Sound is Weird

Just so that this blog doesn't get too quickly anchored as spouting high-falutin' dharma, here's a random observation that's been bouncing in my head lately.

The basics of sound seem simple enough. But the more you carefully examine sound, the weirder it gets. Everyone knows that the pitch of a note is due to the frequency at which it is vibrating (middle C on the piano vibrates at 256 times per second). And the timbre of a sound depends on the mix of higher-frequencies that are vibrating at the same time (the “overtones”). This is what makes a middle C on the flute (few overtones) sound so much purer than the same note on a saxophone (many overtones). Some innovative composers have tried to experiment with this idea – simulating the sound of an instrument that doesn’t actually exist, by having the basic note played by one instrument, and then having another higher-pitched instrument simultaneously play a set of overtones that are not usually associated with that basic note. The most famous example occurs in Ravel’s Bolero (listen starting from 6:26 in the following performance https://www.youtube.com/watch?v=r30D3SW4OVw to hear how the piccolo creates dissonant high notes that simulate the overtones of some impossible new instrument).

Most people also know that when two notes are played at the same time they can create the impression of a third, lower-pitched note also being played. In music these third notes are called “Tartini tones” (after the classical violinist who widely experimented with the idea). It is possible for a skilled composer to write music that deliberately produces these notes, either by having two instruments play in a carefully chosen harmony (perhaps a pair of flutes), or by having a single instrument play two different notes at the same time (such as playing double-stops on a violin). Meanwhile, some musicians who play instruments that can only produce a single note at a time have discovered that they can supply a second note with their voice (think of Ian Anderson’s simultaneous flute and humming in some Jethro Tull songs). And some musicians have put the two ideas together to deliberately produce Tartini tones while they play their single instrument. Consider an example: it is possible to play the saxophone while also vocalizing a different note (singing through the instrument). If a skilled musician sings a C note while simultaneously playing on their sax the G above it, a third Tartini note can be heard at C one octave below what is being sung. If either the sung note or played note changes, so does the Tartini note. This is pretty cool, but very difficult to do skillfully and with control!

The conventional explanation for all of this is “beat frequencies” – the idea that if two sound waves are added together (by being played in the same airspace at the same time), the resulting wave will have pulse to it (as shown in the usual diagram). This pulse is experienced as a third note, with a new frequency that is exactly the difference in frequency between the first two notes.

This explanation is commonly taught in high-school science classes. But surprisingly it is not the whole story, which you can easily confirm for yourself. If you set up a situation like in the diagram by using two pure sound sources (sine wave generators and speakers), and then check to see which frequencies are actually present in the room (with a microphone and a spectrum analyzer), only the two source frequencies will be detected. For example, if one sine wave generator is set to 300 Hz and the other to 700 Hz, the spectrum analyzer will display peaks at those frequencies – but it will not display a third peak at 400 Hz (even though you can hear it as a third tone)! When I saw this actually demonstrated, I was stunned. Something weird is going on. The addition of the sound waves is apparently not really happening in the vibrating air.

Okay. Maybe the addition happens in the ear structures themselves. There might not be a third tone in the air, but there is one in the ear itself (like, how if a tree falls in a forest but there’s no one there, it must not actually make a sound). This is the plausible new explanation that most people come up with when confronted with the surprising evidence from the spectrum analyzer. Except that this new explanation is apparently also false! Sound is weirder still. But how do we know this?

Perhaps you have previously experienced the sound effect known as “binaural beats”? If you haven’t, you really must stop and try it now! Some people are claiming all kinds of wild health benefits from it (some skepticism may be called for here). To experience it you will need to wear headphones (to rule out the possibility of the addition tones happening in the air or in your ear). Put your headphones on and have a listen to an example like this https://www.youtube.com/watch?v=BWYyGMuZSgc. What is being played are two pure notes, a different one for each ear (you can verify this by taking one earphone off and hearing the other side by itself). When you listen to both together, you will clearly be able to experience the third tone. In this example the two source notes are pretty close together in pitch, so the third note (the difference between them) is experienced as a very low pitch or pulsing sensation. Now think about what’s happening here. There is a Tartini tone being produced. But it is not the addition of sound waves in the air (like you were taught in high school). And it is also not the addition of those waves as vibrations of the tiny bones in your ear (since each ear is getting only one of the two tones). The addition is happening inside you mind! But wait a minute. In your mind there is nothing that is actually vibrating. It’s just some neurons firing. So how can the vibrations be adding up to produce the third tone?

There is yet one more weird aspect of sound to think about. We know sound is vibration, which is motion of some sort. If you twang a ruler that is sticking out from a tabletop, you know the ruler is quickly bending up and down to make the sound you hear.  But this transition from motion to “sound” needs a high enough frequency. Things that vibrate slower than about 50 Hz are experienced as motion, not sound. Conversely, things that are experienced as sound are really just things moving and vibrating faster than that. Motion and sound are the same thing. Someone waving their hand at you is making a really low-frequency sound. Your ears cannot hear it. But maybe some other animals could. If you could record it and then speed up the playback, you’d be able to hear it too! That’s easily done in a recording studio. If you record separate audio tracks of two snare drums as loops, one striking regular quarter notes and the other striking quarter-note triplets, you can speed up the playback and transform that rhythm into pitches. Crank the playback tempo way up to 15,360 bpm (i.e., 256 bps, or 256 Hz) and the snares will sound like continuous tones, one playing middle C and the other playing G above it. Sound is weird.