A fifth is not a scale, even a small one. It is an interval.

I don't have time now to wade through all this stuff, but a scan of the earlier posts makes it clear that much of it is derived from Pythagoras' experiments with a "monochord." What Pythagoras discovered was the overtone series. This is inherent in any kind of vibrating body, be it a taut string, a column of air, a ringing bell, a vocal fold. . . .   Often called "harmonics." All over a guitar fingerboard.

Pythagoras went on to derive scales from this. After discovering the octave (half the length of a string—ration, 2 to 1—noticeably "the same note only higher"), he tried one third the length of a string and found a distinctly different note (3 to 1—later on, determined to be an interval of a fifth when fit into the scheme of the other notes he discovered). He tuned another string to this different note and did the same thing: one third the length, and he tuned another string to this note. He continued this process until he found that he was repeating notes he already had. He had twelve distinct notes.

What Pythagoras had done was to discover what we now call the "chromatic scale." Note:   he did not invent it, he discovered it. The notes modern musicians use are not arbitrary, they are inherent in nature.

It's physics. Nothing arbitrary or mystical about it.

But—

Pythagoras, for all his valuable discoveries, including such things as the rule for finding the length of the hypotenuse of a right triangle, was a bit of a nut. His idea was that the Cosmos was made up of numbers. Not just that it could be measured and often defined in terms of numbers, but that the Cosmos consisted—literally—of numbers. A 7 over here, a 4 over there, a 13 somewhere else, all orbiting around each other to the Music of the Spheres and each with a mystical significance of its own.

Well—whatever turns your crank.

The rest of this stuff sounds like it's been filtered through the mind of Edgar Cayce on a bad batch of LSD.

Sorry. There is no great mystical significance to any of this.

Don Firth

P. S. By the way, Michio (first name) Kaku (last name) is a thoroughly grounded theoretical physicist, but he does indulge in a great deal of speculation. As in "Wouldn't it be interesting if--". I've read a lot of his stuff, and you want to be sure you know when he's giving the straight scoop and when he's indulging in a flight of fancy. Fascinating stuff, but caveat emptor. HE makes it quite plain what he's doing at any given time, but lots of people love to skip over that, grab a piece of his speculation, and declare "Michio Kaku says--"   So you gotta be careful when somebody quotes him out of context!