by Todd Borg
Wellsley turned and looked to see where the moan was coming from. Wellsley’s brow was as wrinkled with confusion as Spot’s. Spot moaned louder.
“Sorry,” I said. “Apparently my dog wants to sing along.” I walked over and opened the door.
“Spot,” I said, snapping my fingers. “Quiet.” Then I looked at Lily. “Officer Lily, if your hound insists on singing along, please remove him from the bridge.”
“Yes, sir!”
I went inside and shut the door behind me.
Wellsley slowly played each note of the scale, looking at the readout on the machine. At the top of the scale, he paused and shook his head.
Next, he reached into the piano and pulled part of the felt strip out. He picked up a rubber wedge and held it against a string and struck a key on the keyboard. Again, he moved the wedge, touched it to another string and played another key.
“My God,” he said.
TWENTY-TWO
“Herman Oleson wasn’t demented,” I said.
“No. Not at all. I almost can’t believe it, but the center unisons are in tune. A perfect tempered scale.”
Wellsley leaned over the keyboard and looked into the piano. He glared at the strings as if the force of his look would change what he’d discovered.
“This piano was tuned badly on purpose,” he said. “And he did it in a very clever way such that any piano tuner would immediately realize that the result was intended.”
“How can you tell?”
“Because he only mis-tuned the left string of each set of unisons, while he put precisely the correct pitch on each of the other two, the center and the right unisons. To do that requires using a wedge over and over as you remove the felt. It is twice as much work to do what he did as it is to tune all the strings correctly.”
Wellsley looked at me to see if I was understanding him. “That clearly communicates to any tuner that he adjusted every string with great precision. It was deliberate. No one else would ever figure it out. But to a piano tuner, it’s like he was leaving a message or something.”
“You lost me back on the unisons.”
“Oh, sorry. Come and look into the piano. I’ll show you.”
I walked over next to him. He pointed inside the piano to the strings at the far left of the piano. They were thick and copper colored and were made of coiled wire.
“The lower bass notes of a piano have a single string each.” He pointed a bit to the right. “The higher bass notes have two strings per note.” He moved his finger to the middle of the piano where the strings were not coiled, but single, and shiny silvery steel. “But up here in the temperament octave, there are three strings per note. We need more strings for each note because the thinner, higher-pitched strings don’t make much volume, so more strings give the piano more sound.
“This temperament octave is where we start tuning. Not only do we want the notes to be in a proper relationship with each other, we want to make all three strings of each note - what we call the unisons - be exactly the same pitch as each other. If not, the sound has beats, a sort of a wah-wah-wah waver.” He played a single note. “Hear it?”
It made a strong vibrating wah-wah waver, several times per second, and was unpleasant to listen to.
“If I tuned this note beatless, it would sound pure.” He inserted the felt strip in between each group of three strings. “The felt silences the outer strings, leaving only the center string in each group to vibrate.” He played some keys, running up the scale and back down. Each note sounded pure and beautiful.
“Sounds pretty good to me,” I said.
“Yes. The center strings in each group of three are perfectly in tune. This is how Herman is saying to us that he tuned the piano, that he knew what he was doing. Now, I will pull out the felt and I’ll dampen only the left string of each set of three unisons and let the other two sound.”
He inserted his rubber wedge and played a note. Again, it was smooth and beatless. He moved the wedge to another left string and played that note. It also sounded great.
“You see, out of each group of three, the center and right strings are correct. Together, they are beatless. This is another way that Herman is saying that he has tuned them this way on purpose. They don’t match the left string, but they match each other.”
“And because it was clearly done on purpose, you think it might be a code.”
“Well,” Wellsley said, “I stress the word might. Obviously, the notion seems ridiculous. I’ve never heard of a tuner doing such a thing. What on earth would be the motivation? I’m just looking for some kind of explanation for a bizarre tuning.”
“Okay, let’s proceed with the ridiculous notion. Pretend that Herman put a code into the piano. How do we determine what it is?”
Wellsley shook his head. “I know nothing about codes. What’s that called? Cryptography? You would need a cryptographer.”
“Yes, but the cryptographer would come to you, the piano tuner. They would ask you to measure this phenomenon, this out-of-tune piano, to quantify it.”
“But how? All we have is a piano that has been precisely mis-tuned.” Wellsley shook his head in frustration.
“What can you quantify about the mis-tuning?” I asked.
“I don’t know. The frequencies, maybe.”
“How do you do that?”
“It’s easy with my electronic tuner. It has several functions including a simple frequency readout. When I set that function, I play the note, and it shows the frequency.”
“If the center and right unisons are correctly tuned, then we would measure the incorrect ones, right? The left unisons?”
“Yes, I suppose,” Wellsley said. “I can put the mute between the right two strings of each group, play the key, and see the readout for the left string.”
“How long will that take?”
“Just a few minutes.”
I stepped out onto the front deck. Lily and Spot were down on the small front lawn. He was lying on a patch of grass, and she was riding her bicycle in wobbly circles around him, giggling as if it were the funniest thing she’d ever experienced.
Ten minutes later, Wellsley came out of the cabin, looking much more fatigued than when he first arrived. His eyes were shadowed with dark eye bags. His previously combed and gooed hair was now messed up, strands coming down into his face. It wasn’t that he’d done much work. It must have been the stress of contemplating what would drive a fellow tuner to commit such a crime to such a beautiful instrument.
“Any luck?” I said.
“I suppose I should say, yes, I was able to get the frequencies, but I’ve had no luck in imagining how all those numbers can mean anything.” He handed me a sheet of paper with the letters of the notes followed by numbers.
“I’m a bit of a natural at math,” Wellsley said. “But if the left unison of C-sharp vibrates two hundred eighty-one point six times a second or whatever it says on that paper, instead of two seventy-seven point two, which is what C-sharp is supposed to vibrate at, how is that going to reveal anything? You’d certainly need a cryptographer to decipher it. And besides, no matter how intelligent Herman was, I doubt he’d have learned some complicated math formula.”
Wellsley sat down on the chairlift seat and rubbed the back of his neck while I looked over the paper with its inscrutable numbers.
“And anyway,” Wellsley said, “why would Herman go to such trouble?”
“I’m an investigator, trying to solve a murder. It may be that Herman knew something about the case, something he was afraid to tell anybody.”
Wellsley stared at me. “You didn’t say anything about a murder. What am I getting mixed up in?”
“Nothing. I asked you to analyze this tuning, nothing more. You don’t need to worry. You’re not at risk merely helping me understand what Herman did to his piano.”
My words didn’t ease the worry on his face. I went back to studying the paper with the frequencies. Wellsley had written the frequency of
each note and then, in parentheses, written the correct frequency. The actual numbers varied from the correct numbers by small amounts. And the amount they varied was inconsistent from one note to the next.
I knew nothing of cryptography, either, but my instincts told me that I was looking for a pattern, for something neat and clean and regular. It seemed that a message would stand out by looking like order in the chaos.
Unfortunately, I saw no pattern in either the actual frequency or in the variation from the correct frequency. Every aspect of it seemed messy, and a message, by its very nature, had to be unmessy, unequivocal, clear to the observer.
Wellsley continued to rub his neck and rotate his head for another ten minutes while I added and subtracted and transposed numbers. Nothing I did revealed any order or pattern.
“Tell me again about the wah-wah waver that you mentioned.”
“The beats?”
“Yeah. What is that about?” I said.
“When notes are close in pitch, or when they have harmonics or what we call partials that are close to one another, the frequency interference produces beats. What happens is that the sound waves add to each other at some points and subtract from each other at other points. That produces the wah-wah sound.
“As I mentioned, we tune the unisons of a single note to be exactly the same, which makes them beatless. The intervals between the notes produce beats as well, but that’s a little different. Does that make sense? If I play a C note, I want no beats. But if I play a C and a G together, I want a slow beat.”
“Why do you want a slow beat when you play two different notes?”
“Tuners put slow beats on all of the main intervals. That is what we call a tempered scale. Before the seventeenth century, we tuned some basic intervals, like fourths and fifths, beatless. But that made other intervals like thirds and minor thirds have really fast beats. The really fast beats made certain music played in certain keys sound bad. Thus a piece by Bach could only be played in the key in which he wrote it. You couldn’t transcribe it to a different key, or it would sound terrible.
“So tuners realized that if they put slow beats into the fourths and fifths, then the other intervals didn’t have to have such fast irritating beats. As the evenly-tempered scale took hold, you could play any piece in any key, and it still sounded pretty good. Of course, many purists resisted the change well into the nineteenth century, but now the tempered scale is quite universal in the Western world.”
“Could Herman have done this tuning with a focus on beats?”
Wellsley thought about it. “I don’t think he could have used the beats of intervals as a way to communicate something. If so, how would we know what he wanted us to consider? There would be too many choices. But the beats of each single note stand out as a more obvious message device.”
“You’re saying that he may have wanted you to play one note at a time and consider the beats because the obvious mis-tuning is a red flag.”
“Yes.”
“But how do you quantify it?” I asked. “What are the qualities that tuners pay attention to when they hear beats?”
“There isn’t any way to qualify or quantify beats other than counting them.” He led me back inside the cabin, and struck a note. The beating was pronounced and uncomfortable.
“How do you count them?” I asked.
“By how many times it beats per second. What I’m playing now beats about three and a half times a second.”
“How do you know that?”
“It seems like a good trick, but anyone can do it with a little practice.” Wellsley turned sideways on the piano bench. He smacked his leg with his palm. “I can watch a clock and slap my leg once a second. Or, if I’m pretty good, I can count one-one thousand, two-one thousand, like that. Now watch. I keep hitting my right leg once per second. One, two, three, four. That’s my down beat. Then I hit my left leg with my left hand on the up beat. One, and, two, and, three, and, four, and. I’ve just paced out two beats per second.”
He pointed at my hands. “Try it. First, you go once per second with your right hand. One, two, three, four. Perfect. Now add in your left hand. One, and, two, and, three, and, four, and. See, even you can figure out what two beats per second sounds like.”
I continued to pat my hands on my legs, ignoring his remark.
“Now, I double the pace,” he said. “One, and-and-and, two, and-and-and, three, and-and-and, four, and-and-and.
“That’s an easy way to count off four beats per second. You can do it with your hands, or you can just count silently.
“Now that you know how fast four beats per second is, you compare it to the beats you hear when you play a note.” He hit middle C again.
Immediately, I could tell that the wah-wah-wah-wah waver was close to the four-beats-per-second rate. With a little focus, perhaps I could do as Wellsley did, and realize that it was a touch slower, hence about 3 1/2 beats per second.
“You can see how easy it is to establish the pace of four or three or two beats per second,” he said. “It’s not hard to count. Of course, there is a more accurate way. I can use my little magic machine to count for me.”
“Can you do that? Write down the count of the beats for each of the out-of-tune notes?”
“Sure. Give me another few minutes.”
Again, I went outside to wait. Spot had flipped onto his back so that his bent legs were in the air. His head was turned toward Lily, who lay next to him, also on her back. She had the piece of paper with the outline of Matisse’s paper cutout painting. It was colored with bright crayons. She showed it to Spot, pointing.
“Heat is the horse, and I’m the rider. But you can’t be the clown unless you look funny. Do you look funny, Spot?”
Spot straightened his head. It was now perfectly upside down. His jowls flipped open, exposing his fangs. Lily turned and stared. She exclaimed in a much louder voice. “My what big teeth you have, grandma! You certainly look funny now. Maybe you are the clown.”
Wellsley came out and handed me another piece of paper. Like the previous piece, this one had the notes, followed by the beats per second.
C - 3.6
C#- 2.6
D - 11.6
D#- 6.9
E - 9
F - 2.5
F#- .4
G - 9.1
G#- 2.2
A - 2.3
A#- 1.5
B - .6
C - 7.7
The notes were labeled by letter. But I couldn’t see how the letters of the notes could be part of the code. It seemed that they were irrelevant. The likeliest code was a simple number/letter conversion. 1 = A, 2 = B, and so on.
Without any reason other than that we read from left to right, I thought it would be most logical that Herman would put his message from left to right. So I wrote what the letters would be that corresponded to the numbers, rounding where appropriate. That gave me the following string of letters:
DCLGICAICBBAH
It made no sense. As an alternative, I substituted the logical alternative where the numbers were in the middle, rounding down, instead of up. So 2.5 became B instead of C. 1.5 became A instead of B. 7.5 became G instead of H.
That gave me a new set of letters:
DCLGIBAICBAAG
It still made no sense. Wellsley was gathering his tools, sensing that his work for me was done.
“Another question, if I may,” I said. “I’ve transcribed letters for numbers, but I can’t make any sense of it. Is there any other way that beats are used?”
“No. We just count them and set the strings accordingly.”
“Always beats per second,” I said.
“Yes. Although with slow beats, we count how many there are in five seconds. It’s hard to hear that a beat wavers zero-point-four times per second. But multiply by five, and you get two beats every five seconds, which is much easier to quantify.”
“Right.” I looked at my sheet. “Unfortunately, multiplying these numbers by
five would eliminate many corresponding letters. There’s only twenty-six letters, yet five times these numbers produces several results that are more than twenty-six. I couldn’t assign them letters.”
“You’ve got yourself a real puzzle,” Wellsley said.
“What is the slowest beat that you can count?”
“We can count one beat in five seconds, which would be the equivalent of point two beats per second. At the other end, we can go up to about ten or twelve beats per second. Beyond that, it gets too hard to hear them.”
“Got it. Thanks.”
He finished collecting his gear, I thanked him and paid him, and he left.
Lily had arranged pine cones in lines to designate a series of squares, perhaps the different rooms of a house. Spot was sitting in the middle of one square.
“You are the magenta horse, Spot,” Lily said. “You are in your horse stall. But the clown wants a ride.”
Spot looked at her, then lay down and rolled over onto his side. I could hear his sigh from a distance.
I looked again at the numbers, tried to think like Herman, tried to imagine what happened.
Herman is in his cabin tuning the piano when someone walks in the kitchen door. In order to keep the neighbors from being alarmed, the burglar tells Herman to keep tuning. Herman fears for his life and wants to leave a message about the burglar. He composes a simple sentence or phrase. He can’t write it down, or the burglar might see it. So he wonders if he can put it into his tuning. He realizes he can put beats into his scale. What did Wellsley call it? The temperament. But if the beats are too fast or too slow, they can’t be easily counted or accurately produced.
So Herman thinks about the letters of his message and the numbers those letters correspond to. He needs a system that goes from 1 to 26. But according to Wellsley, his beats should only range from less than 1 per second, up to about 12 per second. How can he adjust for letters ranging from 1 to 26?
Multiply by 2.
So I multiplied the beats by 2, and wrote them down.
7.2, 5.2, 23.2, 13.8, 18, 5, .8, 18.2, 4.4, 4.6, 3, 1.2, 15.4
Then I wrote down the corresponding letters.
