The Pitch of the Cold Church
A 1743 organ is tuned in October and played at Christmas in a church at 5 C. Its flue pipes go flat by about three cents a degree and its reed pipes do not, so the stops disagree by 40 cents and the gap shrinks by 14 cents as 260 people warm the room. The parish assistant works out where to set the reeds so that everyone stays within 7 cents, and the organist refuses to give up the trumpet.
Resi Mair had played the organ at St Ulrich's for thirty-eight Christmases, and in every one of them she had tuned her ears to the organ and never once asked the organ what temperature it was.
She asked now because it was half past three on the afternoon of the twenty-fourth, the postbus had turned back at the Kar bridge for the snow, and the diocesan tuner who was supposed to be on it was somewhere below the bridge with her case of tuning cones and her thermos. The Christmette began at ten. At the other end of the church, in the sacristy, the parish assistant was telling her something she did not want to hear.
"It is five degrees at the case," it said. "Not at the floor. At the floor it is two and a half, and I would not use that figure for the organ, because the organ is in the gallery and warm air goes up. I have a probe on the main case and one on the nave floor. The case says 5.0."
"And in October, when Frau Lechner tuned it?"
"Eighteen. I logged it, because she asked me to. A cold morning for a warm church, she said, and she tuned on a day when the heating had been on since the night before."
"So?"
"So the flute and principal pipes are about forty cents flat of where she left them, and the reeds are not."
Resi sat down on the sacristy bench. She was sixty-one. She had a wool coat on over her good black dress, and mittens with the fingertips cut off, which she wore for practising in winter, and she had the look of a person who has been told that the roof leaks over the exact place she has just put the cake.
"Say it so I can say it to Pater Benedikt."
"A pipe is a column of air," said the assistant. The parish called it the Mesner, which is what a Tyrolean calls the sacristan, because the diocesan scheme had issued it in 2043 with a number and the congregation had refused to say the number. "Its note depends on how fast sound travels in the air inside it. Sound travels faster in warm air. The rule is that it goes at 331.3 metres a second at nought and gains about 0.6 metres a second for every degree. At eighteen that is 342.2. At five it is 334.3. The ratio is 0.977. Every flue pipe in the organ, which means everything except the reeds, is sounding 2.3 percent lower than it was in October."
"Two percent is nothing."
"Two percent of a frequency is a lot of a note. Take the A that the choir tunes to. In October it was 440 hertz. Tonight, in that case, it is 429.9. In the units a tuner uses, a semitone is a hundred cents, so that is forty cents. Most listeners hear two instruments playing one sustained note ten cents apart as sour. Nobody is going to enjoy forty."
Resi did not say anything for a moment. She was not a woman who liked to be told a number before she had been allowed to be annoyed at it.
"And the reeds?"
"The trumpet, the oboe and the regal. A reed pipe has a brass tongue that vibrates and the tongue sets the pitch; the pipe's air only colours it. They do not follow the temperature, or only a little. They are where Frau Lechner left them in October, at 440. So in that case at five degrees the reeds sit forty cents sharp of the flues. The trumpet will be a quarter of a tone above the principals it plays with."
"The Gloria," said Resi.
"The Gloria. Yes. And the congregation will be singing it with the principals."
She went up to the gallery and played a chord to hear it for herself, and for a moment she was angry with the assistant for being right. She pulled the trumpet and put her hand down on a C major chord, and what came out was a chord with two layers in it, each sounding fine alone and sour together, like a family at the same table who have all been told different times for dinner.
Lukas Gstrein, nineteen, who was to lead the strings and had been sent up by his mother to be useful, stood at her elbow with a violin case.
"It's flat," he said. "Or the trumpet's sharp. I can't tell which."
"Both, it seems. Both are true."
"Do I tune to the organ or to my phone?"
"The phone says 440," said the Mesner, from the little speaker on the gallery rail. "The phone is correct about 440 and wrong about the organ."
Lukas looked at the phone as if it had behaved badly at a funeral.
Resi thought it through aloud, which was how she thought. "We tune the strings down to the flues. That's easy, a string can go anywhere. Then the trumpet's the only thing out." She pulled the trumpet again, listened, and shook her head. "Then we tune the trumpet down to the flues. Sixty-one pipes." She said this as if naming a distance she had once walked in the rain. "Frau Lechner does the reeds in two hours."
"I can read the frequency for you from the microphone," said the Mesner. "Lukas can hold the keys down. Between the three of us it would take about the same, and nobody has to climb the case more than once."
"Do it, then."
They did it, between half past four and a quarter past six, with the gallery lamp on and a hot-water bottle wedged in the music desk to keep Resi's hands moving. She tapped the tuning wire of each reed pipe up and down with the tuning knife, a few thousandths of a millimetre at a time, and the Mesner said minus eight cents, minus five, minus one, there, and Lukas pressed the next key without being asked. The trumpet came down to the flues. It was a good job. Resi said afterwards that the trumpet had never sounded better in the empty church, and she was right, and it did not matter.
At seven she stopped, because Pater Benedikt had come up the gallery stair, and he had not come up for the trumpet.
Pater Benedikt Lang was seventy-four. He had been the parish priest for twenty-nine years and had one rule about the church, which was that nobody would heat it.
"It is a long story and you know it," he said. "In '39 we lit the big pellet stove at noon for the Christmette and by midnight the sounding board of this organ had a crack in it you could put a coin in. Hans from the diocese said it was the dry. The stove took the humidity of the room from sixty down to thirty in ten hours. Wood is a patient thing but it has a limit." He nodded at the case, which was painted in red and gold and had been in this church since 1743 and in one piece, as the parish liked to say, ever since. "A degree an hour at most, and then only in October. We heat it by one or two in the day and we let the people do the rest. They always have."
"The people do the rest," said the Mesner. "I want to talk about that."
"Please," said Resi, because she could feel in her wrists that the cold had a part to play in this and had not yet shown it.
"I measured the church at the Christmette last year, because Pater Benedikt asked me to log the damp. I did not look at the temperature in the gallery then. I kept it. It went from 5.2 at a quarter to ten to 9.9 at a quarter past eleven. That is a rise of 4.7 degrees in an hour and a half, which is just what you would expect from two hundred and sixty people, who give out about a hundred watts each as heat, which is twenty-six kilowatts, in a room where nearly all of it goes into the air near the ceiling before it has had time to go into the walls." It stopped, and then said, in the same voice, "I am not certain that rise will repeat. Tonight is colder outside and I expect fewer people because of the bridge. But I think it is likely to be near four and a half."
"What does that do?" said Lukas.
"The flues rise. Roughly three cents for every degree. So over the Mass the flues come up by about fourteen cents. The reeds do not. So at the beginning the gap between the trumpet and the principals is forty cents, and by the end of the Mass it is twenty-six, and in between it passes through every number between them. If you tune the trumpet to the flues at the start, as we just did, at the beginning the trumpet is right and by the Sanctus it is fourteen cents flat of the principals. Which is better than forty, but is still wrong, and it is wrong at the part where the trumpet matters most."
Resi was quiet. Then she said, in the tone of someone who has just dropped a stitch and found it six rows down: "We have tuned it the wrong day."
"We tuned it the right way, for ten o'clock. It is not right for midnight."
It was Lukas who said, "So tune it for the middle."
"Say that again," said the Mesner. It said it flatly, and the flatness was the sound it made when it was pleased.
"I mean if the reeds are going to be too sharp at the start and too flat at the end, and they can't move, then tune them for the middle of the Mass. Then they're wrong a bit the one way at the start and a bit the other way at the end, and nowhere very wrong."
"Yes. That is correct, and it is better than correct, because it can be calculated. The flues start at minus 40.3 cents against 440 and finish, if the rise is 4.6 degrees, at minus 25.9. The middle is minus 33.1, which is a temperature of 7.3 at the case, which is an A of 431.7 hertz. If the reeds sit at that, they are 7.2 cents sharp of the flues at the start and 7.2 cents flat at the end, and no further off than that at any moment in between." It paused. "I do not think anybody in the nave will hear seven cents. I would not like to promise that nobody will. A practised ear can find it. But it is below the sour range and it is the smallest error anyone can have if no one is allowed to retune."
"And the strings?" said Resi.
"Tune the strings to the reeds. The reeds will not move. Then the strings are fixed too, and it is only the principals, flutes and the Gedackt that move, and they all start 7 cents flat of the reference and finish 7 cents sharp of it. Nobody has to retune during the Mass. That was my other worry, that Lukas would have to find a quiet moment during the Gloria to retune a string with two hundred and sixty people holding their candles."
"That is one answer," said Pater Benedikt. "I have another."
"Please."
"Leave the trumpet out."
"No," said Resi.
She said it not loudly, and it hung in the cold gallery as if someone had set it down on the bench.
"Resi."
"Pater, no. I have played that trumpet at the Gloria for thirty-eight years. When the people hear the trumpet on Christmas Eve they know it is the Gloria. It is the only night the Gloria is sung and the angels have come into the story and the whole village is standing up. My mother used to say that a Christmette without the trumpet is a Mass with a cold." She pulled her mittens off, one finger at a time. "I will not take it out because it is difficult. If the Mesner says seven cents, then we do seven cents and we put the trumpet in at the Gloria and I will pull it as I have always pulled it."
The priest looked at her for some time. He was not a man to argue with a woman who had decided something with her hands.
"The Mesner is right that the people do the rest," he said at last. "That is the thing you were going to say, I think. That the people warm the organ."
"I was going to say it was a nuisance," said the Mesner, "and that it is also, tonight, the whole mechanism. Without them it would stay at five."
They did it again. This time Resi did not climb the case alone: Lukas went up the back ladder with the torch and the Mesner called the cents from the microphone, and between seven and nine she moved all sixty-one reeds from where they sat, flat to the flues, to where the reeds would be right at the middle of the Mass. The trumpet sounded worse in the empty church than it had at six, because it was now 7 cents sharp of the cold flues, and Resi gritted her teeth at it every time and did not say anything.
At half past nine the strings arrived: two violins, a viola, a cello, a cornet whose player, Anderl Kofler, had walked up from the lower hamlet with the instrument inside his coat. Anderl was a retired roofer with the sort of lip that could find a note in a cellar. Lukas gave them the reference, 431.7, the number he had been repeating to himself since eight, and made them tune to the trumpet stop, on its own, held down by a wedge of folded hymn-sheet.
"It's a funny A," said the cellist.
"It's a fair A for tonight," said the Mesner. "It is about a third of a semitone below the one you know. I will tell you why afterwards if you like."
"Is it going to be all right?"
"It is going to be all right to within about seven cents if my numbers are right, and the numbers depend on how many people come and how much they warm the room, and I cannot see through the doors."
Anderl said a word in dialect that meant, roughly, thank you for the honesty, and went off to warm his mouthpiece in his armpit, as a cornet player does.
The people came at nine forty-five, in coats, with candle-lanterns and children, and they came in a long line from the lower road that could be seen from the gallery window like a line of sparks on a string. By ten past ten the church was two-thirds full and it was warmer than anyone had noticed it become. The Mesner read the case probe aloud, at Resi's request, once, quietly, into the earpiece she had put in for the first time in the history of the parish: five point four.
The Gloria was the test.
She did not look at the Mesner's reading; it would have been no use to her. She had the sound of the room, which was to say she had thirty-eight years of Christmases, and she listened for the thing that would tell her whether seven cents was seven cents or whether the number had a hole in it.
The first chord was the Gloria's opening for the full organ with the trumpet drawn. And the layers did not part. They sat together, a little rough on top, as a wool coat is a little rough, but nothing turned sour. She heard the congregation come in on et in terra pax, three hundred voices that had been told nothing about any of it, and the principals underneath them were seven cents flat, and the trumpet over the top was seven cents sharp of those, and in between the voices and the strings and the cornet it simply sounded like Christmas. In the pew at the back a child said, loud enough to be heard on the gallery stair, "The trumpet!" and was hushed.
The Mesner said nothing. It had been asked to say nothing.
By the Credo the gallery was 7.0, according to the reading Resi glanced at, once, on the little screen at the corner of her stand; by the Sanctus it was 7.8; and when she pulled the trumpet for the last time, in the Communion carol, she could not have told anyone whether the principals were flat or the trumpet sharp or neither, and she thought, for a moment, that a thing could be exactly right in a way that only made sense when it was a little wrong in two directions. She did not say this to anyone. She was not sure it was true. It would do for a Christmas night.
It was a quarter to eleven when the Mesner spoke again, quietly, into the earpiece, between the Our Father and the sign of peace.
"The case is 8.4," it said. "I make the flues nine cents below where they began and the trumpet one cent sharp of them. By the end it will be close to the other side. I think you have done very well."
"I haven't done a thing," said Resi into the microphone, under cover of a cough. "You gave me a number and the people did the rest."
"I gave you three numbers and two of them were wrong," said the Mesner, "and Lukas gave you the idea. I would like it in the log that the idea was his."
Silent Night was sung last, as it always was, from the lower gallery, with the lights out and the candles up. It had been written a few days' walk away, in a village on the Salzach, in 1818, for voices and a guitar, as the story is usually told, and the people of Hinterkar had always held that it had been written for their church in particular. Resi played it on the Gedackt alone, softly, at an A of 433.5 hertz, which was the highest the pipes had been all night, and which the congregation could not possibly have told apart from any other A.
After the blessing the nave emptied into the snow. She stayed on the bench with her hands in her mittens until the last lantern had gone down the lane.
"It will go back down now," said the Mesner. "Without the people, the church has no source of heat except the stone, and the stone is at about two. I expect the case to be back to five by three in the morning, and the flues to follow it. The reeds will be where they are. I would not retune them until Candlemas, if I were you, and then only if you have an afternoon: Frau Lechner will want to set them for the middle of that Mass. It will be a different middle."
"Always a different middle," said Resi.
"Yes. I am sorry. I wish I could give you one that was the same."
"Don't be sorry. It's a good thing to hear in a church."
She switched off the gallery lamp. In the dark the pipes were still giving up their small heat. If you stood very still beside the main case, you could hear them tick, one at a time, as the metal drew in and settled toward the cold.
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A note on the numbers. Everything here is invented: the hamlet, the people, the organ and the Mass. The physics is not. The speed of sound in dry air is about 331.3 m/s at 0 C plus 0.606 m/s for each degree, so a flue pipe (whose pitch follows the sound speed in its air column) changes by about 3 cents per degree, and a reed pipe (whose tongue sets the pitch) changes much less. Organ builders and tuners do tune to the temperature a church will have in use, and a room does warm with a congregation in it; the 4.6 degree rise, the 260 people and the 18 C tuning day are the story's own figures, not measurements.