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From left to right add 702 cents for musical 5ths of 2:3 or subtract 498 for fourths of 3:4 .

Rotation of the pattern by 180 0 in base 10 avoids recalculation of reciprocals. From left to right add 702 cents for musical 5ths of 2:3 or subtract 498 for fourths of 3:4 .

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From left to right add 702 cents for musical 5ths of 2:3 or subtract 498 for fourths of 3:4 .

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  1. Rotation of the pattern by 1800 in base 10 avoids recalculation of reciprocals. From left to right add 702 cents for musical 5ths of 2:3 or subtract 498 for fourths of 3:4. The largest Sumerian counter of 36,000 correlates the King List with the later Hebrew Jubilee calenderof 50 years (720 days+nights), and centers cyclic error between lateral “natural” musical fifths and fourths and vertically aligned //// major thirds—made equally visible either in ancient integers (computed by diplatio) or modern logarithmic cents. “Music” as ratio theory is a fossil science of coincidental patterns. The ninth value in the 2nd row approximates the “cornerstone” value in the first row, illustrating aural and arithmetical convergence between Spiral 5ths and Just thirds that endlessly be-devil harmonic tuning theory and practice. Along the right ascents / / / / every fourth step displays the deficiency of the natural major third of 5:4 in approximating the cube root of 2, favoring “enthronement” of the tonic reference in row 4. Pentatonic “Ten-ness” in the 3rd millennium BCE during the reign of Gilgamesh made relations visually evident by comparing the 3 leading digits, with an accuracy approximating modern cents.

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