Sound numbers
Music and mathematics have a symbiotic relationship. I was once again reminded of this from watching this video by Numberphile. Both are universal. Both are dominated by patterns. And in both, the patterns need to be beautiful and the ideas must fit in a harmonious manner. As GH Hardy famously said: " Beauty is the first test: there is no permanent place in the world for ugly mathematics." The 19th-century English mathematician J J Sylvester put it thus: “May not music be described as the mathematics of sense, mathematics as the music of reason, the soul of each the same?” This is a wonderful analogy of how closely intertwined the two are. In fact, Gottfried Leibniz, philosopher and mathematician says about music "Music is a secret exercise in arithmetic of the soul, unaware of its act of counting." Many great mathematicians have loved music - and many in particular - have a great liking for Bach. Johann Sebastian Bach is considered as grand master of structural inn