Continuing my personal journey in understanding Tunnel Thru the Air, I happened to consider Mr. Gann's use of the word 'circle.' He used the word 8 times, 5 of which were 'circled' as opposed to 'circle'; pages 76, 88, 174, 287, 322, 394, 400 and 401.
Obviously, 8 / 5 = 1.60 or phi. Obviously, the concept of the circle follows Gann's theme that all things in nature are elliptical (a circle is theoretic perfection of the ellipse) as he writes on page 76:
Remember, everything in this universe is elliptical or circular in motion; that applies both to the abstract and the concrete, the mental, physical and spiritual. Every thought you think makes a circle, and it comes back to you. It may take years but you will get the effects, good or evil, according as the thought was either good or evil. That is a truth we should learn, and the world will be the better for it.
Not so obviously, 8 is the number of notes in the diatonic scale. The diatonic scale attributed to Pythagoras contains 8 notes (do, re, mi, fa, sol, la, si and do - again) that define 7 intervals. The 8th note, ‘do’, is a repetition of the first and is both the beginning of the higher octave and the ending of the lower octave. ‘do’ might, logically, be thought of as the beginning and ending of a circle. ‘do’, also known as ‘c’, is most often consider 256 vibrations per second. Its multiples and divisions by 2 yield higher and lower ‘do’s’ or ‘c’s’and those vibrations are found in nature; 16, 32, 64, 128, 256, 512…. Remember the memory size growth of the first computers…16K then, 32, then 64, then 128….
I’d suggest that we can think of the diatonic scale as a circle beginning and ending with ‘do.’ But we when we write it we write it as a vector. The marriage of the linear and circular perhaps? Deeper…make that the planar and the spherical? File that thought away for the moment as I provide some more support for the meaningfulness of connecting the circle and the diatonic scale.
As Gann often does, a couple disconnected numbers on page 128 are thrown out that seem odd for their inclusion:
A popular author of fiction boasts 9,000,000 copies of his book published in eight years. 240,000,000 copies of the Bible have been sold in the same eight years.
8, 9 and 24. 8 is the number of notes defining the diatonic scale. 24 /8 = 3 which is one of two laws, the Law of 3 and the Law of 7, that define the subdivisions of the diatonic scale. That same 3 defines ‘fa’ at 1 / 3 = .333 and ‘la’ at 2 / 3 = .666. Continuing, 9 /8 = 1.125, the note re. That remainder, .125 and its multiples gives you mi at .125 X 2 = .250, sol at .125 X 4 = .500, si at .125 X 7 = .875.
Not sold on the idea that Gann meant to connect the Bible missive and Pythagoras’ diatonic scale? Read the first lines of the poem on the page after page 128:
Last we passed beside a blacksmith’s door,
And heard the anvil ring the vesper chime,
Then looking in, I saw upon the floor
Old hammers worn with beating years of time.
It is the story of how Pythagoras, walking by the blacksmith’s shop, heard the various tones made by the blacksmith striking different hammers against the anvil and thereby creating differing tones. [Though the ‘story’ is discredited, it remains the written record (see Nichomachus in The Manual of Harmonics) of events that reportedly prompted Pythagoras to, however he accomplished it, create the diatonic scale.] I'll note the poem brings in the concept of "beating years of time" but not add comment….time and circularity…. as in "nothing new under the Sun" etc…..context for another day's essay.
Oh, and did I mention the above begins with page 128; lower c or lower ‘do’?
Back to the idea that the diatonic scale may unite the linear and the circular. But first recall my various essays on “Robert Gordon’s 7 days” (actually, they’re pretty forgettable if you aren’t a TTTA obsessive). RG set forth on a circular trip, east to west, around the Earth in, reportedly, 7 days. Of course, he bounced back and forth, north and south, east and west, between cities during his trip. Ultimately, he returned to New York City on the 7th day plus 5 hours. In those essays I found that, if you segregated the east and west miles (horizontal on the xy axis) from the north and south miles (vertical on the xy axis) the linear Pythagoras theorem calculation of a trip would equal the total distance RG traveled. More to the essays, RG’s trip did not look like a triangle (to say the least) but Gann created the distances necessary to MAKE the math calculate of a Pythagorean right triangle.
Again back to the linear and the circular…planar and spherical. RG takes a circular trip around the spherical Earth proving the hypotenuse of a Pythagorean right triangle…..a linear/planar construct. [There is a formula for a spherical Pythagorean right triangle.]
And now to tie in the Pythagorean diatonic scale. In the “Robert Gordon’s 7 days” essays, you’ll find that a diatonic ‘nothing to all’ scale of 0 to 32768 (based on Russell Smith’s terminology of “all to nothing” being from 0 to 2^15 or 32768) defined Robert Gordon’s 7 days. RG left New York City at 0 miles, circled the Earth with many diversions from the “straight line” and ultimately returned to New York City 5 days and 5 hours later having traveled 33,543 miles later. He left at 0 miles or the lowest possible ‘do’ or note c and returned at 32,768 miles or ‘do’ or note c (shame on you Mr. Gann, your mileage missed the ideal by 775 miles).
[Did I say 5 days and 5 hours as opposed to 7 days as billed? That's another daydream which was previously considered as well…. and answered incorrectly.]
Whew, such are the things I think about in the wee hours between sleep and awareness. I need to get a life.
Jim
No comments:
Post a Comment
Note: Only a member of this blog may post a comment.