Do you remember that probe we sent to Titan? You know, the one that was the first ever to land on Saturn’s largest moon? Well that was the Huygens probe and was part of the Cassini-Huygens mission. I bring this up because it was named after Christiaan Huygens, a man that has contributed a huge amount to science: early telescopic studies of the rings of Saturn, the invention of the pendulum clock, and the discovery of several interstellar nebulae and double stars to name a few. But even if you are familiar with Christiaan Huygens you still may not know that he actually contributed quite a bit to the world of music as well.
Later in his life, Huygens attempted to solve the problem in meantone temperament in the musical scale. So he developed his own 31-tone scale and published it in his books Lettre Touchant le Cycle Harmonique and Novus cyclus harmonicus. In these books he worked out a simple way of calculating string lengths for any instrument, worked out a logarithm in the calculation of string lengths and interval sizes, and then worked out the relationship between meantone tuning and the 31-tone equal temperament.
However, even though many people applauded this development they were still unwilling or unable to accept the changes to the more commonly used Pythagorean 12-tone scale. By using Huygens calculations many instruments would have to be rebuilt and retuned to adopt his scale. There were a few experimental instruments created to specifically highlight the 31-tone scale but, for the most part, most instruments were made to adopt the way the 12-tone scale can produce a true octave.