Let's explore hearing, with the notions of construction, deconstruction, ambiguity, and reconstruction in mind. A useful place to start is with the sounds made by musical instruments. Let's take a piano playing a particular note, say the A above middle C. You can see it on the keyboard in the illustration on the right, and hear it by clicking on that key. We can play the same note on lots of other instruments, a violin, a clarinet, or a trumpet for example. Listen to each of them. You can tell its the same note but the sounds aren't exactly the same. Why is that? What is the difference between the sounds of a piano playing a particular note and the sounds of a violin, a clarinet, or a trumpet each playing the same note?

To answer the question of why different instruments sound different, we need to do some deconstructing. Let's start with the piano. When you hit the A above middle C key on the piano, it produces vibrations in the air that in turn produces vibrations in your inner ear and related signals in your auditory nerve. The vibrations in the air are the input to your nervous system in the case of sound, just as light is the input to your eye in the case of seeing. The upper part of the figure to the left plots the amplitude of those vibrations as a function of time.

The squiggely line doesn't look much like an A above middle C, or, at first glance, like much of anything at all. But if we look more closely, we can see that there's a pattern to the vibration. It doesn't go up and down randomly. Instead it goes up and down in a particular way and then repeats itself, over and over again. Not only is there a large pattern that repeats itself over and over again but there are smaller parts of the pattern that themselves repeat over and over again. Furthermore, the smaller parts of the pattern repeat themselves more rapidly than the larger parts of the pattern.

To make sense of all this, it will help to think first about something simpler, a single repeating pattern or "pure tone." No actual instrument creates a pure tone, but we can easily do it with a computer generating a smoothly varying repeating pattern called a sine wave. If you click here, you can see and hear a sine wave. And you can vary the amplitude of the sine wave as well as how often it repeats (the frequency). Notice that varying the amplitude of the sine wave changes the loudness of the sound. Varying the frequency of the sine wave changes ... the note we hear, the pitch.

A sine wave repeating 440 times a second (440 Hertz) sounds a lot like a piano (or a violin or a trumpet) playing A above middle C. If the sine wave has a higher frequency, its sounds a lot like any of those instruments playing a higher note and if it has a lower frequency its like any of those instruments playing a lower note. Try it yourself. Clearly, there's a close relationship between amplitude of a vibration and loudness and between frequency of vibration and pitch.

That's all very interesting (perhaps?) but the sine wave doesn't in fact sound exactly like a piano (or any other instrument) playing A above middle C. Why not? And what about our original question: why do different instruments playing the same note sound different? Remember the vibration of the piano? It repeated a larger pattern as well as, more rapidly, some smaller patterns. What it consists of is the sum of several different pure tones occurring at the same time, a "fundamental" at a particular frequency and a number of "overtones" at higher frequencies.

The figure to the right shows again the vibrations of different instruments playing A above middle C as well as a 440 Hz sine wave. Below each this time is a plot of the amplitude of each of the different frequencies that are also present in the vibration. Notice that there are no additional frequencies in the case of the sine wave but there are a variety of additional overtones in the case of the instruments. The similar fundamental frequency is what makes them all sound sort of the same. What makes a sine wave sound different from a musical instrument playing the same note, and that make various instruments sound different from one another, are the differing frequencies and amplitudes of the overtones. Musical sounds are constructed from combinations of frequencies of vibration.

There's an interesting parallel between the sound of a musical instrument as a mix of different frequencies of vibrations in the air and the color of an object as a mix of different wave lengths of light. Different people have different sensitivities to the various wavelengths of light. The upshot is that color is not simply a properties of objects themselves. Instead color depends not only on what wave-lengths of light are emitted by the object but also on the sensitivities of an observer to those various wavelengths. Something that appears yellow to one observer may appear a quite different color to another with different sensitivities to wavelengths reflected to the eye by the object. Similarly, the sound of a violin (or any other musical instrument) is not a property of the violin itself but rather of the violin interacting with a listener. A violin will sound one way to an observer with a particular set of sensitivities to sound waves of different frequencies, and quite different to another listener with a different set of frequencies.

If a tree falls in the forest and there is no one there to hear it, does it make a sound? Yes, if by a sound one means a pattern of vibrations in the air. But if by a sound one means the auditory perception of a person standing in the vicinity of the tree, or a musical sound, the answer is no. The sound of a tree falling in the forest is a mix of different frequencies of vibration and so will be heard differently by different people with different frequency sensitivities. It will be absent entirely if a person has no sensitivity to vibrations at any frequency ... or if there is no one there. Like colors, musical sounds are constructions of the brain. They vary from brain to brain and don't exist in the absence of brains.

Different people may hear the sound of violin differently but how about a particular person? Surely the sound of a violin is the sound of a violin is the sound of a violin. Could it be heard differently at different times by one person? The answer turns out to be yes. Ambiguous figures reveal an underlying ambiguity in the input to the eye, so that one can construct different things using the same input (not only in the case of ambiguous figures but quite generally). The same is true for hearing. Since musical sounds are constructions, there is room for them to be reconstructed, heard differently. Vibrations in the air are ambiguous, they can be heard in more than one way.

Let's try out our new found ability to deconstruct to reconstruct, using the sound of a clarinet playing the A above middle C. Click here to see the vibrations in the air and the deconstruction into a fundamental and a set of overtones. Click on the clarinet button to hear the sound. And the click on the ? button. Do you hear a clarinet or something else? Perhaps several different tones being played at the same time? The sound of a clarinet is ambiguous; it can be heard in two (at least) different ways. There are in hearing, as in sight, different constructions that can be made out of the same input.

Which one is "real"? Neither one. What is "real" (to the extent anything is) is a pattern of vibrations in the air. That pattern may be created by a clarinet or it may be created (as here) by an electronic synthesizer generating several pure tones simultaneously. In constructing a particular percept, your brain makes, without your knowing it, an informed guess as to what sound percept is likely to be useful at any given time (just as it does in seeing). It may be wrong about what's useful in any given case, and so its nice to know that its a guess and one can use consciousness to look for a different percept.

Knowing that percepts are constructed not only gives one the ability to hear (or see) things in different ways, it also gives one the power to create things one has never heard (or seen). Every existing musical instrument has a different, characteristic set of amplitudes of overtones when it plays an A above middle C. But there are a lot more sets of amplitudes of overtones than there are existing musical instruments. Using a synthesizer (click here) one can create sounds that are different from those of any existing musical instrument. Try it. Are there ways an A above middle C can sound that you like better than you've ever heard it sound before? You're on your way to creating a whole new set of musical sounds.