Fundamental Theorem of Arithmetic

A mathematical rule which states that any whole number can be described as the product of its prime-factors, with each prime in the series raised to various exponents, 0 or positive.

By extension, this method can also be used to factor rational proportions into the series of primes or odd-numbers, with 0, positive, or negative exponents, the negative exponents representing the denominator of the ratio.

This makes it easier to understand and visualize the mathematical relationships between ratios (especially small-number ratios), to make calculations between ratios by matrix addition rather than fraction multiplication, and in general, to avoid very large numbers in the proportional terms. It is an essential element in lattice diagrams.

[from Joe Monzo, JustMusic: A New Harmony]

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