How to Science [Part 6: Secret Math in Your Brain]

When frequencies of harmonious string pairs are divided, they reduce to simple fractions (2:1, 3:2, 4:3), while dissonant pairs produce complex, non-reducible ratios—exactly the pattern Pythagoras discovered for string lengths.

When frequency ratio is simple (1:2), waves align predictably—one string completes one vibration while the other completes exactly two, creating regular, repeating wave patterns reaching the ear.

Galileo hypothesized that consonance versus dissonance results from how easily ears make sense of incoming wave patterns—simpler, more predictable patterns from simple frequency ratios are “happier” for ears to decode.

Hermann von Helmholtz discovered in the 1800s that the simple frequency ratio rule breaks down for pure tones (like stopped pipe organs) and cannot explain why people prefer simple ratios even when notes play sequentially rather than simultaneously.

A 2016 study by MIT, Baylor, and Brandeis researchers tested 100 members of a remote Amazonian tribe and found no detectable preference for simple frequency ratios, suggesting consonance preferences are culturally learned rather than biologically innate.

If consonance preferences are learned through experience, the answer to Pythagoras’s question lies not in wave physics or ear anatomy but in the 100 billion neurons ears connect to—requiring neuroscience investigation of brain processing.

Using invasive electrode techniques on anesthetized animals (rabbits, monkeys), scientists discovered that for lower frequencies, specific nerve fibers fire at exactly the same frequency as the incoming tone—a remarkable direct encoding mechanism.

Over recent decades, scientists developed non-invasive brain imaging technologies that allow glimpsing inner brain workings without requiring surgery—primarily electroencephalography (EEG) and functional magnetic resonance imaging (fMRI).

Using mathematical models of neuron groups, researchers found evidence suggesting consonance/dissonance perception may result from neural synchronization patterns—yet Pythagoras’s original question remains definitively unanswered.