A mathematical model may explain how the nerves in your ear sense harmony, a team of biophysicists reports. The model suggests that pleasant harmonies cause neurons to fire in regular patterns whereas discordant notes stimulate messier neuron activity.
Strike the middle C on a piano and hold it. Count two white keys to the right and hit the E. The bright and pleasing sound of a major third fills the air. That unmistakable sensation of musical harmony depends on the frequencies of the sound waves that make the two notes. Consonant chords consist of musical notes whose frequencies form simple ratios such as 2/1 for an octave, 3/2 for a major fifth, or 5/4 for a major third. Dissonant chords have frequency ratios of big numbers such as 16/15 or 45/32. But scientists don’t know precisely how the ear and brain sense this mathematical difference.
Now, Bernardo Spagnolo, a biophysicist at the University of Palermo in Italy and collaborators at Lobachevsky State University of Nizhni Novgorod in Russia have come up with a simple neurological model that does the trick. A sound wave sets your eardrum vibrating, which ultimately causes a spiraling membrane within the inner ear called the basilar membrane to vibrate, too. Exactly where along its length the membrane jiggles depends on the frequency of the sound, with higher frequencies causing jiggling farther along the tapering membrane. Those vibrations stimulate neurons that convey the frequency information to the brain.
Spagnolo and colleagues argue that simple circuits among these neurons can also account for the sensations of harmony and dissonance. They used a simple three-neuron mathematical model to mimic the ear membrane-neuron-brain system, as they report this month in Physical Review Letters. In the model, two “sensor” neurons from different points on the basilar membrane and representing different frequencies send signals to a third “interneuron” that combines the two signals into one. All three neurons are designed to act like real neurons, using the “leaky integrate and fire” model in which stimulus pushes the voltage inside the neuron higher and higher until the neuron fires and the voltage drops back down to its original voltage. Thus the neuron takes a breather before it can fire again.
Analysis of the model’s signals gave an elegant result: When the neuron sensors were fed consonant chords like a major third on a piano, the interneuron gave an output signal consisting of regular, well-shaped peaks. Dissonant chords made the interneuron’s output signal blurry. Quantitative analysis of those signals shows that the dissonant chords result in a higher level of disorder, or entropy, in the interneuron output. Long and short, the regularity or randomness of the interneuron’s output reveals whether two tones are harmonious.
If they are right, then these measures could be used to test for consonance in music that is not based on the musical scales or notation developed by European and East Asian societies; for example, pre-Columbian music by certain American tribes, said Dante Chialvo, a neuroscientist at Northwestern University in Chicago, Illinois. "[This music] was transmitted by generations as something that sounds 'right.' It might be that one can record such music and feed it to the model" to see how the entropy of the model spikes compares with that of the consonant and dissonant chords, Chialvo says.