My non-scientific take – music is all about our brain interpreting sound frequency interactions. The difference in frequency between a full octave of a root note is doubling or halving the frequency. Divide that frequency difference by 2 and you almost get the fifth, divide by 2 again, and you almost get the major 3rd. So divide by 2 the fifth, and divide by 4 the major 3rd – the cleanest way to divide the frequency shift between octaves into a chord. To get the minor 3rd, dividing by 5 gets you close, so it’s more complex for our brains to dwell on the frequency interactions.
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