Translator: Dreamscribe
"You two know each other?"
Su-jeong murmured as she watched Seo-ha hurriedly leave his seat.
Gyeo-ul was a celebrity known to anyone who had attended the same school. Since it wasn't a common name, it was unlikely that this was just someone with the same name.
Come to think of it, the two were even the same age.
"What's with that face? You look like someone with something on their mind."
At Theo's question, Su-jeong forced a smile.
But she herself didn't understand why her heart was so unsettled.
* * *
The work of arranging a piano piece for orchestra required an extremely complex process.
'Music is essentially mathematics.'
Pythagoras devised the seven-note scale with mathematical reasoning as its framework.
Halving the length of a string raised the pitch by one octave, and reducing it to two-thirds produced a perfect fifth. The intervals that sounded pleasant to the ear could always be explained by integer ratios, and that order was itself the foundation of modern music.
"Can you tell me now? What did I miss?"
Lawrence asked, looking straight at Seo-ha. His eyes held a mixture of impatience and anticipation.
He had lived alongside music for decades. He had confidence that he could handle the massive apparatus of an orchestra as if it were an extension of his own body.
When he opened a score, he could intuit, almost by instinct, which part needed to step forward and where density had to be pared back.
And yet, in front of this piece, certainty eluded him. He was so frustrated he could barely breathe.
Seo-ha fell into thought.
'Is it really all right to unravel this?'
This piece had been written by him at the peak of his obsession. Every single note had been packed with enough calculation to make anyone sick of it, and every element of the piece had been designed to interlock and turn like the gears of a precision machine.
Seo-ha looked down at the score.
It felt like facing the inner self he had never wanted to show anyone.
"Aren't you going to tell me?"
Perhaps growing restless, the composure was draining from Lawrence's face.
Seo-ha let out a sigh and replied in a small voice.
"...The frequency."
"Hm?"
"The frequency ratios are wrong."
An octave is an interval whose frequencies form a precise 2:1 ratio.
One octave above middle C (261.63 Hz) is 523.25 Hz, and one octave below is 130.81 Hz. He had split the piano's lower register between the cello and the contrabass, and because of the instruments' range limits, the frequency ratios broke down there.
Lawrence's face went blank.
"And there's a lot more besides that...."
Seo-ha spread the score open and began explaining, one by one, the errors Lawrence had made.
"Look here, from measure 17.
A major third ascending from C to E, a minor third ascending from E to G, from G to..."
He rapidly jotted numbers below the staff.
"If you convert each interval into semitone units, you get 4, 3, 7, 7, 5, 4, 3, 2, 1. It's a variation of the Fibonacci sequence. Take the sequence 1, 1, 2, 3, 5, 8, 13..., take the remainders when divided by 12, and arrange them in reverse order."
Lawrence slapped his knee as if something had clicked.
"By 12? Jesus! You meant for the pitches to cycle within a single octave!"
Seo-ha nodded.
Lawrence peered back down at the score he had drawn up.
"Professor, when you split the violin parts, you added an extra voice. The 3 became a 4, and the 4 became a 5. The balance of the sequence was broken."
With a serious expression, Lawrence began discussing with Seo-ha how to correct it.
Listening beside them, Gyeo-ul felt her eyes going round and round.
'What on earth, this is scary. Is this actually a conversation about music?'
For Gyeo-ul, music had always been the realm of emotion.
Her playing changed with her mood. Her tone even differed between sunny days and rainy ones.
Seo-ha, of course, loved that quality in Gyeo-ul's playing, though.
Lawrence didn't know much about math either.
But through experience, he had come to understand that orchestration itself was a highly mathematical act.
Mathematics and music,
The methods differed, but the conclusion they arrived at was the same. They spoke different languages, yet somehow the meaning got across. Gyeo-ul smiled faintly at the thought.
"So, what is it that you want?"
His question resolved, Lawrence asked Seo-ha with a refreshed expression.
"Sorry?"
"Did you want this piece to be performed? Or are you content with it simply existing?"
Seo-ha was silent for a while, then quietly reached out and closed the score. It wasn't a piece worth letting others hear.
Lawrence's face filled with regret. But a composer's wishes had to be respected. Just as he was about to rise from his seat, Gyeo-ul looked intently at Seo-ha and spoke.
"Why? I really love this piece. And you said you can do orchestral arrangements now!"
Seo-ha shook his head.
"There's no narrative arc. This piece is like a diary where a dreary daily routine just keeps going with nothing ever happening. No one's going to like it."
Lawrence chuckled in a low voice.
"There's certainly that aspect to it. But you're wrong to say no one will like it. The prose style of that diary is exquisite beyond compare. Going further, someone might even recognize the structural beauty hidden within."
Hadn't he himself been drawn in by it and come all the way here?
"That's exactly what I'm saying! A piece like this being left as just a practice work, that can't happen! It would be a loss to music history."
"Still...."
Seo-ha trailed off, as if reluctant.
"Yu Seo-ha."
"Yeah?"
"How would you feel if some mathematician produced a brilliant proof and then just kept it hidden? Right now, as a musician, I want to see this piece come out into the world."
"...."
Seo-ha's face was full of stubbornness.
Left with no choice, Gyeo-ul decided to play the card she had been tucking away.
"Remember how you promised before that you'd do one favor for me?"
Seo-ha flinched.
"I remember."
"I'm cashing it in now."
Gyeo-ul knew Seo-ha well. He was the kind of person who, once he made a promise, always kept it.
Lawrence watched the two of them with an intrigued expression.
"...Fine. But not as it is."
If it were released like this, he felt he'd want to sink into the ground from embarrassment.
"Then what?"
"I'll write a second movement."
The time when he had written Ducky's Theme was before he had completed the Four Color Theorem.
His darkest period, when he could see nothing ahead. Since then, there had been no small changes in the image of Ducky as well.
"What?"
The tone was as if he were ordering another cheeseburger.
Seo-ha took a notebook out of his bag. It wasn't composition staff paper but an ordinary notebook.
Scratch scratch.
As lunchtime approached, people came streaming in. The restaurant was growing noisier. A line of people waiting to order had formed in front of the counter.
"Burger with no pickles and two extra slices of cheese."
"Can I upsize the drink?"
"For here. Make the patty well-done, please."
Siiiizzle.
The sound of meat cooking on the griddle, the bang-bang of fry baskets being shaken, and the voices of staff calling out numbers all tangled together.
When someone fumbled about, apparently having dropped their food, bursts of laughter erupted here and there.
Scratch scratch.
But Seo-ha's eyes were fixed solely on the paper. As if none of the noise around him could reach his ears at all.
Unidentifiable symbols piled up on the notebook.
Numbers slipped in between the notes. Fractions were written above the beats, and below the measures, sequences that looked like matrices.
Gyeo-ul sat across from him and watched the sight quietly.
Seo-ha was completely absorbed in composing.
Long, slender fingers held the pencil neatly as they moved. Blue veins appeared and vanished on the back of his hand. Even the sight of his brow furrowing, as if something weren't working out, became a picture.
Gyeo-ul knew that expression of Seo-ha's.
Thump thump.
To hide the sudden quickening of her heartbeat, Gyeo-ul made a needless slurping sound through her straw as she sipped her drink.
How much time had passed?
Around the time the place had grown quiet again, Seo-ha set down his pen.
"It's done."
"May I take a look?"
Lawrence hurriedly took the notebook.
But the score Seo-ha had written could only be read by Seo-ha himself.
"Hmm.... Can you play a little?"
When Seo-ha nodded, Lawrence took out his phone.
Beep beep beep beep.
"I need a favor. Could you find me an empty practice room? A hall would be even better."
Surprisingly, MIT has a dedicated music program (Music & Theater Arts Section).
It's a place where composition, orchestration, and interdisciplinary research bridging music and science are carried out. Lawrence easily managed to secure a hall with a single phone call.
Click.
"Let's head right over."
Lawrence stood up as he ended the call.
Once outside, cold air brushed against their faces. Gyeo-ul glanced back.
'Good grief. To think I'm actually seeing this happen.'
Mozart, she had heard, had often composed in restaurants.
The anecdote that the notes he scribbled on napkins later became masterpieces like The Marriage of Figaro had been passed down like a legend in the history of music.
Apparently familiar with the route, Lawrence walked ahead and turned inward into the campus.
Killian Hall,
a hall with few seats but famous for its extremely precise acoustics. At its center stood a Steinway grand piano.
Lawrence stepped onto the stage and clapped once.
Clap.
A short reverberation traveled along the walls and came back.
Lawrence nodded as if satisfied.
"This will do."
Seo-ha sat down in front of the piano.
He steadied his breath for a moment, then placed his hands on the keys.
Ding.
It was the first movement.
It was a piece he had played dozens of times before, but music is, by its very nature, most accurately rendered by the hands of its creator.
'His playing isn't half bad, either.'
It didn't reach professional level, but it was more than enough to present his own work.
Seo-ha's expression looked pained.
As if tied to a heavy weight and sinking slowly into the sea, Seo-ha steeped himself in the emotions of that time.
'What kind of life did he lead, for him to....'
A single theme was being transformed through various mathematical laws.
'This is the world Seo-ha lives in.'
Gyeo-ul felt tears well up.
It was so heavy, so lonely. The time he had spent supporting himself without leaning on anyone, the weight of that pain, could be felt achingly through the music.
The first movement ended.
Seo-ha immediately began playing the next movement.
'Hm?'
Lawrence's eyes widened.
The harmonic center had shifted. The patterns that had repeated in the earlier section were nowhere to be seen.
And yet, the piece still felt unified.
Lawrence unconsciously began counting the chords.
'C–F–B♭–E♭. ....'
Lawrence caught his breath.
It wasn't that the harmony had changed. Seo-ha had inverted the entire structure of the piece.
'This fellow truly loves Bach.'
The intervals that had descended in the first movement now ascended at the same spacing in the second. But it wasn't only the direction that had been reversed. The notes that had built tension had become lighter. The deliberately unstable chords were, one by one, finding their harmony.
Like a Bach fugue, it used retrograde (Retrograde reversal of order) and inversion (Inversion reversal of interval direction). But it was on a far higher dimension than that. Likely because the elements he used for symmetry were not just one or two.
'How much calculation must have gone into this?'
The entire second movement was a device designed for mathematical contrast with the first.
Beautiful structure, flowing melody, deep, deep emotion.
'Magnificent. A masterpiece.'
At last, Seo-ha's performance reached the point corresponding to the deepest abyss of the first movement.
Seo-ha straightened his back.
And he drew in a deep breath.
Crash.
The pitches that had been suppressed throughout the first movement now pushed one another upward and exploded.
The resonance and melody struck the walls and ceiling, then came pouring back down onto the stage.
The emotions that had been pressed down were liberated in a single instant.
Tears streamed down Gyeo-ul's face.
The performance ended.
Seo-ha wore the unburdened expression of someone who had finally poured out, all at once, something he had long been holding in.
Lawrence, seemingly struck with shock, couldn't speak for a while.
"It rather seems to me you picked the wrong major."
Lawrence was certain.
That Seo-ha had more talent for composition than for mathematics.
He shook his head as if in pity.
A mathematician had written a piece at this level. He could picture vividly, without having to see it, just how many composers this would crush.