“And the sting of each hit. It would ripple out until it met the stings of all the other hits, until eventually, these circles of pain, they overlapped, turned into one thing. And then it stopped. He left. I started to feel less. It was very cold, and I remember feeling grateful for that. Then, later, I was dragged along the ground again, but more gently, by a different man.” She looked at Stagg as she said this. “And I remember being unloaded from the ambulance at the hospital.”
“He said nothing to you, during or after.”
“I don’t think he had anything left to say.”
Stagg started to summarize these details in his notes, the bullet points Penerin would want, how all this might compare to Ravan’s cases. But the image of Jen collapsing on the man’s cock, at the strike to her back, divided his mind, and half of it turned toward the double-axe handle.
His freshman-year roommate once told him about someone he grew up with, Chris, who was, at the time, a Sigma Chi brother at Cornell. He’d met a thick black girl one January night—Lena, a student at Ithaca College, he thought—in a pickup bar in town. She wore a bob cut, with shiny, waterproof hair, the sort that had been relaxed in an attempt to mimic the hair of other races. But in this respect it failed. It looked only like distressed African hair. She wore black skintight leggings, and a black blouse meant to be flowing that was instead packed tight with flesh. Her belly appeared to begin at her sternum and it rolled in waves down her front as she moved.
Chris showed up at the bar already loose from the four pints he’d had at the frat house, around the pool table. It was Sunday night and the bar was less than half full. He sat down, asking for a double Maker’s, one cube. Lena was three stools down talking with another black woman, this one of more common proportions. There was a moderately attractive white girl next to Lena, then an empty stool, then Chris. The girl reminded him just slightly of an ex, her small breasts pressed against a fitting wool sweater. He caught the ex’s eyes—they might as well have been—and nerves seemed to stir in her. A sense of possibility came over her face; he let it be for a minute, in small talk. He made it grow when he asked if she’d like to move down a stool. She did.
The bartender came to see if she could use a drink Chris would pay for. But as she ordered, he slipped around her, bourbon in hand, to the stool she’d vacated. He thanked her for moving and watched vague hopes seep from her face. Seamlessly he chatted up Lena. A few vodka spritzers, some talk about the formative influence of Good Kid, M.A.A.D. City on his life, and then outside, pushing past six-foot snowbanks on the narrow road. To an Ithaca dorm? No, turns out she’s not a student anywhere, just a townie. The fraternity was no place for her. So they made their way to her apartment at the base of the hill.
He watched Lena jiggle up the stairs from behind. The place was clean, it surprised him to see. But the materials were poor: linoleum, plywood, dollar-store spackling, wood-patterned plastic for the table, chairs in aluminum with vinyl cushions, and a couch upholstered in cloth only slightly smoother than burlap.
He thought of his ex as he pulled the clothes from her. The mess of rolling flesh made him smile. He pulled out his cock and pushed it between those heavy lips. Too much tooth. Can’t even suck a dick right. He reverse-fishhooked her with his thumbs, felt the grooves of her molars worn away by ten thousand Slim Jims. With his hands gripping her face, he wrenched open the jaws and pushed himself into the space he’d made. She gagged and tried to close it, but his thumbs were there. He carried on in her mouth this way until she began to froth. He rolled the woman over, told her to fold out the burlap couch. She said some words that didn’t interest him. He was more concerned with the two condom coins he’d pulled from his pocket, for double bagging. The diseases he imagined she had then were many, and the thought of each brought more blood to his groin. He finished his preparations and worked her over from behind. She rocked and rolled and the couch threatened to collapse, but he was determined to finish before the fall.
He did. But as he came, he gave her two sharp shots to the kidney, gripped his hands high above his head around the handle of an imaginary axe, and launched himself into the air with a roar. He brought his fists down on the stem of her neck, his full weight behind them. The metal struts of the couch seemed to crumple as her arms splayed out and she came down in stages under him.
He rolled off her with an athlete’s grace and pulled the sheaths from his cock. He flushed them, taking care not to leave any semen on the bathroom floor or the rim of the toilet. It was five a.m. and the radiator had just come crackling to life. He dressed before her overturned body and the bent couch.
She moaned softly, whether from orgasm, alcohol, or simple blunt force, he couldn’t tell. That was the point, to leave without knowing the meaning of her quivers and coos. The beast had been felled by cock, or fist, or bottle. How she would rise again, in what state, how much she would remember, how she would explain this night—these were questions for other men: brother, father, officer.
Jen had been felled by a man of privilege too, it seemed, someone idle enough for such lovingly scripted cruelties—even if he hadn’t actually fucked her. Though that did make the story odder. They always fucked them. But not this man, a good-looking man at that.
“Okay.” Stagg finished his summary and flipped the page in the pad. “How many girls have left over the last months, would you say, because of these assaults?”
“Left Halsley?”
Stagg nodded. “Or the business.”
“A lot. Half maybe. More all the time.”
“And are they still sex workers, as far as you know?”
“I can’t really say. I don’t know these people, this community, if you want to call it that, very well. But I don’t see why not.”
“Right—but you would think there’d be a lingering fear. Do you know of any who’ve definitely gone in another direction? Away from prostitution.”
She swept the hair from her face as that word came from his mouth. It kept cascading down when she shook her head, yes or no. “Sure. A few. When you go as far as moving, you consider a lot of things.”
“And of the victims themselves?”
“I think at least half are doing other things. Back with family or friends, some in NA or halfway houses, some working regular jobs, retail, that sort of thing.”
“And that’s pretty well known to the other women, what they’ve chosen, you would guess?”
Jen paused and squinted, searching the apartments across the street. “Yes. That I know, actually.”
He stood. “A lot of people are working on this, Ms. Best,” he said. “I’m hoping there’s something to tell you soon.”
She yawned as he spoke. “Can you get me my pills? They’re on the counter.”
He picked up the translucent orange bottle from the kitchen counter. Percocet. He thought to bring it to her but paused between kitchen and couch. He twisted off the white cap and tapped a single oblong pill into his hand and set the bottle on the counter.
“They gave me so few,” she said.
The glass of water Mariela had set out for him remained on the coffee table, untouched. He picked up the chilly glass and condensed water dripped across the table. The last of the ice, just milky slivers now, was dissolving. He held out the pill and the glass to her, one in each hand, as if she might receive them the same way, though she had only one good hand at this point. She took the pill from his palm and pushed it into her closed mouth, between her lower lip and teeth, like chewing tobacco. She returned with the same hand, the good one, for the glass. Before he could lower his own, she put the glass back in it. Only after all this did she look him in the eye, and then only briefly, in a sweep of much else.
Her phone chirped twice.
“Your friend?”
“Mariela. She’s here almost.”
“Good.”
She dropped the phone on the couch and put her feet up over the arm. “Bye,” she said in something just above a whisper.
&
nbsp; “Should I wait for Mariela? I can.”
Jen lay there with her eyes half open, willfully oblivious to him, with the very mien the opioid would anyway force on her shortly. Perhaps she learned this at the hospital, he thought, that it was better to adopt the look of lassitude than to wait for it to seize you. Just as well.
He drank the rest of the water and left.
14
Larent sawed at the string, the open E. A continuous tone rose from the double bass, and from it sprang further tones, harmonics, an infinite ascending series, growing ever fainter. He’d trained himself to hear it, though, a portion of it at least, as Stockhausen could in even the roar of taxiing airplanes.
The series came as a mix of ratios to the fundamental, E, all whole numbers, and small. Loudest, most resonant, early in the series, were the superparticulars: (n+1)/n. Two to one, the octave; three to two, the fifth; four to three, the fourth. Larent followed these tones up through the registers, fixing the intervals with his ear, tracing an elemental order. The first thirty-one harmonics, more than he could resolve, produced a pure, a just—a Ptolemaic—version of the common twelve-note chromatic scale.
He stopped the string a pure fifth above the open E. He held the B against the E still ringing through the amplifier on a delay pedal. The dyad was glassy, luminous, and fragile. Shaving just a fiftieth of a semitone off of it, as the usual tempering did, managed to shatter its coherence, sending waves of sound beating in and out of phase, canceling and strengthening each other by turns.
He carried on forming dyads this way, twelve of them, taking each rising fifth as the new root, locking it in place with the pedal, and bowing a fifth above. He made his way through the circle of fifths, climbing seven octaves this way, seven and a remainder. The E at the top was not an E, could not be. It overshot E by a Pythagorean comma—less than a quarter of a semitone, and nowhere close to superparticular: 531,441 to 524,288.
This wasn’t his mistake. The glitch was in the mathematics itself. You couldn’t return to the root pitch through pure fifths. The circle wouldn’t close. Instead it spiraled upward, a comma for every twelve fifths. To close the loop, to make E meet E, you had to narrow that last fifth by a comma. This was how a wolf was born, a howling, beating fifth.
The spiral wreaked other havoc. The major third you got from building the chromatic scale by stacking pure fifths, the way Pythagoras did, was much wider than the pure one (5:4) drawn directly from the harmonic series. So, to capture those pure major thirds, they tried tempering Pythagoras’s scale. This was two millennia later, during the Renaissance.
That just relocated the problem. Tempering the scale to achieve pure thirds meant that some of those previously pure fifths had to be narrowed, which is to say coarsened, not so much as to breed vicious wolves, but enough to steal the brilliance from the scale you were left with. And even then, a true wolf sat there at the tail, making most of the keys unusable for their dissonance.
If instead you tempered the twelve fifths by different amounts, so that the interval between notes varied throughout the scale, you could make even more keys playable, as Bach did in his Well-Tempered Clavier. All twelve keys become usable to one degree or another, and each takes on a distinctive character, depending on the precise spacing of intervals to be found in it. You have fewer true wolves this way, but then, you also have fewer pure intervals.
What took hold in the nineteenth century, what still reigned today, equal temperament, went the whole distance with tempering. All the keys became equally playable, because all of them became identical. Each of the twelve fifths was tempered by the same small amount. Flattening the spiral in this way made harmonic motion, modulation, effortless. But nothing from the harmonic series—the very origin of the scale—remained, less the octave. So you’d chased away all the wolves, yes, but then you’d done the same to everything pure.
■■■
Larent saw the gap between pure scales, drawn from the overtone series, and the tempered scales that prevailed not as a musical problem but an engineering one. It only afflicted instruments like the piano, whose centrality to the conservatory repertoire neatly explained equal temperament’s reign. While each piano key must be tuned to a single frequency, stringed instruments, and many brasses, can in principle produce notes of any frequency. Just like the voice, the first instrument. Note-space is made continuous, spectral rather than discrete.
Observations of this sort led Larent, halfway through his studies at the small but distinguished New Hampshire conservatory that had produced a string of notable neoclassical composers, to move from piano toward his second instrument, the double bass, his fondness for which, up until then, had been based on its access to the lower frequencies. Just as singers had natural registers, whether baritone or alto or the like, it seemed to him that each instrumentalist had a natural inner range, one where his musical sensibilities were most fully at home. For him, this was in the bass. There was also the physical aspect of it, the kinetic pleasures of standing and bowing with his whole body as compared with that of sitting on a stool and striking bits of ivory.
The conservatory’s curriculum emphasized classical forms to the near-complete exclusion of more recent developments: musique concrète, jazz, nonwestern musics like Gamelan and the Indian classical tradition. The American minimalists, who’d long interested him—Young and Reich especially, and more lately Basinski—were hardly treated at all. The teaching tapered off with Stravinsky, Bartók, and the serialists, whose work, though radical, was defined almost wholly by its negative relation to the classical tradition rather than by any affinity with exogenous forms. Certainly just intonation—a tuning based on the natural physics of sound, the harmonic series—got scanted, and it wasn’t even a foreign tradition so much as a historical one that had been prematurely buried.
After three years, Larent left without his degree. He didn’t want an orchestra spot, or worse, a post in a conservatory where he might pass on the very same theory lessons he’d chafed at. In the seven years since then, he’d felt even less regret than he imagined he might when he left. That didn’t mean he was pleased with himself. There’d been four groups in those seven years, and he was the prime disbander of each. Mostly the other members seemed to agree with him a little too easily. At that point he would walk away, unhappy with his own ideas, which they didn’t seem able to test in the right way.
What encouraged him now, apart from his own ripening views on music, was a certain discomfort with Moto he’d noticed in their most recent practices. Their bland start had been misleading. Moto had ideas, and they were in productive tension with his own. That’s how really interesting things happened, Larent thought, even if no one exactly enjoyed the process.
When his father tired now and again of sending him checks, Larent gave private lessons in bass and piano. These were more about technique than theory or composition. They might be applied to any sort of music. What that meant was that although most of his students would go on to staid classical careers—if they went on to a life in music at all—that fact couldn’t be laid at his feet. There wasn’t a single student of his who didn’t have some settled musical question unsettled for him, who wasn’t given some inkling by Larent of the sheer variety of scalar strategies, even if only through hearing him play Bach on his bass, using the alternative temperaments the German had used in a faraway era before industry or ease.
■■■
Larent set the bass in its stand and let his mind whir ever more furiously, almost without him. Geometry was a dead end, he thought. Pythagoras didn’t offer the right constructive principle. Better to start with the physics of sound and let the mathematics fall out from that. But when you looked at it, the physics seemed to favor something like an arithmetic principle.
Naturally produced tones were always complexes, subsuming a series of simple harmonics, or partials—sinusoidal waves. The harmonic series gave you a set of naturally occurring intervals from which to build scales. And as Larent was real
izing, if you were serious about cleaving to the harmonic series, what mattered was saving the smaller integral ratios, especially the superparticulars, as Ptolemaic scales did. They did far better in tracking the harmonic series than Pythagorean ones, yielding pure versions of the chromatic and diatonic semitones (25:24, 16:15), the minor and major whole tones (10:9, 9:8), the minor and major thirds (6:5, 5:4), the fourth (4:3), the fifth (3:2), and the octave (2:1).
That the notes of a Ptolemaic scale can’t be pinned to specific frequencies—well, why should they need to be? Certainly it’s a problem to realize them on fix-pitched instruments. The variable semitones and tones make any standard piano keyboard inadequate (and split keyboards are too cumbersome to consider).
But with variable-pitch instruments—the voice, strings—you could maintain the pure intervals even through harmonic progressions. Modulation too. You just adjust the pitches of chords built on a given scale degree so that the notes sit in the right ratios to the root. Ratios—relations—not absolute frequencies, are what count.
Riley, Young, Harrison, Blackwood, Johnston: they’d all tried to accommodate just intonation or its approximations within the fixed-pitch orbit of the piano. Even if they did manage to arrive at music that was interesting, sometimes beautiful, and once in a while sublime, the instrument forced them to contort.
Only instruments with an analog structuring of note-space could realize just intonation fully. The piano, the harpsichord before it, these were really digital instruments. Either you sounded A or A#, nothing in between was reachable. It might as well have been zeros and ones.
String quartets and vocalists sometimes try to approach just intonation, but they mostly shy away from the harmonic complications. Certain chord structures, five-note tone clusters, say, can’t be realized in pure intervals. But tetrachords can. Take the justly tuned dominant seventh, the so-called harmonic seventh. It’s common in a cappella music, since the voice, being variable pitch, can adjust to the 7:4 minor seventh involved—the seventh partial in the harmonic series.
Square Wave Page 14