Dear Dr. Livio,
Thank you for the page with the wealth of information on the Golden Section.
I am a researcher in music cognition. My explanation of a space of music includes calling the Pythagorean intervals the melodic reference elements or artistic universals in music. The sharing of the "strong" spectral information between tones of the Pythagorean intervals is most likely the origin of their auditory pleasantness. From a perspective of neurophysiology, it is possible that the sharing (and the supposed relative ease in processing of these intervals) is related to the lesser cost of neural processing as compared to non-consonant compounds. Most likely, these neuropsychological properties were the foundation for a paleo-scale; they were of importance for the musician’s ear just 400 years ago. Yet today we listen to the slightly mistuned intervals which lost their sonic purity with the introduction of tempered scale.
I am an admirer of Matyla Ghyka and I really like his ideas of "built-into" geometrical universals (for example, log relations) which, I believe, affect our perception of the world.
It is possible that some ratios of natural growth are inherent for our perception.
Marina Korsakova-Kreyn, PhD