Can guitar frets perform multiplication?

Can Guitar Frets Perform Multiplication? September 4, 2026

Roscoe, N.Y.

I’m sure that some pictures are worth a thousand words, but others trigger a whole lot of puzzlement. Such was the case with the cover of a book I recently bought entitled Calculating with Tones: The Logarithmic Logic of Music:

This book was published by the Oughtred Society, an organization named in honor of William Oughtred, the Anglican clergyman and mathematician who is credited with inventing the first logarithmic slide rule around 1622. The Oughtred Society was founded in 1991, “dedicated to the preservation and history of slide rules and other calculating instruments.” Their website contains a wealth of useful information on the subject.

Although the Oughtred Society website still has a page dedicated to this book, they don’t seem to be selling it at this time, and a second edition is not available directly through the society.

This cover illustration intrigued me because logarithms are involved both in our perception of musical pitch and in the construction of a slide rule. As I discuss in my web-book-in-progress The Lost Art of Logarithms, logarithms and the slide rule were originally invented to ease the tedious processes of multiplication and other mathematical tasks, but they continue to be vital for many reasons, including the understanding of our perceptions of the natural world.

But this cover illustration seems to imply a direct correspondence between the spacing of tick marks on a slide rule and the irregular spacing of frets on a guitar, and even suggests that guitar frets are spaced in such a way that they could be used to perform multiplications just like with a slide rule. Why else would the book be entitled Calculating with Tones?

The illustration is reproduced on page 34 of the book with a caption that includes a description of both halves of the graphic:

Guitar: Frets are positioned on the neck of the guitar to help locate the individual notes. The distance from one to the next becomes shorter as the frets get closer to the lower bridge. The reduction is logarithmic.

Slide Rule: The scale on the slide rule corresponds to a logarithmic function. When using the slide rule, one carries out multiplication by adding distances. The progressive decrease in distance between marks on the slide rule corresponds to the same thing on the neck of the guitar.

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