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Quest: A Short Story (part 2)

Re. Visual Music.
In a way, it all felt satisfying. It was clear to us that the development of Western music followed a logic dictated by our ears and thoroughly grounded in physics. One curiosity for me was that "pure" music, that which would make use of precise harmonic relationships, could not be achieved by a system of even temperament. When one divides up the octave into equal logarithmic steps, the steps do not match the low-order harmonic fractions. I wondered if there were a system that could produce such a match. My untrained ear, certainly, is satisfied by the current system.

Eddie, however, still seemed frustrated. "What we've found out," he complained, "is only that our music makes sense, physically. But why do we respond, psychologically, the way we do?"

"Pattern recognition?" I offered. We get used to hearing certain combinations and sequences—certain patterns—and we accept them as 'natural' or 'pleasing.'"

He was thougtful. "The other day you mentioned that the eardrum gets pushed and pulled in a recognizable sequence with certain chords, for example . . ."

"Yeah, like an interval of a fifth, the lower note pushes on the eardrum twice for each three times of the higher note, and the ear can hear this easily. I understand that piano tuners use this pattern a lot in tuning pianos."

"What would that look like on a 'scope?"

"We'd need at least two audio generators and an oscilloscope."

"Why not use a microphone, and this keyboard?"

"Because a microphone—any microphone—introduces harmonics of its own. They call it 'color.' And your keyboard probably does, too. It doesn't produce pure sine waves."

"Hey, wait. We can plot them! I can plot graphs in Excel, right here on this old computer!" He swung around in his chair and began hitting the keys.

I picked up my jacket. "Okay, you do that. I got things to do. Let me know how it works out."

The next evening, as I expected, there was a message on my machine. "Hey, you got to see this! Call me!"

I ordered a pizza and returned his call. He arrived at the same time as the pizza. While I ate, he shuffled through a stack of papers, computer plots of single and multiple sine waves, and plots that showed the effects of combining sine waves of different frequencies. "Have some pizza," I offered. "There's beer in the frig."

"No, thanks, I already ate." He pulled two sheets from the stack. "Look at this. This is a single sine wave, right? And this one is two sine waves, one a fifth higher than the other. Even temperament." Sure enough, the curves showed a synchronization of peaks, at a ratio of three to two.

He picked up a slice of pizza. "Well, maybe one piece." He took a bite, laid the slice down, and pulled another sheet from his stack. "Here's the two sine waves, added together."

Resultant curve: Interval of a fifth.I took the plot from him and studied it. There was, ideed, a symmetrical pattern.

"Hey, that's interesting. This is a fifth?"

"Yeah." He leafed throught he sheets. "Here's a fourth."

Resulting wave: interval of a fourth"That's incredible. You can see the relationship at once."

"Remember, the synchronicity will probably drift off in time, since even a fifth and a fourth, in even temperament, are not exact."

"Boy, you're doing your homework. How about a third?"

Resulting curve: interval of a thirdHe pulled out the plot. "The interval is off even more from the four-to-five ratio, but it still shows."

"Okay, now, do you have a three-note chord?"

Resulting curve: Major triad"I got three of them. Here's a major triad."

"Wow, that shows the deviation from pure harmonics, doesn't it? Look at those places where the symmetry breaks down."

Resulting chord: minor triad"And here's a minor triad."

"It's certainly different from the major triad. I'm not sure I could pick it out of a lineup, though."

Resulting curve: harmonic triad"And this," he flourished, "is a triad if the frequencies are adjusted to each other."

"So that's what the string quartet would get if they tweaked their notes to fit each other. Wow. Even if I can't hear the difference, I can sure see it."

"I bet a lot of musicians would freak out if you would show them these plots. They can't relate to graphic representation. It'd all be Greek to them." He looked at me sheepishly. "Okay, don't say it. 'Stereotyping again.'"

"I didn't say it. You did. Now, my question is, does this 'graphical respesentation' satisfy you about why musical notes affect us the way they do?"

"Have to say, it helps."

"Do you now know why Pink Floyd sounds like church music?"

"No."

"So where do you go from here?"

"Dunno. One thing I'm wondering, though, is why they chose a twelve-step system." He was doing his  thumbnails-in-the-teeth bit.

I told him I had been wondering the same thing. "My guess is that it was a convenient place to stop. A lot of earlier cultures used a pentatonic scale—five notes—but they didn't worry about transposing. They had one key. Period."

"What were the five notes?"

"Guess."

"Fundamental, third, fourth, and fifth?"

"Nope. Look at the black keys on your keyboard."

He studied the little keyboard. "Those five keys? Let's see—F sharp, G sharp, B flat, D sharp, and E flat. No way!"

"Do your do, re, mi . . ."

"Do, re, mi, fa—no fa—so, la, ti—no ti—do. Do, re, me, so, la, do." He looked at me. "That's a pentatonic scale?"

"It's one," I said. "I've been reading Percy Scholes." I pulled the book out from under the stack of papers. "What he says is that very likely people started with do, mi, so, and do, and added the re and la as they were singing, as steps down to do and so, because they couldn't hit the last notes very accurately going down." I grinned at him.

"I suppose you're going to tell me that this Percy guy wrote about why notes sound right together back in 1865." Looking at me over the tops of his glasses, he reminded me of an old professor.

"No, that he didn't. Of course, Pythagoras worked on that problem in 500 B.C. But," I added quickly, seeing his disappointment, "he didn't do what you have done in the past couple of weeks."

"I wondered if someone had thought about all this at some point in the past thousand years."

"No doubt. But even if you didn't discover it first, you did discover it. You didn't learn it out of a book or a class in music theory."

"And Percy provides us with a hundred and thirty different scales, each of which has been tried and discarded in the long history of Western music."

"No, but he does give some references to a few others. There's a guy who came up with two thousand and some different ones in 1947. And Rimsky-Korsakof used a scale of alternating tones and semitones in some of his music."

"Whole-step, half-step, whole-step, half-step, whole-step, half-step, whole-step, that's eleven. That'd be weird."

"It's not do, re, me, fa, so, la, ti, do."

He went into the kitchen and helped himself to a beer. He was obviously thinking. "Well," he said, finally, "I guess the fire's out for now, at least."

"You don't have any more obsessions about music?"

"Not that I'm aware of." The last of the beer went down his throat.

"If you were any kind of researcher, you'd write all this up now."

He looked at me steadily. "You do it. You're the writer."

Donald Skiff, December 30, 1997

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