The science behind harmony. Why do certain notes sound more pleasing when played together than others?
In: Physics
There isnt really science behind it, and definitly not physics.
at best there is psychology behind it or maybe sociology. basically “harmony” is a made up and cultural thing. what we call harmony was just made up by the ancient greeks. other cultures have their own version of harmony we find discordent (india is a good example).
at some age after hearing your culture’s harmony long enough, your brain just goes “I guess this is what sounds good” https://youtu.be/IMjlZ-0Qm2Q
Let’s use a guitar as an example. When you pluck a string, the string vibrates, and this vibration transfers to the air which we interpret as sound.
Now, the way the string moves back and forth is not random: the string is fixed at both ends, so it can only moves using those fixed points as “anchors”. [Let’s use this image as a guide](https://upload.wikimedia.org/wikipedia/commons/thumb/c/c5/Harmonic_partials_on_strings.svg/807px-Harmonic_partials_on_strings.svg.png). The main way the string moves is the uppermost diagram (the one that says “0” and “1”), it goes back and forth from one side to the other. That specific vibration is called the “fundamental frequency” and it makes the biggest contribution to how the string sounds. There are other ways the string vibrates: we call them “harmonics”, the image shows the main ones but you might have realized the pattern. Because those segments are shorter, they also vibrate faster, giving sounds that are higher in pitch.
When you play two strings together, and they have different fundamental frequencies, they might sound good or bad together depending on how both harmonics fit together. For instance, if you play a C and a G, the G matches (well, “matches”) all the harmonics that divide the C string in thirds (1/3, 1/6, 1/9…).
Notes sound better together when they have small-numbered integer ratios between them… mostly.
An octave is 2f
A perfect fifth is 3/2f
A major third is 5/4f
A minor third is 6/5f
Where f is the fundamental frequency (the root of the chord).
This would be exact in a Pythagorean scale, but in an even-tempered scale, they are approximations.
Some combinations of notes have frequencies that blend well and those notes produce what is known as consonance, which occurs when sound waves coincide in a pleasing way. This happens when frequencies are related in simple ratios.
The frequencies of some notes clash when played together which results with the effect opposite to consonance aka dissonance in which sound waves interfere in a way that is unpleasant.
So when you hear certain notes sound good together, it’s because their frequencies form patterns that our brains find pleasing.
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.
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