Sacred Harmonics & Phi

[TranceAm]

Originally Posted by herbivore

so what's the reason?

http://www.harmonics.com/lucy/lsd/chap1.html

The Pythagorean system , instead of arriving at the octave after 12 steps i.e. (3^12)/(2^18) becomes 531441/262144 = 2.0272865 instead of 2.0000 as we assume when tuning a guitar by fifths at the seventh fret. This difference or error is known as Pythagoras' lemma. Every system seems to be an imperfect compromise, which is probably why mathematicians and musicians have devoted millions of hours to searching for the perfect scale.

Initially, the idea of 53 notes on a geometric progression seemed to be a sensible solution, and I read that Bosanquet's harmonium on this scale had been in the Kensington Science Museum since the 1880's. I went to find it, but it was in storage. Instead I found Mr. Chew. I told him of my quest and that I had a hunch that the solution was in some way connected with the music of the spheres and the Greek letter " Pi ".

Pi

"That's what Harrison thought."

I enquired further and discovered that John Harrison (1693-1776)John Longitude Harrison (1693-1776), an horologist, had discovered longitude and won a £20,000 prize from Parliament after the personal intervention of George III. I was directed to the Clockmakers' Library in the Guildhall, and there found a treasured copy of A Description concerning such Mechanism as will afford a nice, or true Mensuration of Time; together with Some Account of the Attempts for the Discovery of the Longitude by the Moon; and also An Account of the Discovery of the Scale of Musick, harrison.zip only to be refused permission to photocopy any of it, due to its antiquity. I eventually acquired photocopies of the relevant pages from another source. Harrison had written in such an obscure style that I suspected that he intended to hide its secrets from all but the most diligent enquirer.

The essence of what Harrison said is as follows:

"The natural scale of music is associated with the ratio of the diameter of a circle to its circumference." (i.e. pi = 3.14159265358979323846 etc.)

And it is a crob circle showing Pi.