Underlying paper:
https://www.nature.com/articles/s41467-024-45812-z
This research seems to undercut a comment I previously made:
It would seem that at least some “aesthetic ideas” are in fact “amenable to the scientific methodology”.
I cannot however say that I disagree with the research. I’ve long thought that a degree of roughness or rawness in music often adds to the emotional impact, and that music that is too ‘perfect’ can come across as sterile or abstract.
One thing less to do with the psychological component of beauty perception, but rather with ancient ideas about musical scales: A nice little exercise for students of algebra and number theory, is to prove that there cannot be one equal temperament that preserves more than one rational musical interval.
For example, if a third is a frequency ratio of \frac54 by definition, and an octave is \frac21, then three thirds do not stack to an octave: \frac54\cdot\frac54\cdot\frac54=\frac{125}{64}\neq\frac{128}{64}=\frac21.
In fact, no stacking (power) of thirds can yield any stacking of octaves defined in this way. Even a more general theorem is true: One stacking of one interval can only ever equal a stacking of another, if each of the intervals themselves had been a stacking of a third all along. In formal terms:
Let a,b\in\mathbb Q and without loss of generality b>a>1. If there exist integers p,q>0 such that a^p=b^q, then there must as well exist c\in\mathbb Q,c>1 and integers r,s>0 such that c^r=a and c^s=b.
A simple proof would begin with a decomposition of a and b in both positive and negative powers of prime numbers, knowing that all integers can be decomposed into prime factors, and all rational numbers can be expressed as fractions of integers.