, as fast as possible (not nice), pianissimo (even less nice), legato (outright cruel), and then delivers the coup de grâce: He instructs you to not use any pedal. This is no way to make friends with pianists. But Ligeti makes up for it with the joy of Der Zauberlehrling [The Sorcerer's Apprentice]. Its white-key opening dispels the chromatic nightmare of Vertige; there's a sense of weightlessness; laughing, continually changing accents lead us to a cathartic final "wrong note." Then comes my personal favorite, the beautiful En suspens [In suspense], dedicated to fellow composer György Kurtág (more on this at the end of the notes!). And then the extraordinary Entrelacs [Interlacing]: a series of quiet running fast notes, recalling Automne à Varsovie or Galamb borong, with bell-like tones popping out at different intervals. One set of melody notes comes every 19 pulses, another set comes every 13 pulses; some of the layers are quieter, stronger; gradually this prime number counterpoint accumulates brain-aching complexities.

The last Étude I play (in concert, and in this recording) is the spectacular L'escalier du diable [The devil's staircase]. There is a fourteenth, Coloana infinita [Infinite column] but I have never been able to imagine going on after number thirteen. (It seems Ligeti at one point contemplated ending Book Two this same way, which is my only shred of a justification; I hope you listeners will forgive me!) L'escalier was inspired, improbably, by a bicycle ride in Santa Monica, in which Ligeti found himself battling a ferocious storm. Steinitz refers to it as an "apocalyptic vortex," and that seems like a sufficient description to me; it has that great Escher feeling of always ascending, never descending—a musical trick, a kind of thrilling illusion. What's more, the clanging tritone bass of the ending—the tritone being the "devil's interval"—makes an interesting connection to the opening chords of the Maestoso of Op. 111; and the sense of being pushed along by some irresistible force connects to the ensuing Allegro. The impossible storms, the sense of infinitely rising and searching are the same.


You could lazily write a program note about Beethoven's last Sonata by simply quoting all the beautiful things that have been written about it. There is a thoughtful discussion in Milan Kundera's Testaments Betrayed, for instance, which I highly recommend reading, and a very famous passage in Thomas Mann's novel Doctor Faustus, which I absolutely cannot resist quoting:

The arietta theme, destined for adventures and vicissitudes for which, in its idyllic innocence, it seems never to have been born, is immediately called up and for sixteen bars says its piece, reducible to a motif that emerges toward the end of its first half, like a short, soulful cry—just three notes, an eighth, a sixteenth, and a dotted quarter … But what now becomes of this gentle statement, this pensively tranquil figure, in terms of rhythm, harmony, counterpoint, what blessings its master bestows upon it, what curses he heaps upon it, into what darknesses and superilluminations, where cold and heat, serenity and ecstasy are one and the same, he hurls and elevates it ...
Quotation from Doctor Faustus: the life of the German composer Adrian Leverkühn as told by a friend by Thomas Mann, translated by John E. Woods © 1997 by Alfred A. Knopf, Inc.
It's no accident that Op. 111 attracts literary attention. Though it's music, it doesn't quite behave like it. It seems to be charged with meaning, to communicate in symbols, ciphers, clues.

The Conventional Sonata is a suite of movements: say, a serious first movement, a lyrical second, a playful Scherzo, a bouncy Rondo. Here, Beethoven provides just an Allegro and an Adagio, two opposed poles. He whittles everything down to the absolute difference of the two movements, and a chronology: the sweeping away of one thing by another. As with the greatest Beethoven pieces, the structure itself becomes a message: A question is overwhelmed by its answer. By the time the answer is over, the question is more than forgotten; it has been unwoven, made inconceivable.

The first movement begins in the way of solemn first movements, with a majestic introduction in dotted rhythms—conjuring, among other memories, the opening of Beethoven's "Pathetique" Sonata, Op. 13. Its first gestures are asymmetrical: We leap into loud, dissonant chords, which are then resolved quietly, almost parenthetically. After the third dissonant declaration comes a digression: Beethoven allows the dotted rhythm to wander into the most distant harmonies, the same rhythm but getting ever quieter, stranger, and farther away, as if in a dream.

The emergence from this dream is violent but odd: It is torn between assertion and hesitation, between dramatic statements and second thoughts. This indecision becomes a theme of the ensuing movement (Allegro con brio ed appassionato). The Allegro is mostly consumed with rushing passages, with streams of sixteenth notes—searching, sequencing. But Beethoven scatters tempo slowdowns throughout, of all sizes and shapes. These frictions have a dual meaning. By resisting, they heighten our awareness of a compulsion, a hurrying force; but they also continuously imply an alternative, a world without rushing. The most radical, meaning-laden slowdown happens in the second theme. It's not a theme, really, more a falling fragment, built on a suspended harmony. Beethoven freezes on its irresolution; he allows it to become a beatific impasse, an Adagio. Then, with a storm of sixteenth notes, the precarious perch is abandoned, the movement's relentless urge is resumed.

At the last moment, the first movement wavers into the major key—a strange flickering of the tonal sense. In that same sudden, unsettling major, we begin the magical Arietta.

Thomas Mann's description of the Arietta theme is wrong, weirdly! The main idea (dim-da-da) does not wait to appear until the end of the first phrase. It is the very first thing you hear, this soul of the movement. Much as in the Ligeti Études, Beethoven treats the generative rhythm as a kind of DNA, allowing it to undergo odd mutations, to court chaos. Stripped down to Morse code, the idea is:
long short long … long short long
But in the first variation he chains it together, elides it into:
long short long short long
And then doubles that:
long short long short long short long short long short long
And then doubles that! In the last transformation it becomes amazingly like jazz, with crazed, syncopated dotted rhythms. Of all the profound whiffs of the future Beethoven might have caught, it had to be boogie-woogie?

The evolution from the theme to this proto-jazz has been seamlessly incremental. But looking back at the pure starting point, we might feel that somewhere along the way, we've taken a wrong turn. A sequence of extraordinary events ensues, playing on this sense of disorientation. First, the post-boogie-woogie variation dissolves into a haze. The rhythmic outline is lost, diffused in a million starry notes, although the harmonies are proceeding as before. But then this feeling of being lost becomes actual, tangible, as we go off the harmonic track of the theme, into an ecstatic, free C major. The next step is more disturbing: We go off the track of the key, leaving C major for an uncanny E-flat major. The texture thins, evoking an edge, an extenuation. And after this abyss, which seems irrecoverable, lost beyond lost, we become even more lost: Beethoven writes an endless, soft, drifting passage, fragments of the theme over a sequencing quicksand of harmony.

Many times in his life Beethoven pursued the trope of "losing" the right key and finding it again (as if the composer didn't know the whole time!). It was often a joke, a trick, a clever feint; but not here. Here, for this last Sonata, for this moment of farewell, Beethoven has reserved a harrowing lost-and-found: The theme emerges out of the farthest corner of the labyrinth as if discovered, singing over a stream of harmony, all discontinuities and wanderings forgotten. It is one of the most heartrending passages in the piano literature: an affirmation that says no, no matter what has happened to us, we are not lost. At the climax, Beethoven makes one crucial change: The main idea bursts into a sequence that did not exist in the original theme (but seems as if it had always been meant to be there); he adds continuity to continuity, and allows the generative idea, in Ligeti's words, to "overflow its banks."


One message of this combination Ligeti/Beethoven is that we're still catching up with Beethoven. The Romantic composers followed in Beethoven's footsteps, anxiously, with more than a few daddy issues. But they drew most often on middle Beethoven; many elements of Beethoven's late period were left behind—perhaps too unsettling to deal with at that historical moment. One has to wait for the twentieth century for some of these crazed late urges of Beethoven to find continuation, to find resonance. Ligeti's Études seem at times like a sequel to late Beethoven mania.

The most interesting thematic connection on this album, for me, is between Beethoven's vast timeless canvas and Ligeti's bite-size bits of infinity. Ligeti uses the infinite as a continuous reference point. From simplicity, he ranges into unimaginable complexity; he requests the quietest and loudest extremes; he veers off the top and bottom of the keyboard. And against these thirteen different snapshots, in which the finite and infinite constantly intertwine, we have Op. 111, a work that gradually reveals the infinite, that works its way toward it as an epiphany. In the strange push and pull of 111's first movement, in its odd disjunctions, you have intimations of the impossible. But the last movement slowly fulfills the promise, culminating in the way Beethoven drifts off in the final measures, ends without ending, with an ellipsis, implying the unbounded space of silence to come.

A second crucial connection is the relation to syncopation, to rhythmic mayhem, to jazz (in Beethoven's case proleptically!). Beethoven's boogie-woogie is disturbing to some, bewildering to others, but he gets there by logical steps; the ecstatic syncopations are an outgrowth of forces latent in the theme. And this sense of ecstasy, derived from weird energies hidden in basic ideas, is just as central to the discombobulations of Ligeti. Passages of abandonment are everywhere in the Études: at the end of Désordre, for instance, when the pianist moves into the highest register, using more and more pedal, creating an ever more luminous sound; or in the clanging climaxes of Entrelacs and Galamb borong; or in Ligeti's mesmerized, spaced-out translation of Bill Evans in Arc-en-ciel. All these draw out, in a sense, rhythmic joys of jazz: ecstatic play, the play of freedom against order.

I can't resist pointing to one more connection: the way both the Ligeti and Beethoven works are about separations between dueling, different visions of time. In the beautiful eleventh Étude, En suspens, Ligeti writes the two hands in two different meters. The right hand plays in 6/4 time, a lilting limping waltz, and the left hand plays one-and-a-half times as slowly, in 4/4 time, in its own rhythmic universe. The left hand also plays more quietly—not just in a different meter, but in another layer of perception. The effect of these two different meters and dynamics is haunting: a dance wanting to get going but visited by hesitations, hiccups, uncertainties. After a little while, it hits you: Ligeti has written a kind of outdated genre, a "hesitation waltz." On the one hand, there is the twentieth-century idea of fragmentation, fractions, and metric multiplicity; and on the other, there is the nineteenth-century idea of rubato, a flexible borrowing and giving of time. Ligeti has written both—rubato, but filtered through the mind of the metronome. Past and present tenderly tug at each other. There's no hint of sentimentality or even Romantic nostalgia, but there is burning emotion: Much like the Beethoven, you have this sense of times drifting past each other like tectonic plates, of one world waving goodbye, while another recedes.

—Jeremy Denk, March 2012