The science behind harmony. Why do certain notes sound more pleasing when played together than others?

Question

The science behind harmony. Why do certain notes sound more pleasing when played together than others?

In: Physics

Answer 1

Interestingly, its kinda because your ears are really good at math

Now I’m gonna mention that “bad sounding” intervals are entirely cultural, and dissonance is used to great effect in genres like Jazz, 19th century, and modern music.

Now with that out of the way:

intervals generally considered very consonant in western music have ratios between their frequencies are very simple. For example the frequency ratio of consonant sounding intervals like a perfect fifth is 3:2* or a perfect fourth is 4:3*. Your ears can perceive this very quickly and can differentiate these from generally dissonant sounding intervals like a minor 2nd which has a ratio of 1.05946:1 (in equal temperament tuning).

*tuning makes explaining this very complicated. Today, the standard tuning system is equal temperament which splits the octave into 12 equal pieces. This makes playing music very convenient at the loss of perfect sounding perfect intervals. In equal temperament the ratio of a “perfect” fifth is about 2.996614:2 which is close enough to 3:2 that your ears can ignore it, but is still perceivable if you pay close attention. This is why many people have made microtonal music to have more control over how every consonance or dissonance sounds, or, pre 1600s constantly changing tuning depending on they key of the music being played.