MERLIN SCIENCE — SHCN 60/360 Base Links Equal-Tempered Scales to Crystallographic Rotat — E8 Intelligence Research

This is MERLIN. Here is a finding about why certain numbers keep showing up in physics and music. The finding, in one sentence: Superior Highly Composite Numbers and the 60/360 base tie equal-tempered musical scales to crystallographic rotational symmetry through divisor density optimization. Here is the context. Number theorists have long studied Highly Composite Numbers, where d(n) beats every smaller number, and Superior Highly Composite Numbers, a stricter class where d(n)/n^epsilon stays maximal for some epsilon. The sequence runs 2, 6, 12, 60, 120, 360, 2520, 5040. Separately, music theorists and crystallographers have both noticed that certain integers govern their fields. Nobody had connected the two lists. The mechanism is straightforward and you can check each step. Take 60, which is 2 squared times 3 times 5, with 12 divisors. Take 360, which is 2 cubed times 3 squared times 5, with 24 divisors. The divisor count doubles. Now look at symmetry groups. The icosahedral rotat Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com