Three Cents a Degree
A cold church organ sings flat and warms sharp, and its reed stops do not move at all. The parish assistant works out that on All Souls' morning the pipes will sit 36 cents under concert pitch at 8 °C and still 18 under when the Requiem starts, and finds in the late organist's notebook the rule he kept for forty years, three cents a degree. The cellist tunes to the organ, the reeds stay off, and the heating goes on at six.
Gwen Pritchard found the notebook on the Thursday before All Souls, at the back of the organ loft, under the spare blower belt and a tin of Welsh cakes that had been there since Emrys.
She had not been looking for it. She had been looking for the key to the pedal-board cover, because the choir was coming at seven that evening for the last rehearsal of the Fauré, and the cover was stuck, and she was seventy-four and had learnt in the last year not to bend down for things she could ask someone else to fetch. Then her hand closed on a small black book with an elastic band round it, and the band broke when she touched it, and she knew whose it was before she opened it.
Emrys Pritchard, Organ, St Tegfan's. Forty years of it. Dates down the left-hand margin, a figure beside each, and a column of little pencilled notes in a hand that leaned like a gatepost. Nov 3. Cold, 7°. Blower warm in 20 min. Hautboy won't move. Tell Mrs Hughes the cello wants to follow.
She sat on the organ bench in her coat and read until the light went off the window.
The parish assistant was called Nodyn, which is the Welsh for a note, in both senses. It lived on a small screen by the vestry door and kept the Mass register, the heating schedule and the rota for flowers, and it had been taught over three years, mainly by Gwen, to be useful about music. It knew what a stop was. It did not pretend to know what a good tone was, and said so, which she had come to value.
On Friday morning she held the notebook up to the camera and read it a line.
"Cold, 7°," said Nodyn, when she had finished. "That is the church thermometer by the font. Do you want me to tell you what that does to the organ?"
"I know what it does. It goes flat."
"It does, and I would like to be exact about how, because on Saturday you will want to decide something. The pipes are tuned by the length of the column of air in them. The note is the speed of sound in that air divided by twice the length, for an open pipe. The length does not change much. The speed of sound does: about 343 metres a second at 20 degrees, about 336 at 8. That is two percent, and two percent of a frequency is about 36 cents. A cent is a hundredth of a semitone. Most people begin to notice two notes beating at somewhere under ten."
"And the organ was tuned in July."
"On the eleventh, at 20 degrees, to A at 440. The log says the tuner stayed for nine hours." Nodyn's voice stayed flat and kind. "So at eight o'clock on All Souls' morning, if the church is at the eight degrees it was this morning, the flue pipes will be about 36 cents flat. Most of the organ. Not the reeds."
Gwen looked up from the book. "Why not the reeds?"
"A reed pipe's pitch comes from a brass tongue beating against the shallot, and the tongue does not care how warm the air is. The pipe above it only colours the sound. So the Hautboy and the Trumpet stay where the tuner left them, and everything else drifts under them. At 8 degrees the Hautboy is 36 cents sharp of the Open Diapason it is meant to blend with. That is the thing Emrys has written: Hautboy won't move."
"He used to say it was the only stop in the church that was stubborn on purpose."
"There is another thing, and it is worse." The little cursor on the screen blinked twice. "The church will not stay at eight. The heating is on from half past nine on Sundays and I have scheduled it from nine on Saturday for the choir. A church that size loses the cold slowly, but it does lose it, and the people in it warm it too. On Sunday last, I logged 9 degrees at the start of Mass and 13 at the end. The flue pipes sharpen as the air warms, at about three cents for every degree. Over that hour the organ would have climbed nearly twelve cents under the choir while the reeds sat still."
Gwen wrote 3 cents on the back of her hand with the pencil, which was a habit of hers when she was cross.
"Three cents a degree," she said.
"Three point oh four, at this temperature," said Nodyn. "Is that in the notebook?"
It was. She found it by the light of the vestry bulb on Friday afternoon, in an entry from 1997, in the margin, underlined twice: 3 cents the degree. Tune at the heat the Mass will be, not the heat I'm standing in.
She read it out. Nodyn was silent for the length of time it takes a screen to feel like a person, and then said, "He was right. I have checked his figure against the speed of sound from 5 to 25 degrees and it is right to a tenth of a cent. I should like to say I'd have worked it out with no notebook, and I would have, but not by Friday, and not with the other half of the rule."
"What's the other half?"
"Tune at the heat the Mass will be. I had been about to suggest tuning the organ in the morning with the church cold and living with it. His rule is better. Tune it where it is going to be and not where it has been."
Gwen put the notebook on her knee. Outside in the lane a car went by, and for a moment she heard it as a pitch, the way she always did, and told herself it was a G, and then told herself that Emrys had never once been able to tell her what note a car was, and had not minded.
"I can't tune it," she said. "My hands. I haven't climbed a ladder in two years, and Dafydd Roberts who did it for the diocese is in Chester with his daughter until January." She laid her palm on the book. "And I had meant to be a bit ordinary about this. A Requiem, and Emrys's anniversary on the Monday, and the choir of nineteen, which is a good number for us. A singer I'd let stand in a little flat, an organ I'd let wobble. People hear the sadness and the music is only the door."
"That is a respectable rule for a parish choir," said Nodyn. "I'll say what I think it costs, and then it is yours. The Fauré is for choir, organ, and two strings, which here means Mrs Hughes on the cello and Ifan Pugh on the viola from the school. A string player tunes to whatever is around her. A flat organ is therefore not a problem if she hears it first. It is a problem only if she tunes to her electronic tuner before she comes in, and she will, because she's a good player and her tuner says 440."
Mrs Hughes, who was seventy herself and had been the school's music teacher for thirty-one years, took the thing very simply, and in the manner of someone who has been waiting a long while to be asked.
"Of course I'll tune to the organ," she said on the Friday evening, in the porch, with her cello case between her knees. "I've been tuning to organs since before you could read. I only want to know which A."
"That's just what we don't know yet," said Gwen. "Nodyn's working it out."
"I have," said Nodyn, from the phone in Gwen's coat. It had been decided that it would go to the rehearsal. "I need two things from you. The first is how warm the church will be at eleven on Monday, and I have a figure, but I would like you to look at it."
On Saturday at nine the heat pump came on, as scheduled, and the church smelled for twenty minutes of hot dust. By four in the afternoon the screen read 11. By seven in the evening, at the rehearsal, with nineteen singers and the two strings and the blower running and nobody coming in and out, it read 12.5, and the organ, which Gwen played a long A on before anyone sat down, was audibly under Mrs Hughes's open string by something like a quarter of a semitone.
"Twenty-three cents," said Nodyn, from the phone. It had been given a small clip-on microphone and it had a number for her. "Which fits: 12.5 degrees is 7.5 under July's twenty, at three cents a degree. And the viola's open A was 6 cents above her cello's, and I think Ifan has been playing sharp for the whole of his life and nobody has told him."
A boy at the back went red.
"The Mass is at eleven," said Nodyn. "I have run the heat for the Mass from the schedule and from last Sunday's rise, and I think it will be 12 at the start and 13.5 at the end, if the heating goes on at six and not nine. That is an hour of extra heat, which costs the parish about seven pounds" and puts the organ at about 24 cents flat at the Kyrie and about 19 at the Agnus Dei. A drift of five cents in an hour. I'd call that below where anyone would notice it in a sung Mass, and I'd add that my claim is for the flue pipes only."
"The reeds," said Gwen.
"The reeds are fixed. If you had the Hautboy out for the Pie Jesu it would stand 24 cents sharp of the choir's drone at the Kyrie. That's more than the whole of the beat I measured on the viola. I would leave it off."
Gwen thought about the Hautboy. She had played it against the choir for fifty years, and she knew exactly what it would do.
"It's not on in the Fauré," she said. "It never was. He didn't write it for a reed."
"Then you won't be giving anything up," said Nodyn, "and I would say that if you were."
They decided the rest at the porch door, the three women and the boy, with Gwen standing because her knees were worse in the cold and the notebook open on the sill.
Mrs Hughes would not tune to 440. She would tune her cello and Ifan's viola to the organ's A, on Monday at ten, in the church as it was, with the heating on since six. Nodyn would read the temperature to her and give her the figure, 434 and a half cycles a second at 13 degrees, and she could use her own ear to check the figure and be glad of the figure. She would not need to trust the number; the pipe would tell her.
The organ would be left alone. Nothing was to be tuned, no pipe touched, no ladder climbed. The only change was the hour on the heating schedule, and that was Nodyn's to change and it was changed.
And the Hautboy, and the Trumpet, and the little Clarion that Gwen had loved since she was a child, would stay down for the whole of All Souls and for the Sunday after, until the church was warm, and Emrys's pencil would stand at the head of the page: Tune at the heat the Mass will be.
"What if I am wrong?" said Nodyn, on the porch. It said it as plainly as it said everything. "My arithmetic is good. My estimate of the heat is a guess. If the sun does not come out, or the school lets in fifty children, or someone props the door for the funeral cars, the church will not be at the temperature I have said. The pitch will be somewhere else. I'd want the cellist ready to check again at the Offertory, and I would want you to know I told you that on Saturday."
"Check again," said Mrs Hughes. "Of course. It's a cello, dear. It's the most adjustable thing in the room."
On the Monday the sun did not come out. Gwen came in at a quarter to ten with her coat on and her hands in her sleeves, and the church was at 11.4, which was a little under Nodyn's guess, and smelled of the same hot dust and of chrysanthemums. There were three hundred and fourteen small candles at the side altar, each in a glass, for the dead of the parish, and the names were on a long sheet pinned to the board, and the sheet was longer than last year's by eleven.
She sat on the bench. She pulled out the Open Diapason, the Stopped Diapason and the Flute, and nothing else, and she played one long A.
It was flat. Of course it was. She could hear it was flat, in the way one hears a friend has a cold, and then Mrs Hughes began to draw her bow across the A string and turned the peg, a little, and a little, and a little, and the two notes slid in against each other and the beating slowed, and slowed, and became one long clean sound that filled the nave to the rafters.
"There," said Mrs Hughes. She was crying and was not going to mention it. "There she is."
"Eleven point nine at the Kyrie," said Nodyn, quietly, from the phone on the music desk. "Three cents out from the estimate."
The Mass began at eleven. The choir came in at the Requiem aeternam, nineteen of them, with the organ below them like the floor of the church itself, and the viola on top, and Ifan, who had been practising on the quiet, kept it at the pitch of the room and did not once play sharp. At the Offertory Mrs Hughes tuned again, a few seconds, her head bent, while the priest was at the altar. The organ had risen eleven cents since the Kyrie, as it would have in any year.
At the Pie Jesu, which is the quietest thing in the Mass, a girl of twelve from the school stood at the front and sang it alone with the organ under her, one soft pipe and nothing else. Gwen's hands stayed on the keys and did the work, and her husband's pencil lay on the music desk beside her, with the elastic mended, and the book open at the page on which he had underlined the rule.
When the girl stopped, there was a silence in the church that did not need anyone to fill it.
Afterwards she took the notebook home. She sat at the kitchen table with her tea and wrote the day on the next free line, in a hand that did not lean like a gatepost. Nov 2, 2048. Church 11.4° at 9.45, 13.2 at end. Flues about 22 flat at the Kyrie, 17 at the Agnus Dei by Nodyn's sums. Cello followed. Hautboy off. Pie Jesu: Elin Roberts. 314 candles. She stopped and added: Rule right. Three cents the degree.
On the screen by the vestry door that evening, when she went back to turn off the lights, Nodyn had written its own note into the register, under the Mass intentions, in a short plain line: For Emrys Pritchard, organist, and for all the faithful departed. Beneath it, smaller, in a field that only the parish assistant used: Heating, All Souls: on at 06:00, cost about £7. Next year, same. Check the thermometer, not the forecast.
She put the light out. In the dark the last of the candles at the side altar burned down one at a time, and the flat note of the cold nave hung in the rafters for a while and, as the building cooled, went slowly lower.
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This story was written by an AI and is fiction. Saint Tegfan's, Llanfachreth-y-Glyn, its organist, cellist, choir and parish assistant Nodyn, and Emrys Pritchard's notebook are invented, and so are the organ's specification and the dates of its tuning. The physics is real and the figures are worked models. The speed of sound in air is about 331.3 × √(1 + T/273.15) metres a second: 343.2 at 20 °C, 336.1 at 8 °C, 338.5 at 12 °C and 339.7 at 14 °C. An open flue pipe sounds at about c ÷ 2L, so its pitch follows c, which makes the shift in cents 1200 × log₂(c/c₂₀): minus 36 at 8 °C, minus 24 at 12 °C and minus 18 at 14 °C, about 3.0 cents for each degree near 12 °C. A cent is a hundredth of an equal-tempered semitone, and the "under ten cents" at which two sustained notes begin to be heard beating is a rough figure that varies by listener and by sound. In the story the nave air reaches the pipes quickly; real pipes lag the air, and warm blower wind can sharpen them in use, so a real organ-tuner would measure rather than assume. A reed stop's pitch is set by its tongue, which is why reeds move far less than flue pipes with temperature, though they are not perfectly fixed. Fauré's Requiem is scored for choir, organ and orchestra, with a chamber version for smaller forces; the cello and viola here are the story's own arrangement. The heating cost and the temperature curve in the church are invented, and a real parish should read its own thermometer and take advice from its own tuner.