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More Math

Jan 30, 1994 01:41 PM
by daratman

A frequent quotation I've seen here is "As above, so below". The
other half of that quote is "...but vice-versa". If you visualize
the first half of the statement you will have a picture and its
mirror image, like a sunrise over a pond. Adding the second half
flips the reflection horizontally, like the two faces on a playing
card: As above, so below  O I   but vice-versa  O I

                    O I                         I O

Some other quotes relative to this subject are:

2) "Architecture is frozen Music"
    (If Pythagoras didn't say this, he should have...)
3) "Music is just Math you can hear"
    (...I suppose Bach or Mozart should have said this...)
4) "Philosophy is written in that vast book which stands forever
    open before our eyes, I mean the Universe; but it can't be
    read until we've learned the language, and the letters are
    triangles, circles, and other geometric figures, without which
    means it is humanly impossible to comprehend a single word"
    (...this is from Galileo).

These four quotations have great significance to the ongoing
discussion here, because they are all true. So, ultimately, they
are connected to the same source. Translated into any language
they have the same meaning. Translated into the language of the
Universe, they need no other translation. Someone mentioned that
as we approach this Truth, any linguistic symbolism begins to
break down. Eldon said we can only smile. But there is a point
beyond, where we catch our second wind, our second sight.

Let's say you have a string 84 units long, tuned to 264 cycles per
second (C) and you want to put a fret somewhere that will generate
a tone of 352 cycles per second (F). Where do you put the fret?
Since the ratio of the higher note to the lower note is 352/264
(4/3), the fret is placed 3/4 of the distance from the bridge
(63 units - as above, so below but vice-versa). This represents
the Physical/Metaphysical duality.

If we would like to display the notes, rather than hear them,
consider the string the Diameter of a circle and the tone the
Circumference. The tone generated at 3/4ths the string length will
equal the circumference generated by a diameter 4/3rds the string
length (4 x 84/3 = 112). Since C = PI x D, then C = 22/7 x 112 =
352cps. We can now visualize the size of each note as a circle in
relation to the length of each string segment and fret placement.

And musical tones can be related to and calculated by PI. (F=112PI,
F/2=56PI, 2F=224PI, etc.) Since we seldom deal with perfect circles
but rather ellipses, spirals, and epicycles, PI is not a constant,
but a variable with any denominator. (84 is handy because it allows
a hexagon with sides of 42 units to be inscribed in a circle of
264 units.) The Hebrews apparently liked a Circumference divisible
by 22, the Greeks by 24. Plato's Republic describes a circular city
that can be translated into music, using the Pythagorean concept of
a Musical Universe. (Architecture is frozen Music).

In Myth, Magic and Religion, names of gods and angels have been
calculated, symbolized and written down. The sounds of the letters
themselves vibrate at particular frequencies. They can be drawn,
built, played, chanted and sung. Some combinations are har-monic,
others are de-monic. (Music is Math you can hear).

If you take the Galileo quote beyond poetic allusion, you can
calculate a PI of 22/7 to have a symbiotic relationship with
a square root of Phi at 14/11, allowing them to multiply to the
perfect 4 of a 3:4:5 triangle, and spin into a chambered nautilus.

In Astrology/Astronomy the geometric calculations of planetary and
constellational positions can be translated into structures and
musical compositions. In fact, if you put them on a transparency
and flip them over, you can plot the stars onto the face of the
Earth and build representations of them. The zero point is located
where the sun would be at the Winter Solstice of a particular year.
Someone built a Great Pyramid there. Any connections to HPB?

Daniel Hampson

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