The concept is interesting, but the information doesn't feel well-researched or deep. Or at least, some subjects could have been discussed with professionals in the matter. A mathematician may not know much about things like music theory for instance.
The thing is, that documentary is wrong about ratios in music. 3/2 ratio is only in Just Intonation, starting with the 3-limit system (Pythagorean system) which we haven't really used for centuries because following a sequence of fifths, we will never get to the same note. There will always be what we call a "wolf fifth", which sounds very unpleasant. Other tuning systems have been used since, such as 5-limit, 7-limit (Harry Partch), 11-limit and 13-limit just intonation (Ben Johnston), well-temperament, mean-tone temperament, among many others. Our current most widespread (not only) system has equal semi-tones, which is why we call it "Equal temperament. And since music follows a logarithmic pattern (for every octave, we double the frequency), the actual distance between a note and the next is 2^(1/12). Meaning an actual fifth by today's usual tuning is 2^(7/12) which is admittedly close to 3/2, but is anything but a simple ratio. A fourth is 2^(5/12) Intervals sound good to us mainly because we got used to them.
About 3/2, what we could talk about here is resonance rather than actual current music theory, as it is a fifth in just intonation.
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