Logarithmic Interval Measures

The first persons to use logarithms for calculation of interval sizes were Bonaventura Cavalieri (1639), Juan Caramel de Lobkowitz (1647), and Lemme Rossi (1666). Also Christiaan Huygens was among the first to do this. Earlier calculations of equal intervals sizes, like those of Simon Stevin (1585) and Marin Mersenne (1636) were done by square and cubic roots.
The logarithm, invented by John Napier in 1614, is a mathematical operation that turns a multiplication into an addition, and by the same definition, raising to a higher power into multiplication. Because stacking two intervals involves multiplication of frequency ratios, this is equivalent to addition of the logarithmic measures of these ratios.

Manuel Op de Coul, 2001-2003

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