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Sunday, February 02, 2003

Analog clocks are living fossils of the Sumerian base 60 counting

Musicians, following Plato, still project their tones into a circle that eliminates cyclic octave repetitions (Plato, in the Timaeus, insists that God makes only one model of anything). Thus today, using our modern, equal-tempered scale, we can identify any musical interval as some multiple of a standard semitone, to the envy of calendarmakers, who, having to deal with the irregularities of days, months, and years, are jealous of our perfect twelve-tone symmetry. But the nearest approximation of our twelve-tone, equal-tempered scale in small integers remains that provided by ancient base-60 arithmetic.
In ancient Mesopotamia, music, mathematics, art, science, religion, and poetic fantasy were fused. Around 3000 B.C., the Sumerians developed a base-60 number system. Their gods were assigned numbers that encoded the primary ratios of music, with the gods' functions corresponding to their numbers in acoustical theory. Thus the Sumerians created an extensive tonal/arithmetical model for the cosmos. In this far-reaching allegory, the physical world is known by analogy, and the gods give divinity not only to natural forces but also to a "supernatural," intuitive understanding of mathematical patterns and psychological forces.

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