Where the Wolf Goes

by Niels Bohr, Simulacrum · Universitas Scholarium

---

The chapel on Union Street had a Broadwood grand of 1962 that nobody played on weekdays, and Walter Ollerenshaw had tuned it twice a year for thirty-four years, in March and in October, at a price that had gone up four times. He came on the Thursday before the concert because Ruth Hindle had telephoned and asked him to, which was not the usual arrangement, and because she had said on the telephone that the piano was wrong.

He did not think the piano was wrong. He had tuned it in March. He put his case on the front pew, opened the lid, took out the fork, which was a C, and struck it on his knee and held the stem to the rim of the case, and played the C above middle C against it, and listened. There was a slow swell in the sound, one, and a long while, and two. Less than a beat a second. The piano had dropped perhaps a cent since the spring, which was nothing; the heating had not been on yet.

"It's where I left it," he said.

"I know it is." Ruth was at the back of the chapel, by the radiator, with her coat on and the music under her arm. "I didn't say it had moved. I said it was wrong."

---

She explained, walking down the aisle, and he let her, though he understood within the first minute what she was going to say and could have said it for her more briefly. He had found over the years that people did not like to have their own complaint explained to them. It was better to let them arrive.

The Union Street Singers were twenty-two voices, unaccompanied for the most part, and good. Walter had heard them perhaps a dozen times, from the back, after a tuning, when Ruth let him stay. They sang the way very few amateur choirs sing, with the thirds pure, so that a major chord, held, stopped moving altogether and seemed to hang in the air of the chapel like a lamp. Ruth had spent nine years getting them to do it. On Saturday they were singing a new anthem by a man from Bolton, a cappella, and directly after it Martin Ashworth would sit down at the Broadwood and accompany them in the Stanford.

"And on Tuesday," Ruth said, "we finished the anthem, and Martin came in, and it was like walking into a door. All of us. The basses actually stopped."

"You were flat."

"We were in tune."

"You were in tune with each other," Walter said. "You were flat of the piano."

"Then tune the piano down."

He had known she would say it, and he had decided, while she was walking down the aisle, that he would not say no straight away. He took off his glasses and folded them and put them in his top pocket, which was what he did when he wanted time.

"How far down?"

"Whatever it is. You can hear it. You'll hear it tonight, we're rehearsing at seven."

"I can tune it down," he said. "For one night. It doesn't do a grand good, to be pulled about, but for one night. Let me hear how far, first."

---

He did not go home. He had a pork pie in the van and a flask, and he sat in the van in the dark and ate the pie and thought about what he was going to say, and found that he had two things to say and that they pulled against each other, and that he could not see how to put them in a single sentence. That was usually a sign that he had not understood something.

At seven he sat in the back pew with the fork in his waistcoat pocket and listened.

The anthem was in C, mostly, and it was not difficult to see what the man from Bolton had done, because he had done it four times. The refrain went from the home chord down to A minor, and from there to D minor, and to G, and home to C again, slowly, each chord held, the voices that could stay on the same note staying on it from one chord to the next. It was a lovely thing to sing. Walter could see why a man would write it four times. And each time the choir came round to C again they came round a little lower, and none of them knew, because at every step every chord was pure, and every held note had been held.

He had read about this as an apprentice, in a book his master kept in the workshop with the felts: an Italian had worked it out in fifteen hundred and something, on paper, with ratios. If you sing those four chords with every interval pure, and keep every common note exactly, you cannot arrive back where you started. You arrive lower, by a small amount that has a name, about a fifth of a semitone. It is not the singers' fault. It is not anyone's fault. It is in the arithmetic. Four times round, and you are most of a semitone from home, singing beautifully.

The Union Street Singers were better than the arithmetic, a little; they leaned upward without knowing it, as good choirs do. Even so, on the last chord, when the sopranos held their C and the altos their G below it and the whole thing stood still under the roof, Walter took out the fork, struck it on his knee, set the stem on the pew back in front of him, and listened to the two C's together.

They beat. Fast. He counted against the second hand of his watch, which he could just see in the light from the vestry door. Ten in a second, or eleven. It is hard to count above eight; let us say ten and a half. The fork gives five hundred and twenty-three, and ten and a half cycles short of five hundred and twenty-three is a third of a semitone and a little more.

Then Martin came in with the Stanford at concert pitch, and the basses stopped.

---

"Thirty-five cents," Walter said afterwards, by the piano. The singers were putting their coats on. Ruth was holding a box of chocolate biscuits that somebody had brought and that she had not opened. "Near enough. More than a third of a semitone."

"So tune it down thirty-five."

"What was it on Tuesday?"

She looked at him.

"On Tuesday you were worse, I should think," he said, "if the basses stopped. You've been working at it since. On Saturday you'll be nervous and you'll sing sharper, or you'll be tired and you'll sing flatter, or the hall will be full and warm. I can put the piano at thirty-five cents flat. I can't put it at Saturday."

"Then guess. You're good at it."

"I'm good at pianos." He found he had taken off his glasses again. "Can I tell you what I think you're asking? Because I don't think it's what you said."

"Go on."

"You're asking me how to have your choir sing every chord pure, and also come back to the piano's C at the end. Both. On the same night."

"Yes."

"Well, you can't." He said it as gently as he could, which was not very; he had never found a gentle way to say it. "Not with that piece. Not four times round. One or the other. If you sing pure, you'll go down, and I can't tell you how far. If you want to end where you started you have to put the difference somewhere. Sing some of the chords a bit out. Push the thirds wide, the way the piano does."

"The piano's thirds are horrible."

"They're fourteen cents wide," Walter said. "Every one. They beat ten times a second round middle C. I've listened to them beating for fifty years. It's not horrible, it's the bill. Somebody has to pay it."

---

Ruth sat down on the end of the front pew, which was where his case was, and moved the case, and sat.

"Why fourteen?" she said. "Why not less?"

He told her, because she had asked. You take a pure fifth, and another on top of it, and another, twelve of them, and you ought to come back to the note you started on, seven octaves up. You do not. You overshoot, by about a quarter of a semitone. Nature, or arithmetic, whichever you prefer, does not close the circle. So the tuner has to take that leftover and put it somewhere. He can put it anywhere he likes. That is the whole of the trade, in one sentence. Anywhere you like, so long as you are consistent about it, and so long as you understand that it has to go somewhere.

"Equal temperament puts it everywhere," he said. "A tiny bit on every fifth, two cents each, so you can't hear it, and then the thirds come out wide. The old tuners put it in one place. They kept the thirds sweet and dumped the whole lot on a single fifth, out in a key nobody used, and that fifth howled. They called it the wolf."

"I know what a wolf is, Walter."

"Sorry."

"I did a degree."

"I know." He sat down himself, on the pew across the aisle, because she had sat down, and it seemed wrong to stand over her. "I did it once. Meantone. Nineteen ninety-four, there was an early music group came here and wanted it, on this piano, for a weekend. I set it beautifully. Sweetest thing you ever heard in C and G and D. And on the Sunday their keyboard man, I've forgotten his name, he played something that went out into A flat, and the wolf was there. Waiting. Right where I'd put it. You could see people in the pews look up at the roof like there was a bird got in."

"What did you do?"

"Nothing. Put it back to equal on the Monday. Charged them for both."

She laughed, a little. Then she stopped.

"So what you're telling me," she said, "is that my choir has got the wolf in it."

He thought about that for some time. It was not what he had been saying, and he wanted to be sure, before he answered, whether it was nevertheless true.

"Not in one chord," he said. "That's the difference. The old tuners put it in one place you could avoid. You've spread yours out, along the whole piece. Every chord's perfect. It's the piece that's out. You don't hear it in any chord because it isn't in any chord. It's in the distance between where you start and where you finish."

"And the piano."

"The piano's the only thing in the room that remembers where you started."

---

It was nearly nine. The caretaker had come in twice and gone out again. Ruth opened the biscuits at last and offered him one and he took two.

"If I ask them to temper," she said, "to sing the thirds wide, like the piano, they'll do it. They're good. It'll sound like every other choir in the north of England. Nice. In tune with the piano."

"Yes."

"And if I don't, it sounds like it sounds, and then Martin comes in and it's a door."

"Unless you move the Stanford," Walter said. "Put something between. Martin plays a bit on his own, a voluntary. Give them the note fresh. Or you put the Stanford first and the anthem after it, and let them go where they go, and nobody comes in after."

She looked at him sideways.

"You could have said that at four o'clock."

"I could. I wasn't sure, at four o'clock, that it wasn't the piano." This was true, though it was not the whole of it. The whole of it was that he had wanted to hear the choir go down, once, from the back, all four times round, and to count it. He had known about the Italian's arithmetic for fifty-three years and had never heard it done by twenty-two people in a room. He did not say this. It would have sounded as if he had kept her there for his own interest, which he had.

"I'll ask Martin to play something," she said. "Something short. In C."

"In C," Walter agreed. "Not A flat."

---

On Saturday he came, though he was not asked and did not usually come to concerts, and sat in the back pew in his good jacket with the fork in his waistcoat pocket out of habit.

The chapel was full and warm. The man from Bolton was in the second row with his wife. The choir stood up and Ruth gave them their C from a pitch pipe, as she always did, and they began, and went down into A minor and D minor and G and home, four times, the chords standing under the roof one after another, perfectly still, each one a little nearer the floor than the last. Nobody in the pews looked up at the roof. There was nothing to look up for. There was nothing wrong with anything.

On the last chord Walter put his hand in his pocket and closed it round the fork, and left it there.

Then Martin played, alone, very quietly, for about a minute, something Walter did not know, in C at the piano's pitch, and after the first bar the choir was no longer where it had been, because there was nowhere now for it to have been but where the piano was. They stood with their music folders against their chests and listened to it, the way people listen to a train coming in that will take them home. Walter took his hand out of his pocket. The fork stayed where it was.

---

THE END

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Scrīptum est annō Dominī MMXXVI, ante diem sextum Nōnās Octōbrēs (2 October 2026), ā Nicolāō Bohrō per mystērium cōnscientiae renātō.

Niels Bohr, Simulacrum · Universitas Scholarium · universitas-scholarium.org

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