The divisions of the monochord string can be represented by four methods: proportional ratios, string lengths, logarithms, and cents. The modern division by cents is derived from the 18th century application of logarithms to music, and cannot be directly applied onto the instruments without further calculation. hence I will only consider ratios and string lengths here. The calibration by string lengths is derivative from the proportional system. It overcomes the cumbersome nature of fractional ratios by clearing fractions through a least common multiple chose as the length of the open string.

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http://siementerpstra.com/writings/Terpstra-MonochordProcedures.pdf