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These few equations are the “seeds” of God’s “Grand Design” ( God’s “fingerprint”):

Pi = (6/5) * phi²

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where
e – is Euler’s number, the base of natural logarithms
i – is the imaginary unit, which satisfies i² = sqrt(-1)
Pi – is the ratio of the circumference of a circle to its diameter

phi- is the the golden ratio number 1.618034

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Concentric circles anticipate Ezekiel’s “wheel in a wheel” as the throne of heaven. Within each circle maxima and minima water clock weights of 2:1 anticipate the ratio of cyclic octaves. But equal weight differences between successive months (reversing at the solstices in months III and IX) had to give way to proportional differences between successive semitones when this geometry was applied to music. Rational tonal arithmetic, cleverly mimed by Ezekiel, could anticipate this conceptual equality only via a slight but cumulative excess or deficiency, for in a cyclic octave of ratio 1:2 all equal divisions are defined by irrationals. Thus the Holy Land of a spiritual Israel had to be conquered conceptually in intricate warfare between the excess of primordial “giants” (products of 3) and the deficiency of human “weaklings” (products of 5) among rational numbers, and “weaklings” won only with Divine help in circumventing the lack of real number. Bible narrative brilliantly allegorizes every aspect of Diophantine approximation to modern Equal Temperament, and it does so with exhausting respect for numerical detail–making the Bible a priceless repository of tuning lore and its elementary number theory. The “unhewn” stones of Jewish altars are integers, meaning the natural or counting numbers to which harmonical theory normally was restricted, although its calculation demanded great fluency with reciprocal fractions. From the perspective of any reference pitch all integers except 2n necessarily “sinned” by “missing the mark” to some degree because octave doubling imposed, a priori, a universal matrix (“womb”) tied to integral powers of 2. Problems arose immediately with division into 2 equal parts (requiring the square root of 2) and 3 parts (requiring the cube root of 2).

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