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Generating low-bass notes

technofile  by al fasoldt

Columns and commentaries in a life-long dance with technology

Simple gray rule

Generating low-bass notes in my headphones—and in my head

By Al Fasoldt

Copyright © 1988, The Syracuse Newspapers

Researchers who study sound like to think of their craft as the original field of inquiry. The ancients knew more about acoustics than any other natural science, and the Greeks were able to coax sound waves to spread into the farthest reaches of their large amphitheaters.

Yet acoustics remains out of reach for most of us, dozens of centuries later. Part of the reason may be the essentially subjective nature of hearing.

Unlike vision, in which most of what we see is easy to compare with reality, hearing is full of little traps and pitfalls. Take the problem of pitch, for example. If you play two tones on your hi-fi system, each with exactly the same pitch and each at precisely the same volume, and then make one of them louder, they will suddenly have different pitches.

A frequency meter will tell you that their measured pitch hasn't changed at all, but your ears will tell you the opposite. Which do you believe? Your ears, of course—because the most important rule in audio is that the two most important measuring instruments are the ones at each side of your head.

Studying what happens to our auditory perceptions when they don't match measured reality is part of the science of psychoacoustics. Usually this sort of thing is interesting, but not very useful. But the other day I discovered an eminently practical psychoacoustic effect that most of us make use of every day without even knowing it.

Before explaining my little discovery, I must confess that it was completely accidental. I was pursuing what I thought was an astonishing phenomenon-the amazing capability of my pocket tape player's headphones to pump out the deepest organ bass I have ever heard-and literally stumbled across the reason. It was only then that I turned to a little research to find out what was going on.

I had better start at the beginning.

We don't get many sunny days in the winter where I live, so when the sky turned china blue a few weeks ago and the sun made everything seem new again, I zipped my little tape player into my jacket pocket, unfolded the headphones that came with it, and stepped out for a jaunt.

When I got to the corner, I abandoned my original idea of a hike around the country block in my little village and instead decided to watch a utility crew put in new light poles. The workers had turned off the electric line and were getting their power from a diesel generator tagged like a trailer onto the bumper of one of their trucks.

I watched them as I listened to an old organ recording, one I had made as a demonstration of the low-bass capabilities of my first really big loudspeakers about 15 years ago. The performance was full of extended pedal notes, ranging from 60 Hz or so—which is pretty low as it is—all the way down to 32 Hz and even, in one or two passages, 16 Hz. That's low enough to qualify as thunder.

After two or three minutes I began to realize that I was hearing more than just the usual Walkman-type sounds from my tiny headphones. As the organist stepped down onto the pedals that actuated the huge pipes, rumbles of the deepest imaginable bass poured into my ears. I was hearing sounds that I had never heard from my tape player before.

Yes, it was playing properly, and yes, I was hearing those glorious pedal notes. I became so excited when I tried to push the player back in my pocket that I tripped over the headphone cord. The headphones were yanked off my head.

In that instant, my world of discovery and delight turned upside down. With my headphones dangling near the ground, I realized I was still hearing those bass notes. They were just as loud and clear, only this time they had no organ accompaniment.

One of the workers walked over to the diesel generator and switched it off, and my bass notes disappeared.

My disappointment was total. I had been hearing an ordinary engine's chug-chugs and interpreting them as Bach's mellifluous pedal-point. I stalked off on another path, away from generators and tractor-trailers and other unfriendly noisemakers.

The path led me to another discovery, one that was genuine and much more important to anyone who likes to listen to music.

My embarrassment led me to search for information on how low frequencies are perceived in ordinary listening. I ran frequency-response checks on my portable player's headphones, and then listened to a variety of music on them. I was surprised to find that the test instruments showed them to have almost no bass at all.

When I played a lab tape consisting of the most simple test tones possible, pure sine waves, what I heard matched what the tests had shown. The 'phones had practically no low-bass output.

And yet the bass sounded fine when I listened to music. To be sure, my little headphones couldn't play organ pedal notes no matter how much I turned up the bass control (except, of course, under what we might call "diesel conditions"), but regular bass could be heard with no problem.

Perplexed, I went back to my tests, and found once again that test tones could barely be heard at all when they were down around the frequency of bass guitars and kick drums. Yet, when I played my all-time favorite piece of country music—Hoyt Axton's "Captain America"—the drums and guitars came through as clearly as they do when I play them on my super-fi home sound system.

What was going on? A day spent in research and a few more hours of listening provided the answers.

As it turns out, what we hear when we listen to complex sounds—sounds full of overtones, such as the sounds produced by all musical instruments—comes to our brains through a different process than the way we hear when we listen to such simple sounds as test tones.

Simple sounds are perceived according to their frequencies. A test-tone sine wave at, say, 400 Hz (cycles per second) is heard as a pure (and dull-sounding) tone in the lower midrange, and a sine wave at 2,000 Hz is heard as a pure tone in the high frequency range. What we hear when simple tones are played is the basic frequency of the tone, nothing more and nothing less.

But what we hear when complex musical tones are playing is much different.

The wave patterns of these tones, if we draw them on a piece of paper, are nothing like the steady up-and-down waves of simple tones; they rise and fall in patterns that look like a rugged mountain range in cross-section.

The jagged shapes represent harmonics, which are frequencies that are created at the same time as the original tone. These harmonics are multiples of the basic tone, meaning that their waves wiggle twice as fast, or three times as fast, and so forth.

Our ears do something unusual with these complex patterns of sound waves:

Rather than hearing many frequencies all at once, each more or less on top of the other, our ears sense the structure amid the harmonics. That structure turns out to rest on the "fundamental" tone, the one that started everything going in the first place.

In other words, even though a tone sent out when a guitar string is plucked may be vibrating at frequencies of 240 Hz, 480 Hz, 560 Hz, 1,120 Hz, 2,240 Hz and 4,480 Hz, our ears hear the 240-Hz tone as the pitch of the guitar string.

That's amazing, but the best is yet to come. Through a process that seems more like magic than science, our ears sense the structure of the complex tone under the most difficult conditions-even when the fundamental frequency is too weak to hear. Our ears actually fill in the missing part of the sound wave.

This happens all the time whether we're aware of it or not. Suppose, for example, you are listening to a piano in a large room. Except for the volume of the notes, the piano sounds the same far away as it does close up—despite the fact that scientific measurements will show that the fundamental tones of the lowest bass notes are too faint to hear from the back of the room.

Yet your ears fill in the missing tones, and the conscious part of your hearing never realizes what is actually going on. As far as you're concerned, everything sounds just fine.

This process goes on in everyday life at home, at school and in the office, too. Try to pick out the faint sound of a tuning fork in a noisy room and you'll have no luck at all. But you'll be able to hear someone's voice at the same fundamental frequency, especially if that voice is rich with harmonics—which give the ear more to work with when it reshapes the sound waves.

And of course it goes on any time we hear full-range sound from the tiny headphones that come with our Walkman-style tape players. And I now understand that was just what was happening to me when I heard Hoyt Axton's drums.

In a way, knowing that what I am hearing might not be what is coming into my ears is a sad realization. How am I to judge which sounds are real and which are after-the-fact reconstructions? In this sense at least, I am a prisoner of my own perceptions.

But this is getting too deep, and I have some music that I want to get back to. I'll be darned if I'm going to let a little psychoacoustics stand in the way, even if it's all in my head.

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