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 innovation. He is by far, the most mathematically sound composer. His compositions were replete with patterns, structures, recursions and other precisely crafted features.
Bach has played with the Fibonacci sequence, the patterns of palindromes, and even with the mobius strip.
Musicians too enjoy mathematics. Without mathematics, the fundamentals and the beauty of music would elude the ardent musician.
As Stravinsky once said: "The musician should find in mathematics a study as useful to him as the learning of another language is to a poet. Mathematics swims seductively just below the surface."
Take these 2 videos for example. They are excerpts from a talk by D Srinivas, who explain the mathematics of Carnatic music.
Music, we know, has a way to our soul. It opens up a window to see and feel things that conscious mind cannot fathom. Music, for many, is the closest feeling of being connected to a higher plane. To connect with a higher being or a more evolved self. Ever heard Gregorian chants, or the Vedic chants, or Tibetian music? One doesn't have to belief in God to feel the music.
But it's not just music that leads to this elevated sense of self. The famous mathematician Ramanujan said: "“An equation for me has no meaning, unless it expresses a thought of God.”
To wind it all up, here's a video that demonstrates the mathematics of music, albeit by an automotive company. This was Honda doing content long before CONTENT was a thing.
I fell on to the ground with a droning sound reverberating in my left ear. I was slowly losing sight of my surrounding. I was breathing hard and fast and could feel my breathing on my stomach, but slowly, even that began to fade away. And then... silence. I awoke with the noise of the small crowd gradually getting louder and louder and nearer and nearer. My eyes were open and were having difficulty adjusting to the bright light. I could feel my breathing again but this time - slow and controlled and now, my chest was heaving rather than my stomach. I was sweating profusely and the sudden lack of action was generating immense heat within me and I could feel it on my feet and hands. I felt like an ember emanating heat all over. I could feel the warm floor below me, even though it was wet. I also began to feel the heat below my, on my back, even though I was sweating and my banyan drenched. I moved my arms closer to my hips, folded them to help myself up but somehow, all I could do was th
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