Music, math, and the mind: Why do we perceive musical chords as good or bad?

A symphony resounds, stirring feelings of peace and fear, sadness and joy, all in one piece and all without words. This absence of words in a classical symphony, or any instrumental piece, leaves just musical properties as the cause of an emotional response. Intuitively, most would say that fast tempos and loud dynamics create energy or anxiety while slow and soft songs bring about peace or sadness. This can be explained by differences in neural activation and stimuli that correlate to our natural body rhythms. Intuition is less obvious, though, when considering the melodies and harmonies — why do certain chords give a sense of pleasure, while others leave a bitter taste? 

Musicians actually have a name for these visceral reactions felt in response to different chords. Consonant notes are those that create pleasure or stability, while dissonant notes create unease or instability. Both of these have their place in music, as oftentimes a song’s chord progression will include a dissonant chord before a consonant one. This is called resolution, when a perceived unstable chord transitions to a stable one. Including both of these in music is part of what makes a piece compelling and enhances its emotional value.

Consonant notes are those that create pleasure or stability, while dissonant notes create unease or instability.

For centuries, musicians and scientists have wondered what gives certain chords these characteristics. The ancient Greeks suggested a mathematical relationship between string length in instruments where the produced frequencies exist in whole number ratios; more recent hypotheses propose that beating, when a chord produces an unpleasant wobbling sound, is what makes a chord dissonant. It was not until 2010 that these variables were separated to study what makes consonance and dissonance present in music notes.

A University of Minnesota study by Dr. Josh H. McDermott had students compare their preferences for chords, mixing combinations of harmonics and beating. The students reacted positively to harmonic chords, meaning the frequencies of notes in the chord are multiples of a common fundamental frequency. A fundamental frequency of 440 hertz (Hz), the note A4 for example, would be played along with integer multiples 880 Hz and 1320 Hz to create a harmonic. This is evidence in favor of the Greeks’ hypothesis, where a mathematical relationship, harmonics, creates consonance.

The beating hypothesis was largely debunked; the evidence linking beating and dissonance was weak and inconsistent when compared to that of inharmonic chords. A follow-up study by the same scientist confirmed that beating is not related to dissonance, however it is still disliked by many and merits future study as to why.

While this research strongly suggests harmonics can explain preference for certain musical sounds, there is a confounding variable that may be contributing to the mathematical result. The study unexpectedly found that “harmonicity measures were positively correlated with musical experience” as well as “the strength of consonance preferences.” This indicates that there is a learnt component to preferring harmonic frequencies, likely also corresponding to cultural practices.

This indicates that there is a learnt component to preferring harmonic frequencies, likely also corresponding to cultural practices.

The University of Minnesota study, polling college students in the United States, draws on participants with heavy Western influence in their understanding of music and what is considered “good.” Western music values harmonics, and many of the students with musical backgrounds, even those without, were likely taught to value them as well. It is expected that conclusions would be different across different cultures considering there are a number of chords considered dissonant in Western music that are widely used elsewhere. 

There are a number of other possible explanations that, whether or not they incorporate consonance and dissonance, require future study to better understand music in the brain. In relation to beating, it is thought that the nature of how the phenomenon is created irritates nerve fibers in the ear, which results in a dislike of the sound. There are also theories about a human propensity for predictions and expectations that suggest a sound is good when it meets expectations and bad when it does not. 

Despite music being a driving force across countries and centuries, there is still much to learn about why notes carry the weight that they do. It is remarkable that a sound — consonant, dissonant, beating, or plain — can evoke such profound feelings. It is important to continue this research, as we are just beginning to understand how physics and biology interact to produce centuries-old symphonies that still shake us today.

Frontiers in Psychology (2018). DOI: 10.3389/fpsyg.2018.02118

Current Biology (2010). DOI: 10.1016/j.cub.2010.04.019