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133 lines
4.5 KiB
Plaintext
133 lines
4.5 KiB
Plaintext
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___________________________________________________________________________
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| From : KeelyNet BBS | DataLine : (214) 324-3501 |
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| Sysop : Jerry W. Decker | Voice : (214) 324-8741 |
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| File Name : PHI&RES.ASC | Online Date : 05/22/94 |
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| Contributed by : Joel McClain | Dir Category : ENERGY |
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PHI&RES.ASC
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THE RELATIONSHIP BETWEEN RESONANCE AND PHI, AS DETERMINED BY
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THE FIBONACCI SERIES OF NUMERALS
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Joel McClain
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April 26, 1994
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Because the symbol PI is indeterminate, the Egyptians used PHI in building
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the pyramids. They did this so that they could "square the circle", and
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create a square base which contained the same area as a circle.
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PHI simplifies the math required to square the circle, and is expressed as
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a constant of 1.618. This has come to be known as the Golden Ratio. To
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learn more about the Golden Ratio, please refer to the book "Secrets of the
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Great Pyramid", by Peter Tompkins.
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For the purpose of this paper, it is sufficient to know that this ratio can
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be very helpful in determining the true value in Hertz of notes on the
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diatonic scale. The standardized (1939) frequencies were accepted based
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upon the sound preferences, as opposed to the PI or PHI relationship of the
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notes.
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In a previous paper, I extrapolated the harmonics of standardized
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frequencies, proving the validity of Brown's Constant for determining
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harmonic values. However, this did not take into account the PHI constant
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from the Fibonacci Series, which gives us a more natural starting point.
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Further, there exists a correlation with the Fibonacci Series, which also
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produces PHI, and which can be used for reference. A Fibonacci Series is a
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list of numbers, where each number is equal to the sum of the two previous
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numbers. For example, 1-2-3-5-8-13-21-34-55 is one such series.
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If you divide a number by the previous number, such as 55/34, you get
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1.618, the Golden Ratio. As the numbers increase in value, the ratio gets
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closer to PHI.
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We know from previous study that a note has its first harmonic at the
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frequency of the note times the cube root of PI, which we have named
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"Brown's Constant". The numeric value of this is 1.3313.
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Let's see how we can combine this with the Golden Ratio and with the
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Fibonacci Series to create a diatonic scale that is based upon nature's
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laws, as opposed to men's ears:
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Start with the Fibonacci string of 144-233-377, and let's assign the value
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of 233 to the C note and you get,
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WHOLE FREQ RATIO TO PHI HARMONIC @ FREQ
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NOTE TIMES BROWN'S CONSTANT
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C 233 PHI @ 377/233 310 (F)
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D 263 CD RATIO = CUBE OF PHI 350 (G)
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F 310 DF RATIO = SQUARE OF PHI 413 (A)
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Page 1
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G 350 FG RATIO = CUBE OF PHI 466 (C)
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A 413 GA RATIO = SQUARE OF PHI 550 (D)
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C 466 AC RATIO = CUBE OF PHI 620 (F)
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Now, we have frequencies which are balanced relative to each other, as well
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as based upon natural resonance. To check your answers, relative to PI,
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consider that PI = 4 DIVIDED BY THE SQUARE ROOT OF PHI, so PI = 4/1.272 or
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3.1447, based upon the 377/233 ratio
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As with Brown's Constant, the numbers can vary, as long as the proportions
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are held constant. In other words, if you start your scale with a value of
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377 instead of 233, and observe the same ratios, your chart will be as
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viable as anyone else's.
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Interestingly, the Fibonacci Series was understood by the Egyptians, and
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has been mentioned as a means for deriving "Magic Squares", once again,
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based upon the PHI ratio and relationship.
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I would encourage researchers to learn more about PHI, and to use it for
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resonance based designs, and to use the frequencies thus derived in their
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experiments.
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---------------------------------------------------------------------------
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Page 2
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