Overheard: Music has always been a bit of a mystery to me because I didn’t understand it. As a specific example, I didn’t understand why a major chord sounds nice. Why does (0,4,7) harmonize?
I’ve finally read enough to figure it out. The answer is it doesn’t on a piano so most basic music theory skips that bit and just goes to the ‘circle of fifths’ which is little more than a convenient mnemonic.
Here is the short version for the curious scientists in the room. A major chord has three frequencies in the ratio of 4:5:6. The ‘rule of thumb’ is if the lowest common multiple of each pair of these is less than 8 times the lowest number the human ear will consider the sound pleasant. So in our case, the chord is ‘consonant’ at 20=LCM(4,5), 30=LCM(5,6), and 12=LCM(4,6). Why this rule works is still a mystery to me but I’ll live.
The reason this doesn’t work on most pianos is because they are tuned to divide the octave into 12 evenly spaced semitones. So, for example, the three notes for E-major on a piano are E(41.20Hz), G-sharp(51.91Hz), and B(61.74Hz). As it turns out, they are close enough for the human ear to forgive the differences.
There are different tuning schemes to make chords sound ‘nicer’ but these have other shortcomings. Now you know.
So there you have it. I now lump music in with chemistry as a science where the fundamental theory is too hard to be practical so you resort to a bunch of memorization instead.