Claude Debussy: Doctor Gradus ad Parnassum, Le Coin des Enfants, Petite Suite pour Piano Seul, C Major, 1908

In 1905, Debussy’s daughter with Emma Bardac, nicknamed Chou-chou, was born in Paris. She would only outlive him by a year. Three years later, imagining, as all musicians must, three-year-old Claude-Emma practicing her scales (from a work titled Gradus ad Parnassum, steps to heaven), Debussy wrote his own homage, to piano students, to his daughter, to youth, to musical evolution, to heaven.

[Many people had written under this title before, including Clementi, Johann Fux (whose studies were used by Bach, Mozart, and Beethoven) and Carl Czerny, until the very word “gradus” came to mean a primer, as we have today, in, for instance, Bonds for Dummies. Nabokov gave the name, meaning also “shadow,” to the nemesis of the equally shady John Shade, Nabokov’s poet and prey in Pale Fire.

The graded light, layered revelation, stepped chiaroscuro is the way music reveals itself to us, so that childish scales come to life as motifs, as means to a melodic end, and the rote and inexplicable scales in a Schubert sonata become, in the hands of a Leonskaya, a sweep into space.

In fact Debussy must have been thinking more of Charles-Louis Hanon’s le Piano virtuose, published in 1873, whose first exercise in C Major comes very close to the scale with which Debussy begins his piece.]

Hanon leaves a gap in his scale, and Debussy leaves a bigger gap in his imitation. When this theme returns in the end, that leap between the isolated note and the closer notes of the scale pattern produce a hidden melody low down, played by the thumb.

But initially the dreaming child plays a repeating scale, and then, immediately bored by the routine, imagines a simple melody on top of her homework. This is the simplest of melodies, called a “turn,” or appoggiatura, in baroque music. This section is where Debussy turns traditional music into musical Impressionism, a free-form languid onomatopoeia which in its fantasy of harmonies imitates running water and rustling leaves, the way the painter Monet’s brush copied gusts of wind on the canvas to align human and natural means in order to merge their ends.

Debussy uses the appoggiatura to pay homage to old forms of music on his way to eventual musical epiphanies, as if the first instinct of a child, fed on pedantic scales, might be baroque. As Strauss views evolution chronologically, Debussy also works through the Baroque to Impressionism into the Music of the Future.

To harp on the appoggiatura, there is possibly nothing more natural than just playing the note C, then the note above it, finally repeating the original C. This is also called an inverted trill.

A little girl came out of a foggy La Jolla morning one day at a cafe and said to us, “I know how dogs yawn,” and went on to do imitations, complete with tongue motions, of our dog, who watched her in horror. The beginning of the Gradus is the same urge in musical form, a girl saying, “I know how music goes,” “I know how to do an inverted trill.”

Many composers have begun with this inverted trill formula. Bach uses it in his C Minor Prelude and Fugue. John Williams uses it as his Jurassic Park theme. Alex North used it in the theme for the film, Who’s Afraid of Virginia Woolf? Vivaldi used it as part of the timeless midsummer theme in the Adagio from his guitar concerto in D.

How do you follow such a primordial beginning? In this case, Debussy chooses a descending scale, maybe because Hanon uses both an ascending and a descending scale pattern in his exercise. But it is also suspicious that Schumann used a similar descending scale as a theme for the young girl he loved, Clara Wieck (which scale repeats in both the Schumann Romanze and the Brahms Intermezzo played by the Yeti on the mountain).

Note that a trill has two parts: the ascending and the descending. So the descending “Clara” theme is present in the trill theme of the melody all along. It is hidden in plain sight.

The music sinks downwards because it is driven by history. The accompaniment is also Debussy’s homage to his heroes: rapid notes in the left hand suggest Bach keyboard concertos or Mendelssohn’s Songs Without Words. As well, Debussy wants to get to his next idea, which is the note of E.

Why E? Because it is the second note of the triad, of the C Major chord (C, E, G, C). E seems surprising and entirely arbitrary, until you realize that Debussy has a game plan. He wants E because he is building a cathedral out of the C chord. Its four notes (C, E, G, C) will stand in for the universe, the stages of growth in a musician, as they did for Strauss in his tone poem, Zarathustra (although Strauss, sensing the coming devastation of civilization, had more on his mind, and the C chord had become the last gasp of order, the last chance to recall the past before the future erased it).

So how do you get from C to E? There are many ways. Liszt or Grieg might have just gone there, in an abrupt transition. But Debussy is conjuring up a beginning pianist, and the transition must be something a small child might do. So the rippling C scale continues on down until it hits a note which stops it in its tracks.

If you’re C, what are the important notes in your life, your family members? Obviously, the C chord (low C, E, G, and then the top C). G is important because it is the springboard back to C. It is the note which, in every doo-wop song and in every early rock song, in every Sousa march, in early Broadway songs, in lullabies, in George M. Cohan paeans, jumps dependably back to the beginning (or the end). It is the cheap fix, everyman’s way to end a piece of music.

A harmonic system gradually came into being after the groundless chants of medieval monks, those pagan hymns in strange scales (the seven modes of Ionian, Dorian, Phrygian, Lydian, Mixolydian, Aeolian, and Locrian). In those days, there were a hundred ways of tuning an instrument, such as a lute or an organ. They resulted in some godless noises, and finally the Catholic Church, the pre-eminent authority in the land, banned certain combinations of notes, calling them “the devil in music.” Even when I was young, rural Catholic monseignors banned Bach, as he was a sonic graven idol, a distraction from the serious worship of those fuzzy ecumenical metaphors which on a good day led to epiphany. Meditation only works when the chain of thought is unbroken, or so the Church believed in the days before iPhones.

Organ pipes could be adjusted a hundred ways, and different tuners had their own ideas, as did the pipes, which went rapidly out of whack, so that the flattened tones we esteem in organ music stem from a tradition of chaos and disrepair.

When the piano, or clavichord, or clavier, came into prominence, there was a natural Stepford Wives inclination to reign it in, to turn its ungainly, ungodly gaffes into socially acceptable doilies and petit fours, to suburbanize its excesses and rude tonal excrescences, to Binaca its breath, deodorize its plumbing; the way to a matron’s heart lay in music’s being well-behaved, or well-tempered. None of those Schoenberg chromatics or Boulez shrieks. (In order to deconstruct music, it had to be constructed first.)

This construction was an immense philosophic rewrite of the pagan idea of harmony. Sensualized rhythms and unruly gatherings of notes had to be white-washed, so that Christianity banished indecent sounds to the basement, where they festered until more recent times.

Since the beginning of thought, philosophers have marveled at the relationships of distance which appear to balance the solar system. Planets, asteroids, moons that are not in proper Euclidian balance are discarded by the gravitational system, expelled from the system. The perfectly proportioned harmony of the planets was called the music of the spheres, the formula that determined cooperation in a mysterious universe of forces we still don’t understand: light, matter, antimatter, gravity, space, time. The largest concepts of existence are so far impervious to analysis, although we prize systems that shed some light on them, such as fractals, quantum mechanics, string theory. The impenetrability of the workings of all things should humble the most arrogant of us. Donne comes to mind: “‘twere profanation to tell the laiety our love.” The concepts we most value should remain unspoken, undescribed. As with the Observation Principle, when you name something, it sidesteps the definition, to remain pure. As Richard Wilbur has pointed out, to name a bear tames an otherwise indescribable monster. Calling it a bear takes it for granted.

Plato, Archimedes, Euclid, Laplace, Newton, Lindblad, Planck, and others have posited a proportionality which shapes our ends, along with orbital resonances which tune, or stabilize the planets. Plato, Aristotle, and Archimedes insisted on a golden ratio which produced balance in stars, buildings, and sounds, as well as in mathematical equations. Martin Rees, in Just Six Numbers, describes how esoteric and seemingly trivial constants keep the world in balance. These constants replace the easy concept of a golden mean with a more untidy, fractal close-up of these immense forces.

The instinct to regulate the chaos of tones in the medieval world produced the well-tempered system of tuning, an imitation of a tuned universe.

This system has its own vocabulary, some of it left over from the monkish epoch. Modern music has defined itself in terms of this vocabulary (“tonic,” “dominant,” etc.). Although we seem to use it mainly in program notes, it has serious underpinnings in logarithms, and tries simultaneously to free us from sloppy assumptions about the powers of existence while dictating cleaner ways of harmonizing our emotions.

There are three well-known chords in this system which form the basis of much standard religious, rock, and pop music: the main tone, or tonic; the tone that leads back to the tonic, or dominant; and the chord just below the dominant, the subdominant. In the key of C, C is the tonic, G the dominant, and F the subdominant. Let me sound briefly like a schoolteacher: the dominant note, G, leading to the tonic center of C became an acceptable way to end a piece quickly, but using the subdominant F to C is more spiritual. This latter “modulation” is the sound of “amen” in most hymns (Quaker, Shaker, Anglican, Huguenot, Catholic).

Mozart used the subdominant to signal a piece was about to end, the way Nabokov used butterflies to signal that someone was about to die. Debussy here is being radical by going to the subdominant of F almost immediately, although he has no intentions of ending the piece.

Muzio Clementi, with his Gradus ad Parnassum of 1817, introduced surprisingly modern harmonies into his scale studies to keep them interesting and open up a student’s tolerance of unexpected harmonies. Very few of his studies were didactic. Debussy mocks the kind of rote training which used the simplest pieces of Carl Czerny’s Ecole de Velocité (Opus 299, 1830’s), Clementi, and Hanon’s le Piano virtuose (1873) at the expense of the better pieces.

This is a very roundabout way of showing how the second anchor of E is reached.

Then arpeggios weave around it. Why? Because the first melody was a “turn.” And so here the key note is “turned” with broken chords played above and below it, an impressionistic way to vary the concept of a Baroque trill.

This concept continues to modulate to the higher note of F, which has its own dancing apsaras, weaving around it in distorted harmonies vaguely representative of a muted Turkish Raqs sharki or Cypriot Tsifteteli, which were then trendy, the spinning and weaving of a very suburban belly dancer in the imagination of a proper French gamine from Saint-Germain-en-Laye, living only a few blocks from the cathedral of that tennisy, affluent Paris suburb. If fillettes do not always have the same fantasies as jaded elder roués, men always hope they might.

After weaving around F, the piano returns to E, but this time it is even more chaotic and Impressionistic, the left hand bouncing up and down while the right hand weaves chords around it, until it subsides into a steady rain of triplets around the original note of E. Debussy hoped to imitate in music what Monet did in painting, and Verlaine in poetry. The French countryside was eternally dappled with specks of sunset dust that decade, and artists were determined to imitate nature. After the Romantic era had over-imitated human emotions, Impressionism was a backlash to a purer source of inspiration, nature.

This E is close enough to the original key of C to allow Debussy to bring the original theme back, to return his gamine to her gamut, to her roots, before her next spurt of growth. The initial Hanon scale is almost immediately varied into a gorgeous typical Debussy daydream of gossamer arpeggios underneath a beautiful melody which is in fact the very same melody as the initial one, but this time in the key is E, rather than the initial C.

A small nod is made to the descending Schumann theme, and then the trill motif returns briefly, before the goal of G is reached (the third note of the C chord of C, E, G, C), disguised with a scale and with the trill motif in a new key which leads directly to a slow repeat of the Hanon theme in B Flat and then in A Flat. This becomes the dream section.     Whatever possesses Debussy to go so far afield harmonically, from C to A Flat?

One good excuse is the overtone series. Leonard Bernstein has pointed out that the juvenile taunt of nya-nya-NYA-nya-nya is the same in every culture, and is composed of all the intervals of the overtone series compressed into one octave. When you play a note on a piano and hold it, you don’t just hear that one note. Many of the strings vibrate sympathetically. So you’ll also hear E, G, and some notes that fall in between our well-tuned piano notes. Sooner or later you hear a note which is made up of several notes, but which is close to the “NYA” tone of the taunt. Both B Flat and A Flat are represented fairly early in the series of tones released by playing just that C on the piano, as well as a note which is neither A Flat nor A, but a combination of them.

Both major and minor are present on the piano at the same time, as matter and antimatter are present in the universe. Rather than self-canceling, they simply add complexity. This might be one argument for complex prose or poetry: how can a lush universe be captured by a monotone? Such harmonies also explain systematic plurality, where a person can hold an idea and its opposite in his head simultaneously. The duality of our natures is also present in the music of the spheres (and our life is rounded with a song).

In a piece constructed very consciously of the building blocks of harmony, the final feather in Debussy’s hat is the nod to absolute modernity, to the farthest reaches of vibration, to the most rebellious of notes, the ones banned by the Church for blasphemy. This flaw in the well-tempered scale is what all children understand instinctively: that the very notes approved by society produce the ones that aren’t. Those notes tend to be very faint, so the rebellion is sotto voce, whispered. We thumb our nose discreetly at our elders when we play the piano, as Mozart knew.

And so Debussy’s dreamiest of moments in the Gradus is made from the rudest of tonalities: a silk purse from a sow’s ear, as our finery is secretly woven from petroleum byproducts, and our toys are made of toxic Chinese waste. The beautiful two-note theme heard above the usual repetitive Hanon scale is the descending part of the trill theme, here singled out from the chaos of practicing and slowed down into a sigh.

And then the serious G octave. Although G has already been reached a minute before, it was only in passing. And so Debussy makes his point more emphatically: we have risen from C through E to a very serious G. G is a dramatic foreshadowing of the piano’s jumping back to C again, and in so doing finishing the piece. G threatens to complete the piece. It also promises a fast coda, a virtuosic ending. It is the pinnacle of musical achievement. Present meekly in any child’s chord, G here reveals itself as the antagonist, the nemesis, the prophet, the harbinger of everything to come. From here, there is nowhere to go but hell, or heaven.

The Hanon theme repeats for the third time. Here I like to stress the inner melody of the thumb notes, the low notes separated from the other scale notes by so many intervals that they beg to differ. I also bring out the inner voice of the trill theme, which moves in opposition to the higher melody, as if to say that we are both an idea and its opposite, that we are all notes combined, a human overtone series.

Although every note is the same as at the beginning, now the stakes are higher, and the pace is faster. The little girl has grown up. Adding that demonic A Flat, the NYA-nya, to the C chord now produces an “augmented” arpeggio that glides upward to the triumphant return of the trill theme and the Clara theme. These notes should resound like a trumpet in a hall. Debussy marks them with an emphatic underlining, and indicates that, bit by bit, the piece should become more animated, and more animist, more spiritual.

(Note that a normal chord can be augmented by making its top note sharp.)

The trill notes repeat more passionately, carved out and given their own arpeggios, like the toll of a bell, and then the modern soul of the chord emerges from the chrysalis of the scales and mounts like a butterfly to the ceiling, from where the C chord is flung tempestuously back to earth where it crashes with, of course, Mozart’s subdominant warning of the F chord, and then the expected flourish of the dominant-tonic two-note farewell followed, after a brief pause, by the octave with which the piece began, now entirely fleshed-out, sure of itself, aggressive, and deep-throated.

I ask myself whether the final pause before that octave comes from the gap between the scale notes. Even though the scales are written to be played evenly, the fact that their first note is so far away from the rest of the scale pattern is a kind of leap (which is there from the beginning), until the leap comes forth, fully formed, to assert its uniqueness at the end. Q.E.D. Quod erat demonstrandum. That which was advanced to be proven, has been. The world has been solved, through the obscure logarithms that dictate the tuning of the piano, the tuning of the world, and the growth of a child into Ygdrasil, the Nordic tree of life, that, as the poet Richard Wilbur says, “has the stars for fruit.”