What? Are you tone deaf???

I would guess that all of us who are musically inclined have had the unpleasant experience of singing (or trying to sing) next to someone who just could not get the notes. I'm not talking about the people who can't quite reach up to an E or an F and wind up just a bit flat. I'm talking about the folks who just can't sing the right notes even when the pitch is well within their range. These people are tone deaf.

Florence Foster Jenkins was one such lady with a tin ear. She was a lady of society in the early 1900's who aspired to be an opera star. And she had the funds to back her own performances. A bad combination. She appeared once at Carnegie Hall, and sold out the venue with people wishing to participate in the ridicule.

Jenkins was apparently completely unaware of her total inability to sing on pitch. She thought that people who ridiculed were just jealous. In the play Souvenir, there is a scene where her lifetime pianist is mortified that she was going to listen to a recording that had been made of her. He relented, and she heard her voice for the first time. She was thrilled.

What causes this? How can people not know?

Where hearing takes place

Hearing takes place deep in the ear. People talk about the ear drum, and the hammer and anvil and stirrup and I dunno, the spurs and the staple gun. All those things are great to have in one's inner ear, but the actual sensing of sound comes in that snail-like thing called the cochlea.

Something inside your ear, and something that would be gross to have in your ear

The cochlea is a long tube, filled with hairs. It just happens to be twisted around into the shape of a snail shell, but that's not a functional feature. It just conserves space. If you were to stretch the cochlea out and slice it open, it would look exactly like the diagram below. Absolutely identical. Sound travels from the left to the right. The left side of the picture is near where the sound enters, and the right side is where the tube ends.

Actual photomicrograph of the inside of the cochlea

Ok. I lied. This is not a perfect representation. It is a conceptual drawing. 

But anyway. Each of the hairs has its own resonant frequency due to its size and stiffness. When a specific frequency of sound enters the cochlea, it will set certain of the hairs to vibrating like a bunch of little tuning forks. The vibration is converted to nerve impulses and transmitted to the brain. The louder the sound at that frequency, the more the corresponding hair vibrates, and the stronger the signal passed to the brain. Thus, the cochlea is performing frequency analysis on the incoming sound wave.

This next image is another conceptual drawing, illustrating the mapping between frequency and position along the tube. The opening of the cochlea is sensitive to sound around 16 kHz, which is the upper limit of our hearing. The hairs that are one quarter of a trip around the spiral are sensitive to sound one octave below this, that is 8 kHz. Each subsequent quarter trip around the spiral represents another octave drop, or halving of the frequency.

Where the frequencies hit the hairs in the cochlea

This continues over the entire span of human hearing, or about ten octaves - a factor of 1,024 in frequency. Each octave turn around the spiral has at least 12 discrete steps, since we are able to readily distinguish 12 half steps in a musical. Our frequency resolution is not likely to be more than a factor of five more than this, however, since a half-step feels fairly small.

I should point out that an octave is not necessarily one quarter spin around the spiral. That's just my guess. The salient point is that the individual frequency receptors are spaced out logarithmically.

Maybe the hairs are not working?

If someone is tone deaf, then perhaps the cochlea is not functioning according to spec? This is conceivable... but I'm going to argue that it's not likely.

Here's my argument: if a person can tell the difference between "oooooo" and "ahhhhhh", then the basic hardware must be working. 

I sang an oooooo into the microphone on my laptop and then did a little frequency analysis. The graph below shows the amount of energy at each of the frequencies from 0 Hz to 1.4 kHz. For the "oooooo", there are two spikes: one at the fundamental frequency of about 140 Hz, and the other at one octave above that, at about 280 Hz. The second frequency is called the first harmonic. Almost everything (vocal chords included) vibrates in a complected way that includes multiple frequencies that are multiples of a fundamental frequency [1]. 

Oooooooooo

The diagram below shows roughly which hairs in the cochlea will be stimulated by the "oooooo" sound.

Hairs that  respond to an "oooooo"

I also recorded and analyzed an "ahhhhh" sound. The frequency breakdown is shown in the next graph. The difference is startling. The ahhhhh has the fundamental frequency, and the first harmonic, but it also has an appreciable amount of energy in the third through ninth harmonics [2].

Ahhhhhhhhh

Here is my argument again. If a human ear is capable of differentiating between the oooooo and ahhhhh at a fireworks display, as well as eeeeee, and oh, and also mmmmmm, and nnnnnn, and ellllll... then it is likely that a lot of the mechanism in the cochlea is intact. The fault must lie somewhere in the brain. The part of the brain that decodes sound for the purpose of speech must be getting everything it needs, but the part of the brain that interprets sound as music must be broken somehow.

What do the real scientists say?

A recent article in the Journal of Neuroscience remarkably provides support for my back of the napkin analysis. The folks who wrote this paper had a look at the "arcuate fasciculus" portion of the brain. The AF is a pathway that connects the part of the brain that controls our perceiving of sound with the part of the brain that controls the production of sound. There are two such pathways. People who are tone deaf lack one of these connections. The other connection, presumably, is responsible for distinguishing between ooooos and ahhhhhs.

This answers the question of what causes tone deafness. It's not a lack of training, or a problem in the ear itself, but an anomaly in the brain.

Thanks to Rachel for getting me thinking about this question!

-------------

[1] Softly blowing across a pop bottle gives a fairly clean tone that has just the fundamental frequency. If you  were to simultaneously blow across two bottles, tuned one octave apart, the result would sound similar to an oooooo.

[2] This is equivalent to blowing pop bottles tuned to C, the C that is the next octave up, the G above that, the C that is two octaves above that, the E, G and B flat of that octave, the C that is three octaves up, and the D above that.