Musical Illusions

Let’s play a music game.

Below are 2 pairs of tones, and I want you to write in the comments for each pair, whether you hear the pitches as going up or down.

Once there are enough comments, you’ll see that we all have different answers!

I ran a poll on Instagram for this game, and here are the results:

That’s the beauty of the tritone paradox, which Diana Deutsch, one of my favorite music cognition researchers, talks about in her book called Musical Illusions and Phantom Words.

The Tritone Paradox

The tritone paradox works by using what are called shepard’s tones.

Roger Shepard, a cognitive scientist, was intrigued by the idea that pitch in music is circular (after all, the musical alphabet repeats after G, and we tend to hear all pitches of a pitch class (so all Cs for instance) as basically the same note just higher or lower). which is why pitch class can be represented in a circle like this.

But pitch also tends to have height (metaphorically), so we can think of musical pitch as being more like a spiral, where all the Cs, for instance are stacked on top of each other in the same place horizontally, but C6 is higher vertically than C4.

Inspired by the “impossible staircase” and M. C. Escher’s paintings, Shepard looked for a way to get rid of the height aspect of musical pitch and make it completely circular.

Thus enters the Shepard tone. Shepard created tones that are made up of 10 pure tones or sin waves that are all an octave apart and filtered by a fixed, bell-shaped spectral envelope where the pure tones in the middle are louder than those on the edges of the spectrum.

So now, when you hear two Shepard’s tones, pitch height isn’t a way of comparing the two pitches any more. You can hear C# to D as either C# going up to D in a minor 2nd or C# going down to D in a major 7th.

Deutsch experimented with Shepard’s tones to see if there was a pattern to whether people heard melodic pitch pairs as rising or falling, and people tended to choose the option that used the smallest interval. So C# up to D was generally preferred over C# down to D.

But, tritones are a special case because they divide octaves in half.

The distance between the two tones in a tritone are the same, so people can’t choose based on distance.

Instead people’s brains impose an order onto what they’re hearing, and there is a pattern to it!

If we think of this pitch-class circle as a clock, Deutsch found that different people have different pitch classes mapped to where 12 o clock is, meaning people are generally internally consistent as to which pitch classes are heard as higher (which is about half of them).

A person’s speaking range has a lot to do with the orientation of their internal pitch-class circle, and their speaking range comes from the dialects they were exposed to growing up. So people from London tend to hear the tritones opposite ways from people in Southern California, where Deutsch was teaching when she discovered this paradox.

And tons of follow-up studies have looked at this with different regions in the world and have provided supporting evidence.

So if you want, add where you’re from to your comment, and we can gather some more data!

What I love about Deutsch’s work is that it’s not just about tricking our brains for its own sake. While this is super fun, musical illusions teach us about how our brains work. Deutsch writes,

“Just as the failure of a piece of equipment provides important clues to its successful operation, so perceptual anomalies—particularly illusions—provide us with important information about the system that generally enables us to perceive the world correctly.”

The Precedence Effect

One illusion that shows this clearly is the precedence effect.

I can’t share audio of this one, but imagine you’re sitting in a room with 2 speakers at the front that are far from each other. The left speaker makes a click noise, and the right speaker plays a long, steady tone. And in experiments of this kind, both sounds start at the same time. People tend to hear the sounds as merged into one single sound that starts with a click and continues as the long tone, and they tend to perceive the sound as all coming out of the left speaker only, while the right speaker remains silent.

This effect teaches us that the “where” and “what” parts of sound perception are actually separated in our minds. And this is why if you’re watching a speech in a large crowd, and the person talking uses a microphone and speakers around the space, you perceive the sound as coming from the person talking and not from any of the speakers around the room (unless you really focus on doing so).

The Speech-to-Song Illusion

Speaking of speech, one really fun musical illusion that producers, artists, and meme music makers use is called the speech to song illusion. Deutsch discovered this one while she was editing audio for a presentation, and a phrase she said was, “They sometimes behave so strangely.” And after looping it, she realized that it sounded like singing instead of speaking, and she even was able to transcribe it into sheet music. I’ll let you listen:

This illusion provides support for the idea that singing and speaking are on a continuum instead of two distinct categories, which they historically have been. And rapping posed a threat to that categorization because it falls somewhat in the middle. Deutsch also goes on to explain how just the expression of emotion changes how melodic speech sounds, where calmer speech is more on the strict speech side of things, but when you’re excited, your speaking range becomes much wider and has more pitch variation.

Musical Illusions and Phantom Words

Deutsch goes over many more musical illusions in her book including things like ear worms, perfect pitch, hallucinations and more, so I highly recommend giving it a read if you find these illusions fun! It’s very approachable to even non-musicians, and she included QR codes and links to audio of the examples, so you can listen as you read about each illusion.

So have fun breaking your brain for science!