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 stared at the clock. I watched its every minute and every second. I stared at it until all the noises around me were suddenly put on mute and the only deafening noise was that of the seconds ticking its way into the future. The doctor had told me to wait till 9 pm. It was 7:30 pm and every second was driving me crazy is some very strange way. I could feel my heart beating and realized that it was marching with the beats of the clock’s seconds. I took deep breaths. Paused. Let it all out. Paused. Began to feel my pulse again. No difference. I continued to stare at the clock. I don’t know what I was thinking or whether I was thinking at all. My eyes were glued to the clock. My senses were glued to the clock. My life was glued to the clock. A mosquito suddenly buzzed by and made me shrug my shoulders and blink. When I opened my eyes, like metal to magnet, they went straight to the clock. The second seemed to take a step back before proceeding its untiring rhythmic march into the future....
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