What Could Be the Physical Origin of Pythagorean Scale?

Abstract

The 12-note Pythagorean scale seems to be very fundamental for music experience. I have proposed a model for music harmony relying on icosahedral and tetrahedral geometries and surprisingly a connection with genetic code emerged. Music expresses and generates emotions and the natural idea was the the proposed bio-harmonies could serve as correlates for emotions. Geesink and Meijer propose that twelve note scale could be realized as frequency bands for oscillating square plate. This realization would be condensed matter realization. One can however ask whether the Pythagorean scale could be realized by some universal mechanism at the level of fundamental physics. Guitar string is the obvious heuristic guideline and leads to the proposal that magnetic flux tubes or even associated fermionic strings could provide a purely geometric realization in terms of fundamental lengths of of the string proportional to the inverses of the frequencies of the Pythagorean scale.