Next to this interesting article and comments, I think mention should be made of von Helmholtz's XIX century book "On the sensations of tone". He is considered

Next to this interesting article and comments, I think mention should be made of von Helmholtz's XIX century book "On the sensations of tone". He is considered to be the father of acoustics, and derived the consonance/dissonance of the notes in the diatonic scale from first physical principles. He extracted and computed what is described as "roughness" here as the amount of "beats" between the upper partials of the notes - where beats are the slow phase oscillations caused by two vibrations of very close frequencies. But of course, he first had to study strings and pipes for 8 years, and come up with the (then) innovative concept of upper partials (harmonics). I'm a software person by trade, amateur but very dedicated musician, read this book many years ago, thoroughly enjoyed it, and I heartily recommend it today.