So I don’t know a ton about music theory, but I’m curious about how this works. Why do our brains like to hear chords that are in tune? And how do we explain why something is tuned properly?
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Harmonics is the phenomenon of waves having integer multiples of frequencies, so music sounds good when the different notes (frequencies) match the frequencies of the associated notes (they make the same repetitions at least in part, so have a match that we like hearing). The one note that is double (or triple or whatever) the other in wave number (frequency) will resonate with the other note every second or third or fifth wave, or whatever, adding to the intensity of that wave for that frequency. When playing chords, there are several different possible levels of resonance (not all the notes have to be exact multiples of all the others but they do need to somehow mesh as a whole). That is, if you have one note that is twice the frequency of the main base note (lowest frequency), you could also have another note that is thrice (3x) the base, and the twice and thrice will only resonate on sixes. And so on.
Not exactly clear why we find such pleasure in it when sound waves do that sort of thing, but we obviously recognize it and enjoy it immensely.
The notes of the scale are established based on this idea of integer repetitions (or integer fractional like 2/3 and 3/4 and so on so at some higher frequency they mesh together at a common set of harmonic frequencies; the notes of the scale are chosen because they fit together in that way).
When dealing with scales (different keys), there is a partial commonality in the resonance, so certain keys can be switched to other certain keys and seem to be normal (there is no obvious dissonance, clashing of sound, unless that is what you wanted on purpose, you can choose that to happen). That is, if you hear three notes of a chord, they also can fit well with other possible chords from a different key (those notes can be in more than one key so which key is being used for that set of notes?), so there are certain chord progressions that are natural based on the sequence or set of notes that have been used for the previous few phrases of music. One set of notes (a key) can overlap and hint at another one. This is where the idea of thirds and fifths comes from: some chords have a powerful shared set and switching from one to the other is just natural.
The basic idea though is that music is mathematical in form. Things sound good when the math matches well. One key hints at a future key, and sometimes the music surprises with an unexpected new key that still fits with the opening key, and this is where the musical geniuses earn their acclaim. I did not expect that but it fits so well!
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