One thing not mentioned in the paper is also music. Each octave increases exponentially (each is twice the frequency of the previous). However our ears percei

One thing not mentioned in the paper is also music. Each octave increases exponentially (each is twice the frequency of the previous). However our ears perceive the difference between notes as linear (it is actually linear if you take the log of the frequency). One theory is due to the shape of the inner ear, where the individual hairs that hear sounds each octave apart are spaced lineally.