Hack46.Discover Pitch

Hack 46. Discover Pitch

Why we perceive pitch at all is a story in itself. Pitch exists for sounds because our brains calculate it, and to do that, they must have a reason.

All sounds are vibrations in air. Different amplitudes create different sound intensities; different frequencies of vibration create different pitches. Natural sounds are usually made up of overlaid vibrations that are occurring at a number of different frequencies. Our experience of pitch is based on the overall pattern of the vibrations. The pitch isn't, however, always a quality that is directly available in the sound information. It has to be calculated. Our brains have to go to some effort to let us perceive pitch, but it isn't entirely obvious why we do this at all. One theory for why we hear pitch at all is because it relates to object size: big things generally have a lower basic frequency than small things.

The pitch we perceive a sound having is based on what is called the fundamental of the sound wave. This is the basic rate at which the vibration repeats. Normally you make a sound by making something vibrate (say, by hitting it). Depending on how and what you hit (this includes hitting your vocal cords with air), you will establish a main vibrationthis is the fundamentalwhich will be accompanied by secondary vibrations at higher frequencies, called harmonics. These harmonics vibrate at frequencies that are integer multiples of the fundamental frequency (so for a fundamental at 4 Hz, a harmonic might be at 8 Hz or 12 Hz, but not 10 Hz). The pitch of the sound we hear is based on the frequency of the fundamental alone; it doesn't matter how many harmonics there are, the pitch stays the same.

Amazingly, even if the fundamental frequency isn't actually part of the sound we hear; we still hear pitch based on what it should be. So for a sound that repeats four times a second but that is made up of component frequencies at 8 Hz, 12 Hz, and 16 Hz, the fundamental is 4 Hz, and it is based upon this that we experience pitch.

It's not definite how we do this, but one theory runs like this¹: the physical construction of the basilar membrane in the inner ear means that it vibrates at the frequency of the fundamental as it responds to higher component frequencies. Just the physical design of the cochlea as an object means that it can be used by the brain to reproducephysicallythe calculation needed to figure out the fundamentals of a sound wave. That discovered fundamental is then available to be fed into the auditory processing system as information of equal status to any other sound wave.²

So it looks as if a little bit of neural processing has leaked out into the physical design of the eara great example of what some people have called extelligence, using the world outside the brain itself to do cognitive work.

4.4.1. In Action

An illusion called the missing fundamental demonstrates the construction of sounds in the ear. The fundamental and then harmonics of a tone are successively removed, but the pitch of the tone sounds the same. Play the sound file at http://physics.mtsu.edu/~wmr/julianna.html, and you'll hear a series of bleeps. Even though the lower harmonics are vanishing, you don't hear the sound get higher. It remains at the same pitch.³

4.4.2. How It Works

The way pitch is computed from tones with multiple harmonics can be used to construct an illusion in which the pitch of a tone appears to rise continuously, getting higher and higher without ever dropping. You can listen to the continuously rising tone illusion and see a graphical illustration of how the sound is constructed at http://www.kyushu-id.ac.jp/~ynhome/ENG/Demo/2nd/05.html#20.

Each tone is made up of multiple tones at different harmonics. The harmonics shift up in frequency with each successive tone. Because there are multiple harmonics, evenly spaced, they can keep shifting up, with the very highest disappearing as they reach the top of the frequency range covered by the tones and with new harmonics appearing at the lowest frequencies. Because each shift seems like a step up on a normal scale, your brain gives you an experience of a continuously rising tone. This is reinforced because the highest and lowest components of each tone are quieter, blurring the exact frequency boundaries of the whole sound.⁴

4.4.3. End Notes

1. There are other mechanisms, using neural processing, involved too, in reconstructing the fundamental from a harmonic. There are two main theories of what these are. One involves recognizing patterns in the activity level of the receptor cells over the length of the cochlea, and the other involves using the timing of the responses of the cells.

2. McAlpine, D. (2004) Neural sensitivity in the inferior colliculus: Evidence for the role of cochlear distortions. Journal of Neurophysiology, 92(3), 1295-1311.

3. The missing fundamental illusion is also found in motion perception at http://www.umaine.edu/visualperception/summer.

4. Yoshitaka Nakajima's "Demonstrations of Auditory Illusions and Tricks" (http://www.kyushu-id.ac.jp/~ynhome/ENG/Demo/illusions2nd.html) is a fantastic collection of auditory illusions, including examples and graphical explanations. A particular favorite is the "Melody of Silences" (http://133.5.113.80/~ynhome/ENG/Demo/2nd/03.html).