Wow!  I just learned that Isaac Newton wrote a treatise about music theory, comparing just intonation with equal tempered scales!  

This was in 1643, when he was 22: the year he fled Trinity College to avoid the Great Plague, went to the countryside, invented calculus, and discovered a prism can recombine colors of light to make white light.   

This great new video about Newton's never-finished treatise is probably the most pleasant way to learn about this stuff.

One reason Newton's work is amazing is that while an equal tempered scale (with notes equally spaced) is standard now, it was very unusual in Newton's time.  Much more common was just intonation, where the frequency ratios are simple fractions.   

Another reason Newton's work is amazing: he compared just intonation not only to a 12-tone equal tempered scale, but also to equal tempered scales with 15, 19, 20, 24, 25, 29, 36, 41, 51, 53, 59, 100, 120 and 612 notes!    He discovered that the 12, 53, 120 and 612 note scales work especially well.

The 53-note equal tempered scale actually goes back to the Chinese music theorist Jing Fang (78–37 BC), who discovered that a series of 53 just fifths is very nearly equal to 31 octaves.  Later the same observation was made by Nicholas Mercator.  (No, not the guy with the map, another guy: the one who invented natural logarithms.)  

I don't know if Newton could have known of Mercator's work, but Newton *was* influenced by Descartes's Compendium Musicae.

To fall deeper into this rabbit-hole, read on!

(1/n)

https://www.youtube.com/watch?v=83ytb6AWRAk 

 @b4c50e1b He was an infant in 1643. Even Newton was not that precocious.